From b7445f740cb50779069b9f61d50fb11cb52da4ee Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Tue, 22 Jul 2008 17:21:28 +0000 Subject: [PATCH] mld2p4: configure.ac configure docs/html docs/html/WARNINGS docs/html/images.aux docs/html/images.log docs/html/images.out docs/html/images.pl docs/html/images.tex docs/html/img1.png docs/html/img10.png docs/html/img100.png docs/html/img11.png docs/html/img12.png docs/html/img13.png docs/html/img14.png docs/html/img15.png docs/html/img16.png docs/html/img17.png docs/html/img18.png docs/html/img19.png docs/html/img2.png docs/html/img20.png docs/html/img21.png docs/html/img22.png docs/html/img23.png docs/html/img24.png docs/html/img25.png docs/html/img26.png docs/html/img27.png docs/html/img28.png docs/html/img29.png docs/html/img3.png docs/html/img30.png docs/html/img31.png docs/html/img32.png docs/html/img33.png docs/html/img34.png docs/html/img35.png docs/html/img36.png docs/html/img37.png docs/html/img38.png docs/html/img39.png docs/html/img4.png docs/html/img40.png docs/html/img41.png docs/html/img42.png docs/html/img43.png docs/html/img44.png docs/html/img45.png docs/html/img46.png docs/html/img47.png docs/html/img48.png docs/html/img49.png docs/html/img5.png docs/html/img50.png docs/html/img51.png docs/html/img52.png docs/html/img53.png docs/html/img54.png docs/html/img55.png docs/html/img56.png docs/html/img57.png docs/html/img58.png docs/html/img59.png docs/html/img6.png docs/html/img60.png docs/html/img61.png docs/html/img62.png docs/html/img63.png docs/html/img64.png docs/html/img65.png docs/html/img66.png docs/html/img67.png docs/html/img68.png docs/html/img69.png docs/html/img7.png docs/html/img70.png docs/html/img71.png docs/html/img72.png docs/html/img73.png docs/html/img74.png docs/html/img75.png docs/html/img76.png docs/html/img77.png docs/html/img78.png docs/html/img79.png docs/html/img8.png docs/html/img80.png docs/html/img81.png docs/html/img82.png docs/html/img83.png docs/html/img84.png docs/html/img85.png docs/html/img86.png docs/html/img87.png docs/html/img88.png docs/html/img89.png docs/html/img9.png docs/html/img90.png docs/html/img91.png docs/html/img92.png docs/html/img93.png docs/html/img94.png docs/html/img95.png docs/html/img96.png docs/html/img97.png docs/html/img98.png docs/html/img99.png docs/html/index.html docs/html/internals.pl docs/html/labels.pl docs/html/node1.html docs/html/node10.html docs/html/node11.html docs/html/node12.html docs/html/node13.html docs/html/node14.html docs/html/node15.html docs/html/node16.html docs/html/node17.html docs/html/node18.html docs/html/node19.html docs/html/node2.html docs/html/node20.html docs/html/node21.html docs/html/node22.html docs/html/node23.html docs/html/node24.html docs/html/node25.html docs/html/node26.html docs/html/node27.html docs/html/node28.html docs/html/node29.html docs/html/node3.html docs/html/node30.html docs/html/node31.html docs/html/node4.html docs/html/node5.html docs/html/node6.html docs/html/node7.html docs/html/node8.html docs/html/node9.html docs/html/userhtml.css docs/html/userhtml.html docs/pdf/building.tex docs/userguide.pdf examples/fileread/mld_cexample_1lev.f90 examples/fileread/mld_cexample_ml.f90 examples/fileread/mld_dexample_1lev.f90 examples/fileread/mld_dexample_ml.f90 examples/fileread/mld_sexample_1lev.f90 examples/fileread/mld_sexample_ml.f90 examples/fileread/mld_zexample_1lev.f90 examples/fileread/mld_zexample_ml.f90 mlprec/mld_cprecset.f90 mlprec/mld_dprecset.f90 mlprec/mld_sprecset.f90 mlprec/mld_zprecset.f90 test/fileread/cf_sample.f90 test/fileread/df_sample.f90 test/fileread/runs/cfs.inp test/fileread/runs/dfs.inp test/fileread/runs/sfs.inp test/fileread/runs/zfs.inp test/fileread/sf_sample.f90 test/fileread/zf_sample.f90 Fixed I/O for fileread samples. Fixed precset typo. Updated documentation for building. Included HTML pages. --- configure | 24 +- configure.ac | 2 +- docs/html/WARNINGS | 37 + docs/html/images.aux | 15 + docs/html/images.log | 801 ++ docs/html/images.out | 0 docs/html/images.pl | 657 ++ docs/html/images.tex | 874 ++ docs/html/img1.png | Bin 0 -> 368 bytes docs/html/img10.png | Bin 0 -> 257 bytes docs/html/img100.png | Bin 0 -> 673 bytes docs/html/img11.png | Bin 0 -> 222 bytes docs/html/img12.png | Bin 0 -> 504 bytes docs/html/img13.png | Bin 0 -> 607 bytes docs/html/img14.png | Bin 0 -> 584 bytes docs/html/img15.png | Bin 0 -> 373 bytes docs/html/img16.png | Bin 0 -> 296 bytes docs/html/img17.png | Bin 0 -> 345 bytes docs/html/img18.png | Bin 0 -> 596 bytes docs/html/img19.png | Bin 0 -> 394 bytes docs/html/img2.png | Bin 0 -> 219 bytes docs/html/img20.png | Bin 0 -> 508 bytes docs/html/img21.png | Bin 0 -> 187 bytes docs/html/img22.png | Bin 0 -> 314 bytes docs/html/img23.png | Bin 0 -> 338 bytes docs/html/img24.png | Bin 0 -> 274 bytes docs/html/img25.png | Bin 0 -> 1058 bytes docs/html/img26.png | Bin 0 -> 341 bytes docs/html/img27.png | Bin 0 -> 1265 bytes docs/html/img28.png | Bin 0 -> 298 bytes docs/html/img29.png | Bin 0 -> 456 bytes docs/html/img3.png | Bin 0 -> 684 bytes docs/html/img30.png | Bin 0 -> 407 bytes docs/html/img31.png | Bin 0 -> 474 bytes docs/html/img32.png | Bin 0 -> 241 bytes docs/html/img33.png | Bin 0 -> 755 bytes docs/html/img34.png | Bin 0 -> 217 bytes docs/html/img35.png | Bin 0 -> 283 bytes docs/html/img36.png | Bin 0 -> 731 bytes docs/html/img37.png | Bin 0 -> 337 bytes docs/html/img38.png | Bin 0 -> 314 bytes docs/html/img39.png | Bin 0 -> 529 bytes docs/html/img4.png | Bin 0 -> 556 bytes docs/html/img40.png | Bin 0 -> 1345 bytes docs/html/img41.png | Bin 0 -> 1354 bytes docs/html/img42.png | Bin 0 -> 296 bytes docs/html/img43.png | Bin 0 -> 279 bytes docs/html/img44.png | Bin 0 -> 322 bytes docs/html/img45.png | Bin 0 -> 257 bytes docs/html/img46.png | Bin 0 -> 583 bytes docs/html/img47.png | Bin 0 -> 651 bytes docs/html/img48.png | Bin 0 -> 330 bytes docs/html/img49.png | Bin 0 -> 807 bytes docs/html/img5.png | Bin 0 -> 648 bytes docs/html/img50.png | Bin 0 -> 386 bytes docs/html/img51.png | Bin 0 -> 324 bytes docs/html/img52.png | Bin 0 -> 802 bytes docs/html/img53.png | Bin 0 -> 461 bytes docs/html/img54.png | Bin 0 -> 391 bytes docs/html/img55.png | Bin 0 -> 1062 bytes docs/html/img56.png | Bin 0 -> 1320 bytes docs/html/img57.png | Bin 0 -> 1075 bytes docs/html/img58.png | Bin 0 -> 1355 bytes docs/html/img59.png | Bin 0 -> 261 bytes docs/html/img6.png | Bin 0 -> 819 bytes docs/html/img60.png | Bin 0 -> 441 bytes docs/html/img61.png | Bin 0 -> 312 bytes docs/html/img62.png | Bin 0 -> 181 bytes docs/html/img63.png | Bin 0 -> 257 bytes docs/html/img64.png | Bin 0 -> 295 bytes docs/html/img65.png | Bin 0 -> 325 bytes docs/html/img66.png | Bin 0 -> 8736 bytes docs/html/img67.png | Bin 0 -> 292 bytes docs/html/img68.png | Bin 0 -> 355 bytes docs/html/img69.png | Bin 0 -> 265 bytes docs/html/img7.png | Bin 0 -> 232 bytes docs/html/img70.png | Bin 0 -> 374 bytes docs/html/img71.png | Bin 0 -> 1387 bytes docs/html/img72.png | Bin 0 -> 445 bytes docs/html/img73.png | Bin 0 -> 195 bytes docs/html/img74.png | Bin 0 -> 342 bytes docs/html/img75.png | Bin 0 -> 501 bytes docs/html/img76.png | Bin 0 -> 517 bytes docs/html/img77.png | Bin 0 -> 1471 bytes docs/html/img78.png | Bin 0 -> 279 bytes docs/html/img79.png | Bin 0 -> 222 bytes docs/html/img8.png | Bin 0 -> 372 bytes docs/html/img80.png | Bin 0 -> 486 bytes docs/html/img81.png | Bin 0 -> 456 bytes docs/html/img82.png | Bin 0 -> 229 bytes docs/html/img83.png | Bin 0 -> 554 bytes docs/html/img84.png | Bin 0 -> 200 bytes docs/html/img85.png | Bin 0 -> 345 bytes docs/html/img86.png | Bin 0 -> 303 bytes docs/html/img87.png | Bin 0 -> 210 bytes docs/html/img88.png | Bin 0 -> 280 bytes docs/html/img89.png | Bin 0 -> 190 bytes docs/html/img9.png | Bin 0 -> 213 bytes docs/html/img90.png | Bin 0 -> 370 bytes docs/html/img91.png | Bin 0 -> 223 bytes docs/html/img92.png | Bin 0 -> 272 bytes docs/html/img93.png | Bin 0 -> 634 bytes docs/html/img94.png | Bin 0 -> 257 bytes docs/html/img95.png | Bin 0 -> 200 bytes docs/html/img96.png | Bin 0 -> 216 bytes docs/html/img97.png | Bin 0 -> 648 bytes docs/html/img98.png | Bin 0 -> 678 bytes docs/html/img99.png | Bin 0 -> 372 bytes docs/html/index.html | 266 + docs/html/internals.pl | 190 + docs/html/labels.pl | 197 + docs/html/node1.html | 129 + docs/html/node10.html | 190 + docs/html/node11.html | 774 ++ docs/html/node12.html | 328 + docs/html/node13.html | 258 + docs/html/node14.html | 341 + docs/html/node15.html | 196 + docs/html/node16.html | 90 + docs/html/node17.html | 106 + docs/html/node18.html | 90 + docs/html/node19.html | 433 + docs/html/node2.html | 213 + docs/html/node20.html | 89 + docs/html/node21.html | 106 + docs/html/node22.html | 107 + docs/html/node23.html | 188 + docs/html/node24.html | 88 + docs/html/node25.html | 86 + docs/html/node26.html | 89 + docs/html/node27.html | 93 + docs/html/node28.html | 84 + docs/html/node29.html | 111 + docs/html/node3.html | 75 + docs/html/node30.html | 179 + docs/html/node31.html | 77 + docs/html/node4.html | 85 + docs/html/node5.html | 103 + docs/html/node6.html | 137 + docs/html/node7.html | 97 + docs/html/node8.html | 212 + docs/html/node9.html | 87 + docs/html/userhtml.css | 30 + docs/html/userhtml.html | 266 + docs/pdf/building.tex | 9 +- docs/userguide.pdf | 12020 ++++++++-------------- examples/fileread/mld_cexample_1lev.f90 | 47 +- examples/fileread/mld_cexample_ml.f90 | 49 +- examples/fileread/mld_dexample_1lev.f90 | 47 +- examples/fileread/mld_dexample_ml.f90 | 47 +- examples/fileread/mld_sexample_1lev.f90 | 47 +- examples/fileread/mld_sexample_ml.f90 | 47 +- examples/fileread/mld_zexample_1lev.f90 | 47 +- examples/fileread/mld_zexample_ml.f90 | 47 +- mlprec/mld_cprecset.f90 | 4 +- mlprec/mld_dprecset.f90 | 4 +- mlprec/mld_sprecset.f90 | 4 +- mlprec/mld_zprecset.f90 | 4 +- test/fileread/cf_sample.f90 | 50 +- test/fileread/df_sample.f90 | 45 +- test/fileread/runs/cfs.inp | 11 +- test/fileread/runs/dfs.inp | 7 +- test/fileread/runs/sfs.inp | 15 +- test/fileread/runs/zfs.inp | 9 +- test/fileread/sf_sample.f90 | 50 +- test/fileread/zf_sample.f90 | 45 +- 166 files changed, 13334 insertions(+), 7921 deletions(-) create mode 100644 docs/html/WARNINGS create mode 100644 docs/html/images.aux create mode 100644 docs/html/images.log create mode 100644 docs/html/images.out create mode 100644 docs/html/images.pl create mode 100644 docs/html/images.tex create mode 100644 docs/html/img1.png create mode 100644 docs/html/img10.png create mode 100644 docs/html/img100.png create mode 100644 docs/html/img11.png create mode 100644 docs/html/img12.png create mode 100644 docs/html/img13.png create mode 100644 docs/html/img14.png create mode 100644 docs/html/img15.png create mode 100644 docs/html/img16.png create mode 100644 docs/html/img17.png create mode 100644 docs/html/img18.png create mode 100644 docs/html/img19.png create mode 100644 docs/html/img2.png create mode 100644 docs/html/img20.png create mode 100644 docs/html/img21.png create mode 100644 docs/html/img22.png create mode 100644 docs/html/img23.png create mode 100644 docs/html/img24.png create mode 100644 docs/html/img25.png create mode 100644 docs/html/img26.png create mode 100644 docs/html/img27.png create mode 100644 docs/html/img28.png create mode 100644 docs/html/img29.png create mode 100644 docs/html/img3.png create mode 100644 docs/html/img30.png create mode 100644 docs/html/img31.png create mode 100644 docs/html/img32.png create mode 100644 docs/html/img33.png create mode 100644 docs/html/img34.png create mode 100644 docs/html/img35.png create mode 100644 docs/html/img36.png create mode 100644 docs/html/img37.png create mode 100644 docs/html/img38.png create mode 100644 docs/html/img39.png create mode 100644 docs/html/img4.png create mode 100644 docs/html/img40.png create mode 100644 docs/html/img41.png create mode 100644 docs/html/img42.png create mode 100644 docs/html/img43.png create mode 100644 docs/html/img44.png create mode 100644 docs/html/img45.png create mode 100644 docs/html/img46.png create mode 100644 docs/html/img47.png create mode 100644 docs/html/img48.png create mode 100644 docs/html/img49.png create mode 100644 docs/html/img5.png create mode 100644 docs/html/img50.png create mode 100644 docs/html/img51.png create mode 100644 docs/html/img52.png create mode 100644 docs/html/img53.png create mode 100644 docs/html/img54.png create mode 100644 docs/html/img55.png create mode 100644 docs/html/img56.png create mode 100644 docs/html/img57.png create mode 100644 docs/html/img58.png create mode 100644 docs/html/img59.png create mode 100644 docs/html/img6.png create mode 100644 docs/html/img60.png create mode 100644 docs/html/img61.png create mode 100644 docs/html/img62.png create mode 100644 docs/html/img63.png create mode 100644 docs/html/img64.png create mode 100644 docs/html/img65.png create mode 100644 docs/html/img66.png create mode 100644 docs/html/img67.png create mode 100644 docs/html/img68.png create mode 100644 docs/html/img69.png create mode 100644 docs/html/img7.png create mode 100644 docs/html/img70.png create mode 100644 docs/html/img71.png create mode 100644 docs/html/img72.png create mode 100644 docs/html/img73.png create mode 100644 docs/html/img74.png create mode 100644 docs/html/img75.png create mode 100644 docs/html/img76.png create mode 100644 docs/html/img77.png create mode 100644 docs/html/img78.png create mode 100644 docs/html/img79.png create mode 100644 docs/html/img8.png create mode 100644 docs/html/img80.png create mode 100644 docs/html/img81.png create mode 100644 docs/html/img82.png create mode 100644 docs/html/img83.png create mode 100644 docs/html/img84.png create mode 100644 docs/html/img85.png create mode 100644 docs/html/img86.png create mode 100644 docs/html/img87.png create mode 100644 docs/html/img88.png create mode 100644 docs/html/img89.png create mode 100644 docs/html/img9.png create mode 100644 docs/html/img90.png create mode 100644 docs/html/img91.png create mode 100644 docs/html/img92.png create mode 100644 docs/html/img93.png create mode 100644 docs/html/img94.png create mode 100644 docs/html/img95.png create mode 100644 docs/html/img96.png create mode 100644 docs/html/img97.png create mode 100644 docs/html/img98.png create mode 100644 docs/html/img99.png create mode 100644 docs/html/index.html create mode 100644 docs/html/internals.pl create mode 100644 docs/html/labels.pl create mode 100644 docs/html/node1.html create mode 100644 docs/html/node10.html create mode 100644 docs/html/node11.html create mode 100644 docs/html/node12.html create mode 100644 docs/html/node13.html create mode 100644 docs/html/node14.html create mode 100644 docs/html/node15.html create mode 100644 docs/html/node16.html create mode 100644 docs/html/node17.html create mode 100644 docs/html/node18.html create mode 100644 docs/html/node19.html create mode 100644 docs/html/node2.html create mode 100644 docs/html/node20.html create mode 100644 docs/html/node21.html create mode 100644 docs/html/node22.html create mode 100644 docs/html/node23.html create mode 100644 docs/html/node24.html create mode 100644 docs/html/node25.html create mode 100644 docs/html/node26.html create mode 100644 docs/html/node27.html create mode 100644 docs/html/node28.html create mode 100644 docs/html/node29.html create mode 100644 docs/html/node3.html create mode 100644 docs/html/node30.html create mode 100644 docs/html/node31.html create mode 100644 docs/html/node4.html create mode 100644 docs/html/node5.html create mode 100644 docs/html/node6.html create mode 100644 docs/html/node7.html create mode 100644 docs/html/node8.html create mode 100644 docs/html/node9.html create mode 100644 docs/html/userhtml.css create mode 100644 docs/html/userhtml.html diff --git a/configure b/configure index a6b4b276..71e66674 100755 --- a/configure +++ b/configure @@ -2,7 +2,7 @@ # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.61 for MLD2P4 1.0. # -# Report bugs to . +# Report bugs to . # # Copyright (C) 1992, 1993, 1994, 1995, 1996, 1998, 1999, 2000, 2001, # 2002, 2003, 2004, 2005, 2006 Free Software Foundation, Inc. @@ -576,7 +576,7 @@ PACKAGE_NAME='MLD2P4' PACKAGE_TARNAME='mld2p4' PACKAGE_VERSION='1.0' PACKAGE_STRING='MLD2P4 1.0' -PACKAGE_BUGREPORT='salvatore.filippone@uniroma2.it' +PACKAGE_BUGREPORT='bugreport@mld2p4.it' ac_unique_file="mlprec/mld_prec_type.f90" # Factoring default headers for most tests. @@ -1313,7 +1313,7 @@ Some influential environment variables: Use these variables to override the choices made by `configure' or to help it to find libraries and programs with nonstandard names/locations. -Report bugs to . +Report bugs to . _ACEOF ac_status=$? fi @@ -3844,9 +3844,9 @@ echo "$as_me: WARNING: umfpack.h: proceeding with the preprocessor's result" >&2 { echo "$as_me:$LINENO: WARNING: umfpack.h: in the future, the compiler will take precedence" >&5 echo "$as_me: WARNING: umfpack.h: in the future, the compiler will take precedence" >&2;} ( cat <<\_ASBOX -## ---------------------------------------------- ## -## Report this to salvatore.filippone@uniroma2.it ## -## ---------------------------------------------- ## +## ---------------------------------- ## +## Report this to bugreport@mld2p4.it ## +## ---------------------------------- ## _ASBOX ) | sed "s/^/$as_me: WARNING: /" >&2 ;; @@ -4477,9 +4477,9 @@ echo "$as_me: WARNING: slu_ddefs.h: proceeding with the preprocessor's result" > { echo "$as_me:$LINENO: WARNING: slu_ddefs.h: in the future, the compiler will take precedence" >&5 echo "$as_me: WARNING: slu_ddefs.h: in the future, the compiler will take precedence" >&2;} ( cat <<\_ASBOX -## ---------------------------------------------- ## -## Report this to salvatore.filippone@uniroma2.it ## -## ---------------------------------------------- ## +## ---------------------------------- ## +## Report this to bugreport@mld2p4.it ## +## ---------------------------------- ## _ASBOX ) | sed "s/^/$as_me: WARNING: /" >&2 ;; @@ -4717,9 +4717,9 @@ echo "$as_me: WARNING: superlu_ddefs.h: proceeding with the preprocessor's resul { echo "$as_me:$LINENO: WARNING: superlu_ddefs.h: in the future, the compiler will take precedence" >&5 echo "$as_me: WARNING: superlu_ddefs.h: in the future, the compiler will take precedence" >&2;} ( cat <<\_ASBOX -## ---------------------------------------------- ## -## Report this to salvatore.filippone@uniroma2.it ## -## ---------------------------------------------- ## +## ---------------------------------- ## +## Report this to bugreport@mld2p4.it ## +## ---------------------------------- ## _ASBOX ) | sed "s/^/$as_me: WARNING: /" >&2 ;; diff --git a/configure.ac b/configure.ac index a660aa3c..4878df3a 100755 --- a/configure.ac +++ b/configure.ac @@ -38,7 +38,7 @@ dnl NOTE : odd configurations like ifc + gcc still await in the mist of the unkn ############################################################################### # NOTE: the literal for version (the second argument to AC_INIT should be a literal!) -AC_INIT([MLD2P4],1.0, salvatore.filippone@uniroma2.it) +AC_INIT([MLD2P4],1.0, bugreport@mld2p4.it) # VERSION is the file containing the PSBLAS version code # FIXME diff --git a/docs/html/WARNINGS b/docs/html/WARNINGS new file mode 100644 index 00000000..07a60fab --- /dev/null +++ b/docs/html/WARNINGS @@ -0,0 +1,37 @@ +No implementation found for style `pstricks' +No implementation found for style `fancybox' +No implementation found for style `ifpdf' +No implementation found for style `hyperref' +No implementation found for style `ifthen' +No implementation found for style `graphicx' +No implementation found for style `rotating' + +redefining command \thepage + +The userhtml.aux file was not found, so sections will not be numbered +and cross-references will be shown as icons. + +? brace missing for \setlength + +No number for "Applicationofthemulti-levelhybridpost-smoothedpreconditioner." + +No number for "Preconditionertypes,correspondingstringsanddefaultchoices." + +No number for "Setupandapplicationofthedefaultmulti-levelSchwarzpreconditioner." + +No number for "Setupofahybridthree-levelSchwarzpreconditioner." + +No number for "Setupofanadditivethree-levelSchwarzpreconditioner." + +No number for "Setupofaone-levelSchwarzpreconditioner." + +No number for "Parametersdefiningthetypeofmulti-levelpreconditioner." + +No number for "Parametersdefiningtheone-levelpreconditionerusedassmoother." + +No number for "Parametersdefiningtheaggregationalgorithm." + +No number for "Parametersdefiningthecoarse-spacecorrectionatthecoarsestlevel." +couldn't convert character ecaron into available encodings + + ...set $ACCENT_IMAGES to get an image diff --git a/docs/html/images.aux b/docs/html/images.aux new file mode 100644 index 00000000..4dcb91b3 --- /dev/null +++ b/docs/html/images.aux @@ -0,0 +1,15 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global \let \oldnewlabel\newlabel +\gdef \newlabel#1#2{\newlabelxx{#1}#2} +\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\let \contentsline\oldcontentsline +\let \newlabel\oldnewlabel} +\else +\global \let \hyper@last\relax +\fi + +\providecommand*\HyPL@Entry[1]{} +\HyPL@Entry{0 << /S /D >> } diff --git a/docs/html/images.log b/docs/html/images.log new file mode 100644 index 00000000..162a207b --- /dev/null +++ b/docs/html/images.log @@ -0,0 +1,801 @@ +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2008.5.20) 22 JUL 2008 18:30 +entering extended mode + %&-line parsing enabled. +**./images.tex +(./images.tex +LaTeX2e <2005/12/01> +Babel and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng +erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, + french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc +us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por +tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, +turkish, ukenglish, ukrainian, loaded. + +(/usr/share/texmf/tex/latex/base/article.cls +Document Class: article 2005/09/16 v1.4f Standard LaTeX document class +(/usr/share/texmf/tex/latex/base/size11.clo +File: size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +) +\c@part=\count79 +\c@section=\count80 +\c@subsection=\count81 +\c@subsubsection=\count82 +\c@paragraph=\count83 +\c@subparagraph=\count84 +\c@figure=\count85 +\c@table=\count86 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) (/usr/share/texmf/tex/latex/pstricks/pstricks.sty +Package: pstricks 2006/08/10 v0.32 LaTeX wrapper for `PSTricks' (RN,HV) +(/usr/share/texmf/tex/generic/pstricks/pstricks.tex +`PSTricks' v1.15 <2006/12/22> (tvz) +\pst@dima=\dimen103 +\pst@dimb=\dimen104 +\pst@dimc=\dimen105 +\pst@dimd=\dimen106 +\pst@dimg=\dimen107 +\pst@dimh=\dimen108 +\pst@hbox=\box26 +\pst@boxg=\box27 +\pst@cnta=\count87 +\pst@cntb=\count88 +\pst@cntc=\count89 +\pst@cntd=\count90 +\pst@cntg=\count91 +\pst@cnth=\count92 +\pst@toks=\toks14 +(/usr/share/texmf/tex/generic/pstricks/pstricks.con) +\psunit=\dimen109 +\psxunit=\dimen110 +\psyunit=\dimen111 +\pslinewidth=\dimen112 +\pst@customdefs=\toks15 +\pslinearc=\dimen113 +\everypsbox=\toks16 +\psframesep=\dimen114 +\pslabelsep=\dimen115 +\psk@shift=\dimen116 +\pst@shift=\dimen117 +\theoverlaybox=\box28 +) +File: pstricks.tex 2006/12/22 v1.15 `PSTricks' (tvz) +(/usr/share/texmf/tex/latex/xcolor/xcolor.sty +Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) +(/usr/share/texmf/tex/latex/config/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package xcolor Info: Package option `override' ignored on input line 216. +Package xcolor Info: Driver file: dvips.def on input line 225. +(/usr/share/texmf/tex/latex/graphics/dvips.def +File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR) +) +Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337. +Package xcolor Info: Model `RGB' extended on input line 1353. +Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355. +Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356. +Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357. +Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358. +Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359. +Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360. +)) (/usr/share/texmf/tex/latex/fancybox/fancybox.sty +Package: fancybox 2000/09/19 1.3 +Style option: `fancybox' v1.3 <2000/09/19> (tvz) +\@fancybox=\box29 +\shadowsize=\dimen118 +\@Sbox=\box30 +\do@VerbBox=\toks17 +\the@fancyput=\toks18 +\this@fancyput=\toks19 +\EndVerbatimTokens=\toks20 +\Verbatim@Outfile=\write3 +\Verbatim@Infile=\read1 +) (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2001/10/25 v2.2f +\@emptytoks=\toks21 +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 132. +) (/usr/share/texmf/tex/generic/oberdiek/ifpdf.sty +Package: ifpdf 2006/02/20 v1.4 Provides the ifpdf switch (HO) +Package ifpdf Info: pdfTeX in pdf mode not detected. +) (/usr/share/texmf/tex/latex/hyperref/hyperref.sty +Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX +(/usr/share/texmf/tex/latex/graphics/keyval.sty +Package: keyval 1999/03/16 v1.13 key=value parser (DPC) +\KV@toks@=\toks22 +) +\@linkdim=\dimen119 +\Hy@linkcounter=\count93 +\Hy@pagecounter=\count94 +(/usr/share/texmf/tex/latex/hyperref/pd1enc.def +File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +) (/usr/share/texmf/tex/latex/config/hyperref.cfg +File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +) (/usr/share/texmf/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options ( +HO) +) +Package hyperref Info: Option `bookmarks' set `true' on input line 2238. +Package hyperref Info: Option `bookmarksnumbered' set `true' on input line 2238 +. +Package hyperref Info: Option `bookmarksopen' set `false' on input line 2238. +Package hyperref Info: Option `plainpages' set `false' on input line 2238. +Package hyperref Info: Option `pdfpagelabels' set `true' on input line 2238. +Package hyperref Info: Option `colorlinks' set `true' on input line 2238. +Package hyperref Info: Hyper figures OFF on input line 2288. +Package hyperref Info: Link nesting OFF on input line 2293. +Package hyperref Info: Hyper index ON on input line 2296. +Package hyperref Info: Plain pages OFF on input line 2303. +Package hyperref Info: Backreferencing OFF on input line 2308. +Implicit mode ON; LaTeX internals redefined +Package hyperref Info: Bookmarks ON on input line 2444. +(/usr/share/texmf/tex/latex/html/url.sty +Package: url 1999/03/02 ver 1.4 Verb mode for urls, email addresses, and file + names +) +LaTeX Info: Redefining \url on input line 2599. +\Fld@menulength=\count95 +\Field@Width=\dimen120 +\Fld@charsize=\dimen121 +\Choice@toks=\toks23 +\Field@toks=\toks24 +Package hyperref Info: Hyper figures OFF on input line 3102. +Package hyperref Info: Link nesting OFF on input line 3107. +Package hyperref Info: Hyper index ON on input line 3110. +Package hyperref Info: backreferencing OFF on input line 3117. +Package hyperref Info: Link coloring ON on input line 3120. +\Hy@abspage=\count96 +\c@Item=\count97 +\c@Hfootnote=\count98 +) +*hyperref using default driver hdvips* +(/usr/share/texmf/tex/latex/hyperref/hdvips.def +File: hdvips.def 2007/02/07 v6.75r Hyperref driver for dvips +(/usr/share/texmf/tex/latex/hyperref/pdfmark.def +File: pdfmark.def 2007/02/07 v6.75r Hyperref definitions for pdfmark specials +\pdf@docset=\toks25 +\pdf@box=\box31 +\pdf@toks=\toks26 +\pdf@defaulttoks=\toks27 +\Fld@listcount=\count99 +)) (/usr/share/texmf/tex/latex/base/ifthen.sty +Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) +) (/usr/share/texmf/tex/latex/graphics/graphicx.sty +Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +(/usr/share/texmf/tex/latex/graphics/graphics.sty +Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) +(/usr/share/texmf/tex/latex/graphics/trig.sty +Package: trig 1999/03/16 v1.09 sin cos tan (DPC) +) (/usr/share/texmf/tex/latex/config/graphics.cfg +File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive +) +Package graphics Info: Driver file: dvips.def on input line 90. +) +\Gin@req@height=\dimen122 +\Gin@req@width=\dimen123 +) +\c@theorem=\count100 +\c@corollary=\count101 +(/usr/share/texmf/tex/latex/rotating/rotating.sty +Package: rotating 1997/09/26, v2.13 Rotation package +\c@r@tfl@t=\count102 +\rot@float@box=\box32 +) +\c@subroutine=\count103 +\c@example=\count104 +(/usr/share/texmf/tex/latex/pstricks/pstcol.sty +Package: pstcol 2005/11/16 v1.2 LaTeX wrapper for `PSTricks' (RN,HV) + +Package pstcol Warning: ************************************ +(pstcol) The package `pstcol' is obsolet! +(pstcol) You should use `pstricks' directly: +(pstcol) \usepackage{pstricks} +(pstcol) ************************************. + + +! LaTeX Error: Option clash for package pstricks. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.21 + +The package pstricks has already been loaded with options: + [] +There has now been an attempt to load it with options + [noxcolor] +Adding the global options: + ,noxcolor +to your \documentclass declaration may fix this. +Try typing to proceed. + +) (/usr/share/texmf/tex/latex/base/inputenc.sty +Package: inputenc 2006/05/05 v1.1b Input encoding file +\inpenc@prehook=\toks28 +\inpenc@posthook=\toks29 +(/usr/share/texmf/tex/latex/base/latin1.def +File: latin1.def 2006/05/05 v1.1b Input encoding file +)) +\sizebox=\box33 +\lthtmlwrite=\write4 +No file images.aux. +\openout1 = `images.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 152. +LaTeX Font Info: ... okay on input line 152. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 152. +LaTeX Font Info: ... okay on input line 152. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 152. +LaTeX Font Info: ... okay on input line 152. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 152. +LaTeX Font Info: ... okay on input line 152. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 152. +LaTeX Font Info: ... okay on input line 152. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 152. +LaTeX Font Info: ... okay on input line 152. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 152. +LaTeX Font Info: ... okay on input line 152. +Package hyperref Info: Link coloring ON on input line 152. +(/usr/share/texmf/tex/latex/hyperref/nameref.sty +Package: nameref 2006/12/27 v2.28 Cross-referencing by name of section +(/usr/share/texmf/tex/latex/oberdiek/refcount.sty +Package: refcount 2006/02/20 v3.0 Data extraction from references (HO) +) +\c@section@level=\count105 +) +LaTeX Info: Redefining \ref on input line 152. +LaTeX Info: Redefining \pageref on input line 152. +\@outlinefile=\write5 +\openout5 = `images.out'. + + +Package hyperref Warning: Rerun to get /PageLabels entry. + + +latex2htmlLength hsize=349.0pt + +latex2htmlLength vsize=680.80026pt + +latex2htmlLength hoffset=0.0pt + +latex2htmlLength voffset=0.0pt + +latex2htmlLength topmargin=0.0pt + +latex2htmlLength topskip=0.00003pt + +latex2htmlLength headheight=0.0pt + +latex2htmlLength headsep=0.0pt + +latex2htmlLength parskip=0.0pt plus 1.0pt + +latex2htmlLength oddsidemargin=22.0pt + +latex2htmlLength evensidemargin=70.0pt + +\centeroffset=\skip43 +LaTeX Font Info: Try loading font information for U+msa on input line 184. +(/usr/share/texmf/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2002/01/19 v2.2g AMS font definitions +) +LaTeX Font Info: Try loading font information for U+msb on input line 184. +(/usr/share/texmf/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2002/01/19 v2.2g AMS font definitions +) +l2hSize :displaymath238:15.72917pt::0.0pt::349.0pt. +[1 + + + +] +l2hSize :tex2html_wrap_inline265:7.48248pt::0.0pt::8.76004pt. +[2 + + +] +l2hSize :tex2html_wrap_inline586:9.30704pt::9.30704pt::83.67497pt. +[3 + + +] +l2hSize :tex2html_wrap_inline588:8.7125pt::8.7125pt::55.89207pt. +[4 + + +] +l2hSize :tex2html_wrap_inline592:8.7125pt::8.7125pt::84.68239pt. +[5 + + +] +l2hSize :tex2html_wrap_inline594:8.7125pt::8.7125pt::99.38406pt. +[6 + + +] +l2hSize :tex2html_wrap_inline596:7.48248pt::0.0pt::9.15695pt. +[7 + + +] +l2hSize :tex2html_wrap_inline598:8.10416pt::8.10416pt::25.90352pt. +[8 + + +] +l2hSize :tex2html_wrap_inline600:7.60416pt::0.0pt::5.8286pt. +[9 + + +] +l2hSize :tex2html_wrap_inline602:7.48248pt::0.0pt::12.41005pt. +[10 + + +] +l2hSize :tex2html_wrap_inline606:7.07185pt::0.0pt::10.16177pt. +[11 + + +] +l2hSize :tex2html_wrap_inline608:9.62923pt::9.62923pt::43.62254pt. +[12 + + +] +l2hSize :tex2html_wrap_inline610:9.62923pt::9.62923pt::65.17778pt. +[13 + + +] +l2hSize :tex2html_wrap_inline616:10.66058pt::10.66058pt::58.85606pt. +[14 + + +] +l2hSize :tex2html_wrap_inline618:10.66058pt::10.66058pt::27.83247pt. +[15 + + +] +l2hSize :tex2html_wrap_inline620:10.02922pt::10.02922pt::11.68126pt. +[16 + + +] +l2hSize :tex2html_wrap_inline622:10.02922pt::10.02922pt::16.9712pt. +[17 + + +] +l2hSize :tex2html_wrap_inline624:11.46367pt::11.46367pt::56.33008pt. +[18 + + +] +l2hSize :tex2html_wrap_inline626:8.10416pt::8.10416pt::33.19717pt. +[19 + + +] +l2hSize :tex2html_wrap_inline628:11.46367pt::11.46367pt::41.86319pt. +[20 + + +] +l2hSize :tex2html_wrap_inline630:7.07185pt::0.0pt::6.24812pt. +[21 + + +] +l2hSize :tex2html_wrap_inline634:10.02922pt::10.02922pt::13.50749pt. +[22 + + +] +l2hSize :tex2html_wrap_inline636:10.96367pt::0.0pt::18.2182pt. +[23 + + +] +l2hSize :tex2html_wrap_inline638:7.60416pt::0.0pt::14.11334pt. +[24 + + +] +l2hSize :tex2html_wrap_inline640:11.46367pt::11.46367pt::124.12694pt. +[25 + + +] +l2hSize :tex2html_wrap_inline644:10.02922pt::10.02922pt::16.9712pt. +[26 + + +] +l2hSize :displaymath564:33.45825pt::0.0pt::349.0pt. +[27 + + +] +l2hSize :tex2html_wrap_inline646:10.02922pt::10.02922pt::13.3212pt. +[28 + + +] +l2hSize :tex2html_wrap_inline652:10.02922pt::10.02922pt::42.50967pt. +[29 + + +] +l2hSize :tex2html_wrap_inline654:7.72179pt::7.72179pt::58.3423pt. +[30 + + +] +l2hSize :tex2html_wrap_inline656:10.02922pt::10.02922pt::47.85603pt. +[31 + + +] +l2hSize :tex2html_wrap_inline660:7.57185pt::7.57185pt::11.78078pt. +[32 + + +] +l2hSize :tex2html_wrap_inline662:10.02922pt::10.02922pt::88.43413pt. +[33 + + +] +l2hSize :tex2html_wrap_inline664:7.57185pt::7.57185pt::6.05675pt. +[34 + + +] +l2hSize :tex2html_wrap_inline668:7.57185pt::7.57185pt::14.87756pt. +[35 + + +] +l2hSize :tex2html_wrap_inline672:11.46367pt::11.46367pt::71.66493pt. +[36 + + +] +l2hSize :tex2html_wrap_inline674:10.58096pt::10.58096pt::13.6964pt. +[37 + + +] +l2hSize :tex2html_wrap_inline676:10.02922pt::10.02922pt::13.50749pt. +[38 + + +] +l2hSize :tex2html_wrap_inline678:10.02922pt::10.02922pt::39.05879pt. +[39 + + +] +l2hSize :displaymath565:33.45825pt::0.0pt::349.0pt. +[40 + + +] +l2hSize :displaymath566:33.45825pt::0.0pt::349.0pt. +[41 + + +] +l2hSize :tex2html_wrap_inline680:7.60416pt::0.0pt::25.90352pt. +[42 + + +] +l2hSize :tex2html_wrap_inline686:7.98248pt::7.98248pt::15.88345pt. +[43 + + +] +l2hSize :tex2html_wrap_inline692:7.98248pt::7.98248pt::18.01262pt. +[44 + + +] +l2hSize :tex2html_wrap_inline694:7.57185pt::7.57185pt::14.24352pt. +[45 + + +] +l2hSize :tex2html_wrap_inline696:9.30704pt::9.30704pt::60.92035pt. +[46 + + +] +l2hSize :displaymath567:16.30702pt::0.0pt::349.0pt. +[47 + + +] +l2hSize :tex2html_wrap_inline700:7.98248pt::7.98248pt::21.70126pt. +[48 + + +] +l2hSize :displaymath568:17.04697pt::0.0pt::349.0pt. +[49 + + +] +l2hSize :tex2html_wrap_inline704:10.26059pt::10.26059pt::23.72566pt. +[50 + + +] +l2hSize :tex2html_wrap_inline710:7.98248pt::7.98248pt::18.29398pt. +[51 + + +] +l2hSize :displaymath569:17.04697pt::0.0pt::349.0pt. +[52 + + +] +l2hSize :tex2html_wrap_inline714:10.26059pt::10.26059pt::34.67923pt. +[53 + + +] +l2hSize :tex2html_wrap_inline720:10.26059pt::10.26059pt::23.72566pt. +[54 + + +] +l2hSize :displaymath570:28.68124pt::0.0pt::349.0pt. +[55 + + +] +l2hSize :displaymath571:17.88034pt::0.0pt::349.0pt. +[56 + + +] +l2hSize :displaymath572:28.68124pt::0.0pt::349.0pt. +[57 + + +] +l2hSize :displaymath573:17.88034pt::0.0pt::349.0pt. +[58 + + +] +l2hSize :tex2html_wrap_inline734:7.48248pt::0.0pt::12.3644pt. +[59 + + +] +l2hSize :tex2html_wrap_inline738:9.12923pt::0.0pt::52.16011pt. +[60 + + +] +l2hSize :tex2html_wrap_inline740:7.60416pt::0.0pt::21.40202pt. +[61 + + +] +l2hSize :tex2html_wrap_inline742:7.60416pt::0.0pt::4.03026pt. +[62 + + +] +l2hSize :tex2html_wrap_inline744:7.98248pt::7.98248pt::11.892pt. +[63 + + +] +l2hSize :tex2html_wrap_inline746:7.98248pt::7.98248pt::14.30252pt. +[64 + + +] +l2hSize :tex2html_wrap_inline748:7.98248pt::7.98248pt::36.32253pt. +[65 + + +] +l2hSize :tex2html_wrap860:139.25392pt::133.77895pt::349.0pt. +[66 + + +] +l2hSize :tex2html_wrap_inline776:7.98248pt::7.98248pt::15.98515pt. +[67 + + +] +l2hSize :tex2html_wrap_inline784:9.94032pt::9.94032pt::15.98515pt. +[68 + + +] +l2hSize :tex2html_wrap_inline798:7.98248pt::7.98248pt::13.91736pt. +[69 + + +] +l2hSize :tex2html_wrap_inline802:7.98248pt::7.98248pt::31.03764pt. +[70 + + +] +l2hSize :displaymath574:20.71762pt::0.0pt::349.0pt. +[71 + + +] +l2hSize :tex2html_wrap_inline804:8.7125pt::8.7125pt::41.27534pt. +[72 + + +] +l2hSize :tex2html_wrap_inline806:7.22179pt::0.0pt::4.31995pt. +[73 + + +] +l2hSize :tex2html_wrap_inline808:9.62923pt::9.62923pt::17.16011pt. +[74 + + +] +l2hSize :tex2html_wrap_inline812:9.94032pt::9.94032pt::44.73853pt. +[75 + + +] +l2hSize :tex2html_wrap_inline814:9.30704pt::9.30704pt::54.03362pt. +[76 + + +] +l2hSize :displaymath531:29.29593pt::0.0pt::349.0pt. +[77 + + +] +l2hSize :tex2html_wrap_inline816:7.98248pt::7.98248pt::14.70099pt. +[78 + + +] +l2hSize :tex2html_wrap_inline818:7.48248pt::0.0pt::9.09842pt. +[79 + + +] +l2hSize :tex2html_wrap_inline820:9.30704pt::9.30704pt::46.61087pt. +[80 + + +] +l2hSize :displaymath542:15.72917pt::0.0pt::349.0pt. +[81 + + +] +l2hSize :tex2html_wrap_inline822:7.48248pt::0.0pt::7.89314pt. +[82 + + +] +l2hSize :displaymath546:15.72917pt::0.0pt::349.0pt. +[83 + + +] +l2hSize :tex2html_wrap_inline824:7.07185pt::0.0pt::7.75627pt. +[84 + + +] +l2hSize :tex2html_wrap_inline826:9.12923pt::0.0pt::29.49117pt. +[85 + + +] +l2hSize :tex2html_wrap_inline983:7.60416pt::0.0pt::26.06703pt. +[86 + + +] +l2hSize :tex2html_wrap_inline1324:7.07185pt::0.0pt::8.68147pt. +[87 + + +] +l2hSize :tex2html_wrap_inline1328:7.57185pt::7.57185pt::17.58084pt. +[88 + + +] +l2hSize :tex2html_wrap_inline1342:7.07185pt::0.0pt::4.50171pt. +[89 + + +] +l2hSize :tex2html_wrap_inline1346:8.7125pt::8.7125pt::32.78915pt. +[90 + + +] +l2hSize :tex2html_wrap_inline1348:7.60416pt::0.0pt::5.99211pt. +[91 + + +] +l2hSize :tex2html_wrap_inline1352:7.57185pt::7.57185pt::17.58084pt. +[92 + + +] +l2hSize :tex2html_wrap_inline1374:9.62923pt::9.62923pt::71.50383pt. +[93 + + +] +l2hSize :tex2html_wrap_inline1378:7.57185pt::7.57185pt::11.36446pt. +[94 + + +] +l2hSize :tex2html_wrap_inline1382:7.07185pt::0.0pt::6.80576pt. +[95 + + +] +l2hSize :tex2html_wrap_inline1384:7.57185pt::7.57185pt::6.30898pt. +[96 + + +] +l2hSize :tex2html_wrap_inline1386:9.62923pt::9.62923pt::80.83733pt. +[97 + + +] +l2hSize :tex2html_wrap_inline1388:9.94032pt::9.94032pt::82.71652pt. +[98 + + +] +l2hSize :tex2html_wrap_inline1390:9.62923pt::9.62923pt::27.98401pt. +[99 + + +] +l2hSize :tex2html_wrap_inline1392:9.94032pt::9.94032pt::83.21068pt. +[100 + + +] (./images.aux) ) +Here is how much of TeX's memory you used: + 4265 strings out of 94074 + 55276 string characters out of 1167173 + 134209 words of memory out of 1500000 + 7519 multiletter control sequences out of 10000+50000 + 10304 words of font info for 41 fonts, out of 1200000 for 2000 + 645 hyphenation exceptions out of 8191 + 30i,8n,37p,306b,390s stack positions out of 5000i,500n,6000p,200000b,10000s + +Output written on images.dvi (100 pages, 72052 bytes). diff --git a/docs/html/images.out b/docs/html/images.out new file mode 100644 index 00000000..e69de29b diff --git a/docs/html/images.pl b/docs/html/images.pl new file mode 100644 index 00000000..af31e37c --- /dev/null +++ b/docs/html/images.pl @@ -0,0 +1,657 @@ +# LaTeX2HTML 2002-2-1 (1.71) +# Associate images original text with physical files. + + +$key = q/w=M^{-1}v;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$w=M^{-1}v$|; + +$key = q/w;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$w$|; + +$key = q/W_i^{delta};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^{\delta}$|; + +$key = q/{displaymath}M_{2LA}^{-1}=M_{C}^{-1}+M_{1L}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. +\end{displaymath}|; + +$key = q/M_{1L}^{-1};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M_{1L}^{-1}$|; + +$key = q/M_l;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M_l$|; + +$key = q/W;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W$|; + +$key = q/W_i^0subsetW;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^0 \subset W$|; + +$key = q/E={(i,j):a_{ij}neq0};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$E=\{(i,j) : a_{ij} \neq 0\}$|; + +$key = q/nlev;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$nlev$|; + +$key = q/A_i^deltaw_i=v_i;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A_i^\delta w_i = v_i$|; + +$key = q/M_{1L};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M_{1L}$|; + +$key = q/R_i^delta;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$R_i^\delta$|; + +$key = q/op(M^{-1})=M^{-T};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$op(M^{-1}) = M^{-T}$|; + +$key = q/W_i^{delta-1};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^{\delta-1}$|; + +$key = q/cup_{i=1}^mW_i^0=W;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\cup_{i=1}^m W_i^0 = W$|; + +$key = q/delta=0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\delta=0$|; + +$key = q/rinW;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$r \in W$|; + +$key = q/theta=0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\theta = 0$|; + +$key = q/{displaymath}Ax=b,{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +Ax=b, +\end{displaymath}|; + +$key = q/Re^{n_i^delta};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\Re^{n_i^\delta}$|; + +$key = q/R_CinRe^{n_Ctimesn};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$R_C \in \Re^{n_C \times n}$|; + +$key = q/y;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$y$|; + +$key = q/{displaymath}A_C=R_CAR_C^T{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +A_C=R_C A R_C^T +\end{displaymath}|; + +$key = q/l;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$l$|; + +$key = q/v_i=R_i^{delta}v;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$v_i = R_i^{\delta} v$|; + +$key = q/N_r;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$N_r$|; + +$key = q/P_C=R_C^T;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$P_C=R_C^T$|; + +$key = q/{displaymath}M_{2LH-PRE}^{-1}=M_{C}^{-1}+left(I-M_{C}^{-1}Aright)M_{1L}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. +\end{displaymath}|; + +$key = q/v_i^{delta}inRe^{n_i^delta};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$v_i^{\delta} \in \Re^{n_i^\delta}$|; + +$key = q/{displaymath}M_{RAS}^{-1}=sum_{i=1}^m(tilde{R}_i^0)^T(A_i^delta)^{-1}R_i^{delta}.{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T +(A_i^\delta)^{-1} R_i^{\delta}. +\end{displaymath}|; + +$key = q/A_l;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A_l$|; + +$key = q/n_C;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$n_C$|; + +$key = q/W_i^delta;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^\delta$|; + +$key = q/A_i^delta;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A_i^\delta$|; + +$key = q/{displaymath}M_{AS}^{-1}=sum_{i=1}^m(R_i^{delta})^T(A_i^delta)^{-1}R_i^{delta},{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T +(A_i^\delta)^{-1} R_i^{\delta}, +\end{displaymath}|; + +$key = q/delta>0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\delta > 0$|; + +$key = q/w_i;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$w_i$|; + +$key = q/w=sum_{i=1}^m(R_i^{delta})^Tw_i;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$|; + +$key = q/p;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$p$|; + +$key = q/A_i^delta=R_i^deltaA(R_i^delta)^TinRe^{n_i^deltatimesn_i^delta};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in +\Re^{n_i^\delta \times n_i^\delta}$|; + +$key = q/thetain[0,1];MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\theta \in [0,1]$|; + +$key = q/A=(a_{ij})inRe^{ntimesn};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A=(a_{ij}) \in \Re^{n \times n}$|; + +$key = q/tilde{R}_i^0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\tilde{R}_i^0$|; + +$key = q/M_{2L-A}^{-1};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M_{2L-A}^{-1}$|; + +$key = q/{displaymath}P_C=SP,{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +P_C = S P, +\end{displaymath}|; + +$key = q/M_{C};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M_{C}$|; + +$key = q/{displaymath}N_r=left{sinW:|a_{rs}|>thetasqrt{|a_{rr}a_{ss}|}right}cupleft{rright},{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath}N_r = \left\{s \in W: \vert a_{rs}\vert > \theta \sqrt{\vert a_{rr}a_{ss}\vert} \right\} +\cup \left\{ r \right\} , +\end{displaymath}|; + +$key = q/R_i^{delta};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$R_i^{\delta}$|; + +$key = q/R_C;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$R_C$|; + +$key = q/>0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$>0$|; + +$key = q/(tilde{R}_i^0)^TinRe^{n_i^deltatimesn};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$|; + +$key = q/A_1=A;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A_1=A$|; + +$key = q/M;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M$|; + +$key = q/x;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$x$|; + +$key = q/G=(W,E);MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$G=(W,E)$|; + +$key = q/{displaymath}array{{l}w=M_{1L}^{-1}v,z=w+M_{C}^{-1}(v-Aw);array{{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +\begin{array}{l} +w = M_{1L}^{-1} v, \\\\ +z = w + M_{C}^{-1} (v-Aw); +\end{array}\end{displaymath}|; + +$key = q/P;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$P$|; + +$key = q/A_C;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A_C$|; + +$key = q/n_i^delta;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$n_i^\delta$|; + +$key = q/M^{-1});MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M^{-1})$|; + +$key = q/{displaymath}M_{C}^{-1}=R_C^TA_C^{-1}R_C,{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +M_{C}^{-1}= R_C^T A_C^{-1} R_C, +\end{displaymath}|; + +$key = q/i;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$i$|; + +$key = q/R_i^{delta}inRe^{n_i^deltatimesn};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$R_i^{\delta} \in +\Re^{n_i^\delta \times n}$|; + +$key = q/in[0,1];MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\in [0, 1]$|; + +$key = q/{displaymath}array{{l}w=M_{C}^{-1}v,z=w+M_{1L}^{-1}(v-Aw),array{{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +\begin{array}{l} +w = M_{C}^{-1} v , \\\\ +z = w + M_{1L}^{-1} (v-Aw) , +\end{array}\end{displaymath}|; + +$key = q/p,t;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$p,t$|; + +$key = q/Re^n;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\Re^n$|; + +$key = q/t;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$t$|; + +$key = q/PinRe^{ntimesn_C};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$P \in \Re^{n \times n_C}$|; + +$key = q/S;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$S$|; + +$key = q/D^{-1}A;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$D^{-1}A$|; + +$key = q/M_{C}^{-1};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$M_{C}^{-1}$|; + +$key = q/v;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$v$|; + +$key = q/R_C^T;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$R_C^T$|; + +$key = q/delta;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\delta$|; + +$key = q/ge0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\ge 0$|; + +$key = q/{displaymath}M_{2LH-POST}^{-1}=M_{1L}^{-1}+left(I-M_{1L}^{-1}Aright)M_{C}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. +\end{displaymath}|; + +$key = q/op;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$op$|; + +$key = q/G;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$G$|; + +$key = q/omega;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\omega$|; + +$key = q/P_C;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$P_C$|; + +$key = q/W_C;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_C$|; + +$key = q/W_i^0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^0$|; + +$key = q/op(M^{-1})=M^{-1};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$op(M^{-1}) = M^{-1}$|; + +$key = q/W={1,2,ldots,n};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W=\{1, 2, \ldots, n\}$|; + +$key = q/framebox{minipage{{.85textwidth}{smalltabbing{quad=quad=quad=quad[-1mm]{v_1=v{;[{>{y_l=y_l+r_l{textbf{endfor}[1mm]{w=y_1{;tabbing{}minipage{};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\framebox{ +\begin{minipage}{.85\textwidth} {\small +\begin{tabbing} +\quad \=\quad... +...= y_l+r_l$\\\\ +\textbf{endfor} [1mm] +$w = y_1$; +\end{tabbing}} +\end{minipage}}|; + +$key = q/A;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$A$|; + +$key = q/i=1,ldots,m;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$i=1,\ldots,m$|; + +$key = q/y=op(M^{-1}),x;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$y = op(M^{-1}) x$|; + +$key = q/{displaymath}S=I-omegaD^{-1}A,{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +S = I - \omega D^{-1} A , +\end{displaymath}|; + +$key = q/SinRe^{ntimesn};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$S \in \Re^{n \times n}$|; + +$key = q/theta;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$\theta$|; + +$key = q/{displaymath}M_{ASH}^{-1}=sum_{i=1}^m(R_i^{delta})^T(A_i^delta)^{-1}tilde{R}_i^0.{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath}M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T +(A_i^\delta)^{-1} \tilde{R}_i^0. +\end{displaymath}|; + +$key = q/op(M^{-1})=M^{-C};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$op(M^{-1}) = M^{-C}$|; + +$key = q/W_i^deltasupsetW_i^{delta-1};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^\delta \supset W_i^{\delta-1}$|; + +$key = q/vinRe^n;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$v \in \Re^n$|; + +$key = q/W_i^deltabackslashW_i^0;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$W_i^\delta \backslash W_i^0$|; + +$key = q/m;MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|$m$|; + +$key = q/{displaymath}P=(p_{ij}),quadp_{ij}=left{array{{ll}1&quadmbox{if};iinV^j_C0&quadmbox{otherwise}array{right..{displaymath};MSF=1.6;LFS=11;AAT/; +$cached_env_img{$key} = q|\begin{displaymath} +P=(p_{ij}), \quad p_{ij}= +\left\{ \begin{array}{ll} +1 & \qu... +...\in V^j_C \\\\ +0 & \quad \mbox{otherwise} +\end{array} \right. . +\end{displaymath}|; + +1; + diff --git a/docs/html/images.tex b/docs/html/images.tex new file mode 100644 index 00000000..860a21bf --- /dev/null +++ b/docs/html/images.tex @@ -0,0 +1,874 @@ +\batchmode +\documentclass[a4paper,twoside,11pt]{article} + +\usepackage{pstricks} +\usepackage{fancybox} +\usepackage{amsfonts} +\usepackage{ifpdf} +\usepackage[bookmarks=true, bookmarksnumbered=true, bookmarksopen=false, plainpages=false, pdfpagelabels, colorlinks, linkcolor=blue]{hyperref} +\usepackage{ifthen} +\usepackage{graphicx} + +\newtheorem{theorem}{Theorem} +\newtheorem{corollary}{Corollary} \usepackage{rotating} + + +\pdfoutput=0 + + + +\setlength \textwidth{1.15\textwidth} +\pagestyle{myheadings} + + + +\newcounter{subroutine}[subsection] +\newcounter{example}[subroutine] \makeatletter% +\providecommand{\subsubroutine}[2]{% +\stepcounter{subroutine}% + \subsection*{\flushleft #1---#2 \endflushleft}% + \addcontentsline{toc}{subsubsection}{#1}% + \markright{#1}}%% +\providecommand{\examplename}{Example}% +\providecommand{\syntaxname}{Syntax} + +\makeatother% +\providecommand{\example}{\stepcounter{example}% +\section*{Example~\arabic{example}}} + +% +\providecommand{\precdata}{\hyperlink{precdata}{{\tt mld\_prec\_type}}}% +\providecommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}}% +\providecommand{\spdata}{\hyperlink{spdata}{{\tt psb\_spmat\_type}}}% +\providecommand{\Ref}[1]{\mbox{(\ref{#1})}} + + + +\usepackage[dvips]{pstcol} + + +\pagecolor[gray]{.7} + +\usepackage[latin1]{inputenc} + + + +\makeatletter + +\makeatletter +\count@=\the\catcode`\_ \catcode`\_=8 +\newenvironment{tex2html_wrap}{}{}% +\catcode`\<=12\catcode`\_=\count@ +\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}% +\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}% + \expandafter\renewcommand\csname #1\endcsname}% +\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}% +\let\newedcommand\renewedcommand +\let\renewedenvironment\newedenvironment +\makeatother +\let\mathon=$ +\let\mathoff=$ +\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi +\newbox\sizebox +\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt} +\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt} +\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt} +\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt} +\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt} +\setlength{\textwidth}{349pt} +\newwrite\lthtmlwrite +\makeatletter +\let\realnormalsize=\normalsize +\global\topskip=2sp +\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float +\def\@float{\let\@savefreelist\@freelist\real@float} +\def\liih@math{\ifmmode$\else\bad@math\fi} +\def\end@float{\realend@float\global\let\@freelist\@savefreelist} +\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float +\let\@largefloatcheck=\relax +\let\if@boxedmulticols=\iftrue +\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt} +\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize + \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}% + \def\phantompar{\csname par\endcsname}\normalsize}% +\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}% +\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }% +\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }% +\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup % + \let\ifinner=\iffalse \let\)\liih@math }% +\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}% + \expandafter\box\next\egroup}% +\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}% +\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox + \ifdim\dimen0>.95\vsize + \lthtmltypeout{% +*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95 vsize ***}% + \ht\sizebox.95\vsize \dp\sizebox\z@ \fi + \lthtmltypeout{l2hSize % +:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}% +\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist + \lthtmlmathtype{#1}\lthtmlvboxmathA}% +\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}% +\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup + \let\@savefreelist\@freelist \lthtmlhboxmathB}% +\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}% +\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox + \global\let\@freelist\@savefreelist}% +\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}% +\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}% +\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}% + \lthtmldisplayA{#1}\let\@eqnnum\relax}% +\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}% +\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB} +\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA + \vrule height1.5ex width0pt }% +\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}% +\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}% +\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % + \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline} +\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % + \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath} +\newcommand\lthtmlindisplaymathZ{\egroup % + \centerinlinemath\lthtmllogmath\lthtmlsetmath} +\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{% + \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi + \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} +\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{% + \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt% + \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt% + \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} +\def\centerinlinemath{% + \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi + \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 + \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax} + +\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize + \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill + \else\expandafter\vss\fi}% +\providecommand{\selectlanguage}[1]{}% +\makeatletter \tracingstats = 1 + + +\begin{document} +\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}% +\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}% +\makeatletter +\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}% +\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi% +\lthtmltypeout{}% +\makeatother +\setcounter{page}{1} +\onecolumn + +% !!! IMAGES START HERE !!! + + + +\newlength{\centeroffset}% + +\begingroup +\renewcommand{\thepage}{toc} +\endgroup +\stepcounter{section} +{\newpage\clearpage +\lthtmldisplayA{displaymath238}% +\begin{displaymath} +Ax=b, +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline265}% +$A$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{section} +\stepcounter{section} +\stepcounter{section} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{section} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline586}% +$A=(a_{ij}) \in \Re^{n \times n}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline588}% +$G=(W,E)$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline592}% +$W=\{1, 2, \ldots, n\}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline594}% +$E=\{(i,j) : a_{ij} \neq 0\}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline596}% +$G$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline598}% +$\delta > 0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline600}% +$\delta$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline602}% +$W$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline606}% +$m$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline608}% +$W_i^0 \subset W$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline610}% +$\cup_{i=1}^m W_i^0 = W$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline616}% +$W_i^\delta \supset W_i^{\delta-1}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline618}% +$W_i^{\delta-1}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline620}% +$n_i^\delta$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline622}% +$W_i^\delta$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline624}% +$R_i^{\delta} \in +\Re^{n_i^\delta \times n}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline626}% +$v \in \Re^n$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline628}% +$v_i^{\delta} \in \Re^{n_i^\delta}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline630}% +$v$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline634}% +$R_i^{\delta}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline636}% +$\Re^{n_i^\delta}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline638}% +$\Re^n$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline640}% +$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in +\Re^{n_i^\delta \times n_i^\delta}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline644}% +$W_i^{\delta}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath564}% +\begin{displaymath} +M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T +(A_i^\delta)^{-1} R_i^{\delta}, +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline646}% +$A_i^\delta$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline652}% +$v_i = R_i^{\delta} v$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline654}% +$i=1,\ldots,m$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline656}% +$A_i^\delta w_i = v_i$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline660}% +$w_i$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline662}% +$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline664}% +$p$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline668}% +$p,t$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline672}% +$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline674}% +$\tilde{R}_i^0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline676}% +$R_i^\delta$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline678}% +$W_i^\delta \backslash W_i^0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath565}% +\begin{displaymath} +M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T +(A_i^\delta)^{-1} R_i^{\delta}. +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath566}% +\begin{displaymath} M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T +(A_i^\delta)^{-1} \tilde{R}_i^0. +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline680}% +$\delta=0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline686}% +$A_C$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline692}% +$W_C$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline694}% +$n_C$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline696}% +$R_C \in \Re^{n_C \times n}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath567}% +\begin{displaymath} +A_C=R_C A R_C^T +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline700}% +$M_{1L}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath568}% +\begin{displaymath} +M_{C}^{-1}= R_C^T A_C^{-1} R_C, +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline704}% +$M_{C}^{-1}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline710}% +$M_{C}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath569}% +\begin{displaymath} +M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline714}% +$M_{2L-A}^{-1}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline720}% +$M_{1L}^{-1}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath570}% +\begin{displaymath} +\begin{array}{l} +w = M_{1L}^{-1} v, \\ +z = w + M_{C}^{-1} (v-Aw); +\end{array} +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath571}% +\begin{displaymath} +M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath572}% +\begin{displaymath} +\begin{array}{l} +w = M_{C}^{-1} v , \\ +z = w + M_{1L}^{-1} (v-Aw) , +\end{array} +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath573}% +\begin{displaymath} +M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline734}% +$M$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline738}% +$w=M^{-1}v$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline740}% +$nlev$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline742}% +$l$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline744}% +$A_l$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline746}% +$M_l$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline748}% +$A_1=A$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlpictureA{tex2html_wrap860}% +\framebox{ +\begin{minipage}{.85\textwidth} {\small +\begin{tabbing} +\quad \=\quad \=\quad \=\quad \\[-1mm] +$v_1 = v$; \\[2mm] +\textbf{for $l=2, nlev$\ do}\\[1mm] +\> ! transfer $v_{l-1}$\ to the next coarser level\\ +\> $v_l = R_lv_{l-1}$\ \\[1mm] +\textbf{endfor} \\[2mm] +! apply the coarsest-level correction\\[1mm] +$y_{nlev} = A_{nlev}^{-1} v_{nlev}$\\[2mm] +\textbf{for $l=nlev -1 , 1, -1$\ do}\\[1mm] +\> ! transfer $y_{l+1}$\ to the next finer level\\ +\> $y_l = R_{l+1}^T y_{l+1}$;\\[1mm] +\> ! compute the residual at the current level\\ +\> $r_l = v_l-A_l^{-1} y_l$;\\[1mm] +\> ! apply the basic Schwarz preconditioner to the residual\\ +\> $r_l = M_l^{-1} r_l$\\[1mm] +\> ! update $y_l$\\ +\> $y_l = y_l+r_l$\\ +\textbf{endfor} \\[1mm] +$w = y_1$; +\end{tabbing} +} +\end{minipage} +}% +\lthtmlpictureZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline776}% +$R_C$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline784}% +$R_C^T$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline798}% +$N_r$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline802}% +$r \in W$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath574}% +\begin{displaymath} N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\} + \cup \left\{ r \right\} , +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline804}% +$\theta \in [0,1]$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline806}% +$i$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline808}% +$W_i^0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline812}% +$P_C=R_C^T$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline814}% +$P \in \Re^{n \times n_C}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath531}% +\begin{displaymath} +P=(p_{ij}), \quad p_{ij}= +\left\{ \begin{array}{ll} +1 & \quad \mbox{if} \; i \in V^j_C \\ +0 & \quad \mbox{otherwise} +\end{array} \right. . +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline816}% +$P_C$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline818}% +$P$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline820}% +$S \in \Re^{n \times n}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath542}% +\begin{displaymath} +P_C = S P, +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline822}% +$S$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmldisplayA{displaymath546}% +\begin{displaymath} +S = I - \omega D^{-1} A , +\end{displaymath}% +\lthtmldisplayZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline824}% +$\omega$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline826}% +$D^{-1}A$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{section} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline983}% +$\theta = 0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{section} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1324}% +$w$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1328}% +$\ge 0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1342}% +$t$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1346}% +$\in [0, 1]$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1348}% +$\theta$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1352}% +$>0$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1374}% +$y = op(M^{-1})\, x$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1378}% +$op$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1382}% +$x$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1384}% +$y$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1386}% +$op(M^{-1}) = M^{-1}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1388}% +$op(M^{-1}) = M^{-T}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1390}% +$M^{-1})$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +{\newpage\clearpage +\lthtmlinlinemathA{tex2html_wrap_inline1392}% +$op(M^{-1}) = M^{-C}$% +\lthtmlinlinemathZ +\lthtmlcheckvsize\clearpage} + +\stepcounter{subsection} +\stepcounter{subsection} +\stepcounter{section} +\appendix +\stepcounter{section} + +\end{document} diff --git a/docs/html/img1.png b/docs/html/img1.png new file mode 100644 index 0000000000000000000000000000000000000000..0423c177022d6bced713f8ddddf7b0f4a5b46097 GIT binary patch literal 368 zcmV-$0gwKPP)0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*H?ny*JR49>SV1NUD28Im`T@DN#48#HM4GBP!k4V)Zzy_r`Km->9 z!-W+M3=GV!B$$8>KA^ESu(2Fq=;-KRU>MCZd;sYI$%3NjD%-bRDJ6vwNTfdK&0m@riho2v-` O0000QMgv5h}`41V4JAyJARum*0U=Ws& zif9aBzRosb$>alUj0#UDec)a6khvo%CF8)A>%R{jeC*GB`InkN`(sAt)BJ2JjK1;n zXzrH0p>Qf<-v;h4Mk)@bwVDYp#2aTaTzQbski@`nk6&W?6}bkGyBIuO{an^LB{Ts5 D)zMkS literal 0 HcmV?d00001 diff --git a/docs/html/img100.png b/docs/html/img100.png new file mode 100644 index 0000000000000000000000000000000000000000..1bb60423c160a8db6868a3993794ceba8acb5008 GIT binary patch literal 673 zcmV;S0$%-zP)RHR400001 zbW%=J06^y0W&i*JA4x<(R7i>KR6S@EK@|S>huyhc!fv5fDb_+rsvM}n&MU2w3#70S zw-ix0u(41WuW=$dI1Bqbw9r)72$oxj^$}1I3xloA5{?i=&^I&t<7`guP!a_5u{-l- z-kWc}o%d#e67JK&3;>Q9akv1aXyPrmXI$|NU?FG;n|B46-mFIBV*poeBZa27WWzq) z!0QMdFd_YOq(yvZsd5Q;hK^$qH5oy1u-5o&T22%{rs8CDc#q@E$`3NA-j^gdm^}AKDuiWI zwT2~A(Jn)>td$`)wEHbE;o)Zoe#{!DzwvjZn{W% zXK1PCMtXycg^zzGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0XZ?AE{-7_Gm{e>7-M+&3e1kXDhTpF_j|X3WfGf>49|@N*V@e3*uJsm{Bii!&N5+E z8#fPE#MDJhX1%IB);tckBqV;y%&;@6Xl`9CX(27qx2b8yY{?%i5@{?33=I0|{N>-0 R?}1#;;OXk;vd$@?2>{g@L^l8c literal 0 HcmV?d00001 diff --git a/docs/html/img12.png b/docs/html/img12.png new file mode 100644 index 0000000000000000000000000000000000000000..acc3daa3c158ebef3aaf5b7cac3d39f8272ef916 GIT binary patch literal 504 zcmVRHR400001 zbW%=J06^y0W&i*Ic1c7*R5*?0R8305KotIBhIEqJPLH6A3NEC2{^kY9&~#EEPyvA^ zj=`{1KDx{oJisO}tukMWjGzq(W2oGVj`rDsFad)iOX+J9SK!>AJ2H>=xgR_#KUM_z zz_!|q&dk(zIKT$Uu~KFt$n8(*Ge*ND&L0U(MI}j_F8(~lM^cjB$E(S z;>IYVs!FOYLKX$KO_@U#+GiyEFfK^AWqBkR64i+mmQI;xy;g?Ib8-U-O}_wH4)wlH zUVnpf@qf#c?H;T-q|(iSE=|JnC<+Nq71uqcmGcDV(%7_>Za(OtK{LW`f`(Sun;}Oy zp_g%UrS$8Zi^ry)AjobdJGijE92LFe(?iUQgLfBwkK~J13ob^{PTX9(1CADgF5)t2 u%x_n7-H%sys?h3w=hlBm`T17-O+EovKZ{Cn(k?py0000RHR400001 zbW%=J06^y0W&i*I-AP12R7i>KRXa}tK@c8}^H@0GC@Hak#Kv6gjLn&tNVE_eYfS8n z(VwttbA?9iD2yRimPcVlLn*Pj#LCjdA8-I7aJFQWZC3J|XSz=9(dCWAp?+=oJoa9ESD;c$I%FEE26QS^ArRTFB zMn4?i6d{`lG^gl=(so_Wm0q%P#95v0qa;woJC(n(LqMGH5YtNlG1%6iB3s5$ElUtC z)y>o}04*QLO*yVC!va5*vbb4ClLl%G{WhQ`NX)Tq!N^4RkwHzP zyUgQJh9PdQ&e)M{RbT9y+>PCX?=6qt9%F2iL4jadr+mU%Oovy+)nxPGQsN0z6Vi|# zbJHDI>R_V|-N;G8Or8sa+K$i$>|zg9ui4aQpzJ(1y3xVb9EmmpwNrpAEua$OtwYaW zsN*QYvX~Uu>-sd|*h2j*P8mc~vEr5~-ISZgRHR400001 zbW%=J06^y0W&i*I#z{m$R7i>KR6R=rK@fcxHUhrGG#O5>T*l_HOTTi8;|iMDW4ge7v2TnZ4Ns z3|InUo@5FTtHzf^EcO)m6TstFbTH_>h4<{D;0M_d)vpBihoUE2I(C7ywDV-hvgeZp zMN(P`y=WuMFI=xN4IU}!2cRN)CQ!0yaa~RQf(%!p&}te+TB;nbuSu&DEU{oT+NMX* zlZMCWe+E1sF`S5QL-!6m@Wzy5CS*xn+l?zjD5mtz+Vz^Ys|+KCa9OpST_(kHXvd2Q zoOz)@(G9k{0g)P84s$WIVHtuu9O3qJw0wm=#hvg!`cNjh##|54=`TuL#u5McHfGOb zh<#tM^rTmd$v>^D>Ole!@=hl^-JuhX4)u!tdh0Iv1fPtyxTxjxA8jKud%m0 zwhAQgJ1#E=f1zVV_1VY05j4%EE{EwON!6e9OA%nY+25a-jEfk`#SnMyXNmstyLbnG W&QYzZyYrX;0000$r{DK)Ap4~_T zaz1;yIEGmCCMPg3sim>8g|YcuxPRcl0sbTz2SGgs!9Q%gJiZRIWV`JwZZI6#lgX~n zp!tqTjIE80tC#|@>I!YUV>0$gL7K8kX){_7z4vRCcST~*46X@ Pz0ct3>gTe~DWM4f^vQs0 literal 0 HcmV?d00001 diff --git a/docs/html/img16.png b/docs/html/img16.png new file mode 100644 index 0000000000000000000000000000000000000000..e335597d11e9c0d335ff6c28953dc9f07484794b GIT binary patch literal 296 zcmeAS@N?(olHy`uVBq!ia0vp^VnD3U!py+H*tdJ?G$6+yz$e6Y^XAPfR;-vaXU>EP z6IxnYDk>^+a&i(95<)^kJUl#XY-|h+3{+H9BqStwczA%CUPYds2c#HFg8YIR9G=}s z19Fymx;TbNOifN;U}9!#fenp~jUSnq?YWtmjXh?~WR#!5 zp!Tz}k;R;S#@z#o3{!&-tQO|ZXb#{^m?Z6F$mE;+=)q$qtJaN-Nr&6nChV7xvRZg+ zhJr{w!^&@h{AvmtUkiNmN&dmG$Vy6knPE%{yVb--->1sWdOow3H+&RiZdRHhd;EZY sL_F-Dfziy03-%Um*Rbsz)7=R*<^^DY@~1-h8Q)78&qol`;+01nz@hyVZp literal 0 HcmV?d00001 diff --git a/docs/html/img17.png b/docs/html/img17.png new file mode 100644 index 0000000000000000000000000000000000000000..87b6bd9e6b32c6e86bb6ef35b38465981062792e GIT binary patch literal 345 zcmeAS@N?(olHy`uVBq!ia0vp^azL!k!py+HI5+2N5|CpM;1lAydGqEKD^|>zGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0Xf$_T^vI+CMG8^Fr~4j95{dAK=Tn@hAtHo2FV_thy!eFd~L_LdG_$>IHaDbQBc&& zd1Y{bMd4Z6uLB3pb8ouzklAI*P>u zd}JhcNICE@uJGbtuv)}{hna(w&4PrF zMqWaKSz?)C19N{hv-3%DHet55?l-&&cE{Px+VXXn3W9Igu^9aEU@#I?rtvf};Z4c0k44$rjF6*2UngDZ~a325w literal 0 HcmV?d00001 diff --git a/docs/html/img18.png b/docs/html/img18.png new file mode 100644 index 0000000000000000000000000000000000000000..c5de69c16afc031384c15b557d4cb770ac84ca14 GIT binary patch literal 596 zcmV-a0;~OrP)RHR400001 zbW%=J06^y0W&i*I(n&-?R7i>KR6R(;KotJ2Nz)|PrU8eFg9^Io;2`2=C+X-Uju96f zgt|GN;7{=f1#xkzizqG;K?j$LxGPR>E{;MF5l3Gxi3velMa0E#xclDAm-mx<7a#@K zPJ7aD&`oO*E(Gn}O_ZiwJ%$GG1Wj|GS3rgsXqBS{aySbT*sv8(Lst4=o$0TTv5Puj zGb_@M{V-osEXS11ywiKm9Z7V~O9!-X+pEI2McEWEe73og%{x^4*8K%p7Q77PgACVG zHTV8z{eOeRnC0AUo>uZZTeOQgb7C?cO$;HoI(tG5M!fR@k#wH^(HK>NL&ddR>Xba-Ur!3L&NsFgV z+W$u@jEnE-*FXMo86SFq9pw5 zd6hO{xEK+`qBD@p3MgFzp<%jEjtlm@&-=n+)rtr8q#u`4sMG8@B^&#=46go2ZKDz8 zipb==R}_*BigZVZz;igcc<)X3@_~@|q~yvI)YoiSM_3Qr0000RHR400001 zbW%=J06^y0W&i*I2uVaiR49>SV1R-I1_o{z`~Uy{A0Vs-0dE5a1_2BSt_B98Kq62% z=K%!OlZl zvEYUW0?0~9r0ZA18Q=}Pn;G^BMBJLO07;Pf7{s#{93L1sKd~)fn*ijnIDB9O z1<@3ks*WEWB@BE5JdHp$BQQ!qieB&Dy&Gg#hr|a+IsyZJ250TVl;6EM!0D9zXS0O*4NB{r;07*qoM6N<$f^^-7DF6Tf literal 0 HcmV?d00001 diff --git a/docs/html/img2.png b/docs/html/img2.png new file mode 100644 index 0000000000000000000000000000000000000000..1e94caa5d04d23957dbcd544a96380602be39da0 GIT binary patch literal 219 zcmeAS@N?(olHy`uVBq!ia0vp^LO{&V!py+Hn6rMEP z6IxnYDk>^+a&i(95<)^kY;0@{3=C9MR3s!MczAe#I_7GRHR400001 zbW%=J06^y0W&i*IdPzh!)aJPZuH5Dqs3CnF&f zG0gzk!3czXKzA{)H!!?*=r3SqVBi8t8ax1zOe7nM9W*1Di~(SZCjm?`N%C>50JHM> zxEdHZK`j0@4jzaiCZP8~LQGs7KoTNmOC=}K5h5;Ea#QNVQZRkHj!TmX}I0%1j45ll`TN~R#?TFIwK5{xq@OJ;ll zGsA-6qFf35U|M|lZUsZiJAj#?4Pc7L0GL`7!ORUXvpF8{LnOHk!4#i>I!p>`7cliX y@HG^mc`*ZO3&hRX0Y?Ka83f>IB&=o>-~a$696yu9gmT>g0000H literal 0 HcmV?d00001 diff --git a/docs/html/img21.png b/docs/html/img21.png new file mode 100644 index 0000000000000000000000000000000000000000..0047cbf6dbeeb2537507e3aedcd0ff4fe2281386 GIT binary patch literal 187 zcmeAS@N?(olHy`uVBq!ia0vp@K+MO&%)r1{7`D3{$WagQ331)LdGm@DD<({s(9+UU zQBjeTlar8;5E2sN;o)IpW22&?!o$M@(%4b78%Qyh1o;IsI6S+N2IM$-x;Tb#%uG&j zVB!jxmCeMg?6anc+rwa^!GfkHCblwmg}n?bQk$8X{SM?5G<;>4ke1?~kio$D!C*tP fYQ%EpQbvZ-B=%KWHa{-{O=IwM^>bP0l+XkKWJ5NT literal 0 HcmV?d00001 diff --git a/docs/html/img22.png b/docs/html/img22.png new file mode 100644 index 0000000000000000000000000000000000000000..f1a95ef7cfb8b39bc6099fb9c489a0592750c748 GIT binary patch literal 314 zcmeAS@N?(olHy`uVBq!ia0vp^l0dA^!py+HSij+%G>~Hu;1lAydGqEKD^|>zGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0XaK7T^vI+CME;5JxF$7<>dLp!N)GJy@7*`m5t}Xu>%M8GJ5DU%wn8Wb|9oF%Rr#! zL6QhV&>J5414)1RWDPRIbj$?U-bf!1QSZojAheIcXx4A$36GLXJ}`8BG-`@HdMt?H zi~41*w#5OpK>}IQmSvL|EEaA#e!Fj-8{4<#0&<_l7o4{gUhweD*2cz4<@FA%E$R0! zRx>QDS7l}n&=n53t=&i6n+FnGH9 KxvXzGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0XY{uT^vIsrX~ZmB|J%ckj&8dlZQu!C*Xr(8>6U*L4jIBhTk_3TuWAmNjrgYZqRd&ZOp0|ZQ+h0YY@TQ=PvXIZ zk7<4EJbT1{NEju)vb3lxQ8CSW literal 0 HcmV?d00001 diff --git a/docs/html/img24.png b/docs/html/img24.png new file mode 100644 index 0000000000000000000000000000000000000000..afd1d14a6dcd1ecb9620fdc739af1859102373a4 GIT binary patch literal 274 zcmeAS@N?(olHy`uVBq!ia0vp^Qb5el!py+HSYPqU8OSjR@Ck9-B=7;IW*cIfukF&E)I~&7kvrHi_=_va@widTOewzZh$4>89_O&?~NHaW%myes( S>}?5j8-u5-pUXO@geCw&Ggu7( literal 0 HcmV?d00001 diff --git a/docs/html/img25.png b/docs/html/img25.png new file mode 100644 index 0000000000000000000000000000000000000000..eaa0572e3ddcfedec0de0805a526ea8ff34aaa5a GIT binary patch literal 1058 zcmV+-1l{|IP)RHR400001 zbW%=J06^y0W&i*Kph-kQR9J=WR!xW$M-={Qx~IE(x@Wpo!a^e0!eSPJI7Zz?$U+|^ zh`G#3_Mp(BhTW5stEY|{(+avHf)H~VNLbce$Ac2Q?B4V?9`bWs^fJd*7a4+ruc~@x zdN#AWx=Vz>d@%35dO!7Ey{?}DHUJ0Q5>nVOP~FIJb5yxx5nQ5W`X$j?+t%T}C8E16 zmnv-m8o2dDS*(hn%@%iXC4n++Gua2hqvXV7^E5#Um=r98FYSRO3Bo#3vqWv?1)zQp zqEm#Fcq;0Ko$yrf1lEM)b(_~$A`>De?56WoiZ1!zKu?BfS1VID zZ6T(#_|&yp9FH8v2 zP>iqkBiNi|Gip@o8mm_7rXy;z0P-$J<+t!W|q41oqntGf40;m>IDJ-h2eTDorB3F`+_3>w4 z{6kXFslT@SzKt-#e~031Zg4VL*Kd2^%elcRFK@auG+>xk=}P_qObm^&YM=E7j@N(f zNjhC0a4pZ zI0igYSvn|CJv#@o*tyj|R>J+JIRQ~fP8mqa{vGU07*qoM6N<$f(MH6DgXcg literal 0 HcmV?d00001 diff --git a/docs/html/img26.png b/docs/html/img26.png new file mode 100644 index 0000000000000000000000000000000000000000..162a577b5bd3d91a827b396cc489da7fa56f11b3 GIT binary patch literal 341 zcmV-b0jmCqP)RHR400001 zbW%=J06^y0W&i*H(@8`@R49>SU;qM624)5X;Adc9L*g1RFmMM<05Xu(z`+6rZU%)5 z4EzlY0u1~tydWW7Z0az80@$Vl%wXmG3JnlZZUzU05+zy<*}ki9Mm-(a?XfcTP;p#jyUU~rW}_mB^oAXM)Q2ai7uOzWE%v+egM71z!mTTEWrMOA!Rox`uJEIzyd5^*adnS5|GULQoztJ0;CmT0zd=&4X{|6 naR5z#qXA8Tr;$AGPz3-0&6^`aJN!sc00000NkvXXu0mjfYz22O literal 0 HcmV?d00001 diff --git a/docs/html/img27.png b/docs/html/img27.png new file mode 100644 index 0000000000000000000000000000000000000000..bc885b3c3007b3066c192ee146d8bac0536031fd GIT binary patch literal 1265 zcmVRHR400001 zbW%=J06^y0W&i*LZ%IT!R9J=W7(0v`RdCk(@$=fwnkEGlSO`QxB3U3#0x8Psl)|Dp zmw^ISqRCY;R0tvTa^%7u0mTKy2~lhTQ51@^L=y>tEYYMwmY_)Kf(8n-NP$FrWM<~Q zx8AkybiNClLnlV(H}mGr@6G$n+XGmDdZ9N>XEc(H7$6!V?bWbxJZ!>hxFD&7mxFhU z{xYhsjEqKzC*X5W_IilLoMbtW>L1iVv;caVUCD|3JtI|2m3!2pXbY;$Xj9YlmhmT- zPg#i&OsBoQ#u92=CTVeKrv&xf&>ccwOQhr`fd8_#NPQw4o*(7xP0Wr|qg96y4~b~b z;kW}ffW>l4MR?3%GU$|Q-x(|H({j9~=m9QnDw$L*C!bHjRS+_cvuzu2+k#KF{J^G# z!#`0AED$kj)@}?E8ovf-3qJp#CWO@2rh8yDnWIdy4zB(x-aF!bqoiDcd{U3&U_g;F zh)U=i!PdAo(WK&yRPZBB+G9oxZH=4o<91)u$;?^F(B4;K5xh|@{Y!(y6x}_9w_^u( z^2WiHEVtg@U+Sn}O0evXa5d%)K2v%^m$)`H>PnEiD3gLZQ`Q73=ESKRgpECoKQDz~ z12<_FAGZVV{>L7c%oA+6@1dPIZl`c@E96_J2kUuP0o@B&1=7IkTT}_K91pENA@meL z%Ei~UR|^5^_#_qI0abDEXc`F*3Wx|*g*7ZF?Ql9oJW>WQGo5~xocKef+l*2)ATArF z9xGuSo>6L_!wRXC(tur6=zbFTkjX3gq-4Sq{Dw%3lCH4;=ip4FbvVgf4o@pY8K@{k zP#No$a-oyCQh6A#BqxeQno)K|;ySk(uZ!zup?ENXgTc;0_TCXdYk!e{2ZYG&_@$K& zCS3RlgZ z)g0~U7Pw+uu-%ObbSKMP6K`|pE-BSuRxEqPIz*Wv>!c;)6R>B~Hy}?X~Qc)km z;~`jW$X0-nA8%n+9)aRlPfi$M1=d#KBMwD^=<|!OFrUDDp3{8RLbw<%%m*KD*1g5~ z z{9VrA_7Xr-ZtK{=*+2 bM*;r;h(aCSS+Aqf00000NkvXXu0mjfzBE?; literal 0 HcmV?d00001 diff --git a/docs/html/img28.png b/docs/html/img28.png new file mode 100644 index 0000000000000000000000000000000000000000..6de566e684a1153e5a34868680ff1190b60d6ecb GIT binary patch literal 298 zcmeAS@N?(olHy`uVBq!ia0vp^l0dA^!py+HSij+%G>~Hu;1lAydGqEKD^|>zGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0XZu?T^vI+CMG8wVEDtyBf}xrp~?SDJ3%Xz?GdxXo`yzQowp4uStL~&IJWWkFey|W zW!(^AewcHHiME(D2Xh~DLKpX=h|~!yb@=2RLL8deJ1%czR5^O$LqmUK<4eQi;w$Vl zIkxu7SbH+eDG*b>;5*4b(dM&0PYmau0KVA=%-P}^xir={JY;p+Z^3*xZ^3RwnP)6) tZFMHxH+D~~>=B<>X|q;j$D9fVhBhv#yIHkMP66G_;OXk;vd$@?2>@{&V}Aeu literal 0 HcmV?d00001 diff --git a/docs/html/img29.png b/docs/html/img29.png new file mode 100644 index 0000000000000000000000000000000000000000..bf7b6e325bd592e8ebb837016a4bcf330f6da98d GIT binary patch literal 456 zcmV;(0XP1MP)=0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*IMoC0LR5*?0Q$0(=P!v7+Fnwv$z6?$Up@VBN2=4C}Xy`A#82F4{pHRS=3}M#qefcK1hQEV%ey(iHjPK)cjn?k*ItTkLF6vZbL3S( zdht2URUEkoOQ~>Zi&AwhUI0HU;?crjSRZSxd;FsqudI3x&sVpw?&FoJ8}+l$MDJz} zIcAwDngJ6`TcnBsshn+O>f0YIY1mA@mjNSNix5PP>CFi{0+#B$11tJ_;T}%XCDECh yN+dd(;%UKdh4tZ`Q-gSIx~y#AYG~~Ir}zX~G&_9LrB5aR0000RHR400001 zbW%=J06^y0W&i*JDoI2^R7i>KRKIW2KotHi{*g=L#0DYM3XseK3>`9dL2_YXtHod7 zcBwky0g0u9OGIT5Ly8b86CTSJ2Br*TKyAg84T&i$qN-ekP&c^qom1PfNZJLd@JaXH z-Mx43d-v`KkcWEn>VWHuutQ9O$whYqL)3vqz?rz>1P{3QfCzn<`E|-4*ZnFYo{rCD ztq&Nu0<2~@A}-XVTj64HrJ}(C{E>%+ndvA_k@U0+yFwA6T0*_P%=S!2TaX1%G3zm< z0oRk+n!Bgh5b!lh>I1da$pjt-C6oqhpJ%utJ!jfH&pXm$*MtfZN!r^EyI69LN*8OS zsy(n1_#O?F4wm`cLtEG)Jat7deheWtIxYPIH9QtlafC}uiS6m)g+UL^lTU4ycnERPAe9+<))9rXv3YRD0=Uc&GdzS+X9!(2UCUG(io zJM4Gh+n05DFKi31pntW>k{N@Hx$okra7L#=dS4oEEhyd@gZ#&N#N_XAGUDI*r}Kxd S_-!iy0000RHR400001 zbW%=J06^y0W&i*I6-h)vR5*=eV1R)RAkJXG0RO?@1B{!{0A%_D8B7>zz)XI)AQwYN z1C+;#X)I2_0mKb34nISO1B3+@f^l{t8JIx4(f^SEG3q~Hh_GPF$T10Q08*V09>)*X z1`Y-uAmn3U=0kX7Py!wZrR9K20lEaE00T!yM+1t47PkRV;sT})7Jg7@m162B-~d_N z2;p!n;RCvZ0|+A+HZXDqAlb$SrIAzG&;kE(0P;*TN99f-*?=zuRYXi6MhEBShz|D7 z1Q3%=YymMk3RW=iCNM&Bj4x5HV*bF8!@$u1W`C5#&|#$jDX7{Yn0XPftZ87l%D~T} zfYmq#2K0Q$flD16h@)~D3kd2M1y}*DY=8@V007l2jbp-YA}0U<002ovPDHLkV1kPt Bk`n*` literal 0 HcmV?d00001 diff --git a/docs/html/img31.png b/docs/html/img31.png new file mode 100644 index 0000000000000000000000000000000000000000..bed3021a7051043e8ce90c791f6b07e5da5ae073 GIT binary patch literal 474 zcmV<00VV#4P)RHR400001 zbW%=J06^y0W&i*ISV=@dR5*?8R4q@$KoEWXxbDK0q!_?)BqwmxAW8ZUu0frE;e)_vYH4{gKiYB zHoz21&IaBH2pO&gccs*+i&ceJP`9A$lOv2x6cbIv_1yqg09IZ`IRwK@Zy6DLF5!`+~PVu`8_vL4#@_ejPa3n%%Jt;tn!zu>ZiU%CR2=V|g4@T6`5(>k1@Hs^rT_o{ literal 0 HcmV?d00001 diff --git a/docs/html/img32.png b/docs/html/img32.png new file mode 100644 index 0000000000000000000000000000000000000000..8f2424d59c6b3bd531fe9c9d9abc8b70dfc92e07 GIT binary patch literal 241 zcmeAS@N?(olHy`uVBq!ia0vp^;y^6V!py+H*cnir0p#cg_=LD_-n@CmiWPI_%$YD@ zLQ6|aMMXtUPEJBXLP$u6hlhuajg5hUfr^TXgoFf8hn{&U3y@+g3GxeOaCmkj4ah0- zba4!kn3|m6z{+_-MvTqpz;`|mj)n-Xh?Iv7b0^Og_b4nEz40ixP2PaZz`9`tD=*I( zhhGPqnI>eovYvUh`iZo!go{rC$0G}d#LbRHR400001 zbW%=J06^y0W&i*JaY;l$R7i>KRXu1FK@|RWZ|8Py?`Ib~<$06y@|P1)>0ZdFp7 zvriN|?zBk2CUaekZSAIn%_s6Mibk`DcAP|eK=Wys_rpRDuY=Eu5cu@oNM}|%Av7Z) zrZ)YakAFY-2u!@Fj%Hwo-L03h8AE1z&ua3j5CzKVv>TEHRk2{z!?{Ksh5_i@LRT1J|9`5c?FHjO}M#T9PI6PRUj&XhtO$(zJ< zw;nj^mT+B_3j;A@lY|S~+Be?nRIx>}G;27ele46Rl;b{q+6sS0h|(!z%R;z%pT4TB zy1>7O6OFT8nrEtX{1q%OAaXRt(7c?qqHFn}u>m|e7HIUv{qdS^@LQS}fJIUnV+&c>r9R5|xy1d-uJ5W%;z+b+v1D27aI) zmo>~P56*fqhuW-gFyexsh`N)>Rq5SsN&afZp$YWWGdwN?B#{iif_(lPWz8=kevMqf lTo?Xyu=RX_)&>4Q`~(e{hDvbfv|s=L002ovPDHLkV1lNiS_l9D literal 0 HcmV?d00001 diff --git a/docs/html/img34.png b/docs/html/img34.png new file mode 100644 index 0000000000000000000000000000000000000000..00fe6e51919ee5b58e42d8e5b0c3c7b3c6ac6e0d GIT binary patch literal 217 zcmeAS@N?(olHy`uVBq!ia0vp@KrGL~%)r37^G=p0kYf@x5)wQ-JU~saB2Ui)Qj8@*e!&b5&u*jv zIpLlzjv*W~lM@=68QS;-*o>LE9@HKw!nA_tr4K{Un@7?T`x<`K@V()8DB0W4&(KlF6!@&PS>`Y!yBt5~tq(cxfL1Vg My85}Sb4q9e00YcL761SM literal 0 HcmV?d00001 diff --git a/docs/html/img35.png b/docs/html/img35.png new file mode 100644 index 0000000000000000000000000000000000000000..52fd7ba575040cf497a10a092ae5e0bfa624c515 GIT binary patch literal 283 zcmeAS@N?(olHy`uVBq!ia0vp^(m*WF!py+HI5}tbGa$zxz$e6Y^XAPfR;-vaXU>EP z6IxnYDk>^+a&i(95<)^kJUl#XY-|h+3{+H9BqStwczA%CUPYds2c#HFg8YIR9G=}s z19E11x;TbNOifO3VCCZBVHdD5W1Gjq#&h7@fdhXVL{DTee6%nSUBFPMkj5&+=kP0y zS>9Ql@#_u-^(kUZR;wc?G$t}JGhb#EW^3bh*vRZ)F3s?guaTKYS0Vi}rwsGt%|6z` z4I;tU``8qYp1XPA1FOmz_Q1vZ2mUd*YRHR400001 zbW%=J06^y0W&i*JSxH1eR7i>KRWWE3K@@$nx3@dFU9$@!Boe|EBI#UEY|<M!Q#>xCE=eiUYjltXw6f1SZ$a2pwahE8 z%1@p$MB%la#=>v|m?l<-@8nqMeV4@q?@nyfqTbH9w#o$B7=U z4;-fE>vqTeauMU8d&MZ+XE}5VrdPkhd|%-|ouv~dPeOYlYfkYW;s=_saxq+ZFHHad N002ovPDHLkV1jM2O``w+ literal 0 HcmV?d00001 diff --git a/docs/html/img37.png b/docs/html/img37.png new file mode 100644 index 0000000000000000000000000000000000000000..e8b8da925bc41399b238c3143ee017d4b6c21fc9 GIT binary patch literal 337 zcmV-X0j~auP)P001fk0{{R4!!F&$0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*H&q+iSU|?Y2XF!1e|3M@tlHmUj3=FOyMgt3oG+;mn0t^gn zEkK&h0jLScVK@L%jH2W}#8^1soB$#}Kd07xn-wOxEUCpRAC|yA2 j@v0N&A?kwvNZ~Hu;1lAydGqEKD^|>zGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0XaK7T^vI+CME;5JxF$7<>dLp!N)GJy@7*`m5t}Xu>%M8GJ5DU%wn8Wb|9oF%Rr#! zL6QhV&>J5414)1RWDPRIbj$?U-bf!1QSZojAheIcXx4A$36GLXJ}`8BG-`@HdMt?H zi~41*w#5OpK>}IQmSvL|EEaA#e!Fj-8{4<#0&<_l7o4{gUhweD*2cz4<@FA%E$R0! zRx>QDS7l}n&=n53t=&i6n+FnGH9 KxvXRHR400001 zbW%=J06^y0W&i*Ik4Z#9R5*>@Q$0(=Kp1|Krs*YVOmK1$vpBeQC^&k9gHA^OfSH^` zGB`NN6|58lEe_8437Hgh&`DfG#l@fCcti067w>XuBT3QCp%2`9$Me4Te%=8JH80!9 zA*#q!%?ce4)e%cBD3M1^ipMc7N=Q{Obe@Iq;8FuH(1BN*0#kl%vGl(^{f54+_PWf? z(K$R96x^mUT$wlJQtKo2yUNf)qVft66mHI?D|z_A{UfRqiSnI=LU01ji3oJ+ARHR400001 zbW%=J06^y0W&i*Is!2paR5*?8R6R?>Kp1|~#3WW?x>_n^tXqc)#l?(nc6AGmBACG+ zkfD@Q5c3l{xVaRkqD#TaL2#^FXQvyA)JfmFeAzZZQ4t3pxZL~k+%fAgaSt#UaVQpuRFtrB3!z|1CNfB`Bu)1xdQ9<}5B~AWV)&^=O2c&4BS)&C z&|Fy&s)UK!2Kvh`tyv{Tn~q0N84HLSG+lD+Ghj$6nVqC;Q0WSiLDGuUL&D#Y8vF1B zzuI+^`VG==tWQtdqJE0#@_Ct=-~S&&!GZnC-W!aqIqw5XSUMj$hcBLf9|-@3FhDC# z-qGV^ra%o?>A~bsqJt<8h4#u&I=db{_GkDP#P8#Hf@b7zyG!Co_N4Q)*dSd8lk0fa zDv^JQs+er)jA$G+=J`5rW9mh&IuVyH;nzH5L|+D{H@nW<#A uDt_M_C}C=DX3jKYRmb&atmn9TXY>0000RHR400001 zbW%=J06^y0W&i*Lzez+vR9J=WSWSo=MHGJ1|I;(GJqHg0S^WO(t41%AUlYJ6%Q`v5^obQvWSPl(_VzuY-Gu0 ze6N1GduDq7#?2T*KIpF3^jEf1ec;RM=ROj8new9yXQ}9HC;ac=-A~CG zuGC>OUeogc>{u7|Mp-G(2|qaS!MpUT@$V_r3lM;nmvBNN-Xf06h_n(CB&VU(B>)B* zm-Q!L@is6%8?RlzpKQyMoagFl{WQUIB+sKol2nkY*O6JNF|cPb455R2+Psk}6`l;(KJ45X+qYvo@E%4~EBefX)nIf}a)n;xAB!f?DwlI& zPLJLUpCvH9h$27dM?w0|#^(vH8k>v7*at)r@|G4}p;fU6Cxw3P*P*{sZd z`KJ2zf~<8jg%dz&cab8z?nKPne>2+GXT$MSKB{=hsqZc{3T@`wgSOcj4m=xSq>iZr?7a~u zGa48BYJr~}ufdrib@!E47O)cZ08c5Cb(!4gF|?Z0ZOIyH#;t5)u_gzJmbTO3Cw!E8 zRcAxZxRnW1uRwa@)wBF*y~oGk1&OiIh6Y4w^ME%yZ($B0nmLe6NuJ&a$xBuZ9TNs5 zs(j@NBYU19XcL2MqKtH*6M{IQ^$1K2(xf1ZT0Rdf+!u$k*r%!PHSq00j|9BKJ7WH5 z>TW=K3e}`p^ZJF(JI+N}OOj@8a`y&vKWp+o!<4xOG4SX zTL4GDliWG{S1EwoS4XNv{P_kdn~qwv|Bif3U7zO6a0`sI zf@%CUs=$c|4e^mWvg+gOdw4>2_l&ImksE>x4s9*h&xfENSG4WVLs;20I;b^535W4F znCPIxkfu}IU!~RP2brhjCu1WOrUc4+1Lo1*55Vl9!#d=f6T>6(;@rq8U8r_ONA@y0 zU}j`wIAvv}`^ayhTc7&_cgpWD?Spn48NW7$vjaCZ73a)ZSp{pod764uAq?m2<2zuj zd}%L2HfJP%<(99nw@CPM&Vty$fxRDXB27aaz`cw-r3kuvF_`Kzltk$^#tl z?KMgUufiu_hl8T&UZx!MoTRI`7+aaGzO2QxFxzJ-s;$wwVyLTv<*~1T_6~D7#l92R z$H?JRQM}pRS?pjjiMyGjYDAMzR(qORHR400001 zbW%=J06^y0W&i*L$Vo&&R9J=WSWRdoMHK$JXS%1SXC^(Dm6aTJ1ciVuJ7`=`h}(oc z1P^8|9uzSxUa|*q@RWmKB`&dJlnf{mMRX2|VLfC{iy+8cgm@e9q6cC0qKHVlEbFqn zFuqsSf0=YP*CIRsCMQ_p0i>dObh}KHAkY2B}WK|3z1E8n5oStH22=(|GMQUw8 z3%yYSy~8TDMz#2M&<|$G#9$EY`_7=hm{f2|5y8y_{h{<7Q8qbcKNE2Wk(2Y>RQkXx zFr($8MRVgBa9ItNW2F^Z+&WNW+B=+`{~@$R{is!#$w78_&7W0tjiR;FkYr1?4Gx); zRif5m3ExL*gBE04#RqFP1q(%1j!s0;(J|!=Nrj#!odQb3IB3h`pAW z(64MZ=dD)QZ6G?o<3a5}j!c+c+LlouXuDQM(|N3+i5EtaGYX}~T{h(?Fkl=u&l(9S zLqW+=-q-IjQ*4w@@+a_q<`i}i&!ab?PiShmk7PccA%L^8`yk6SftGpwT_eyqiUr*& zCMlO`Xk*Ql?;E%VPDx8R%3FV0xkedfhZGB ztBa~&X`LZCSwcCm{BEqj-i&?QQa)J~k9AuYODk6+xwd3>5SWo%?L1wJN-j`|Q0K=a ztyVd?S|ROpm{Hkj$(vZ&*}Fzi&ROGi&ANUX6>7C1*4Wl z8l%M7kV+$|aBAUm)mrtjd8QUG1EOm0POyC^=kxDG^%sKW z+FoP+epn(cQ@zl*7QSA*?jZ|Kyp{zv{7aCw3(Kh|O#H&k z_pZt7Ea!az!^--VW6o!Uo$bi!3Q6U!;?bJyX`x_Qc0DWPdMGtbA;5Gk>R4FUT_@Y4 z6pY9@UYt?~r(9?}N05xd_Sa~g?!)f8ZbI-^s-|x0vzVX7+e|&>Qp%t&M@!(jJ-#hO z!tC3;i0y!s1Oqi(C|_d_vX2sVcr6cFl=T3GLL}?-wz- z^~kFTcadFh!Td^K?v_~WBHlN~;%_UM@lU)(#J`eaXhPTmfCv^Pb$8Jx> zR!4-zhI_--V(3G28hVfuSb}y1PTX`8tyd~H<{Ldia2{A4W z+J}}I8TO?ZN3ZOd<6GJ4FO5~{cz)G+xHnF1l?N=D#K!rH)xQmY0k9(W5?kgO2`z11B$BJirjdv_z^QM3`A9 zqai?kN8=GDb`AEFmKMgA!#f)oMK`D@Y)o7h!(hd(#$sahkfGV#o&5r%g4vbQgwm~)6UZ?L@Ck9oS*HPHxEyqKpivlVNJH$2!+jO=AT&bah+#;L*q%tlRU@HePda*d$s`s ZL$ki5pzpfITR;agc)I$ztaD0e0sy|xSeF0* literal 0 HcmV?d00001 diff --git a/docs/html/img44.png b/docs/html/img44.png new file mode 100644 index 0000000000000000000000000000000000000000..58cf296560f7ccce46fa64acc7c8e3ed71a33935 GIT binary patch literal 322 zcmeAS@N?(olHy`uVBq!ia0vp^3LwnF%)r3-EjT<7$T0};331)LdGm@DE9T6ZGhxDn zmX?-^ii(_^oP>mgkdP1$4-Xp~8v_Fa6%`c;2?-t^9-yXIk*DVYDaMi@zhDN3XE)M- zoCBUNjv*QolM@_R?>Nk1NGkYI%y5#6Pt1gsr$&xjLgI&G)(=TVCC(RK6GV(_9xxdH zkdzjxkkDh0%`&zopr0MX`WxBvhE literal 0 HcmV?d00001 diff --git a/docs/html/img45.png b/docs/html/img45.png new file mode 100644 index 0000000000000000000000000000000000000000..c2a3dea4819d97579860bc4e0e384ca431226508 GIT binary patch literal 257 zcmeAS@N?(olHy`uVBq!ia0vp^Qa~)v!py+HShMcK4IsxLz$e6Y^XAPfR;-vaXU>EP z6IxnYDk>^+a&i(95<)^kJUl#XY-|h+3{+H9BqStwczA%CUPYds2c#HFg8YIR9G=}s z19Iv;T^vIsrY0viurfKsFg)M5*)V}QM!vy?MVpzqER!YSS(?QG_9glSAA|!uMG~^x zF7(LDNC@{d^sus59AIKIj*t*h@JlvW(B{j+m^?izoN3PSgLe;b@Ca{{e4D7SPL|o7 zxtS-Rim_w+oW}W<53IW0tv;~8^+QB>3CD$FQyF$n6y~g-dG0pQDGZ*jelF{r5}E+c CIaGrH literal 0 HcmV?d00001 diff --git a/docs/html/img46.png b/docs/html/img46.png new file mode 100644 index 0000000000000000000000000000000000000000..852b2b0be53a3757367dace6d8eaf55aff7669ae GIT binary patch literal 583 zcmV-N0=WH&P)RHR400001 zbW%=J06^y0W&i*I#Ysd#R5*?8R6R(;KotJ2iRrb*CJIVXhb%f*T^vLzxZAb>K;T4B$#5v1fsu~U3QLeCkT>b3>ai)?}~qi}U@ytvUKNeAx% z{pa7R{C9%h7T(;&1kO!=<@)yv4`M{A>aPQ=5oaoV<*N`Mo%K<0@D3kB?Iqktf|+0%c-~kQ{%FRV^!7 zF-E4}^XGiWsX42Bj$GUPruG2)&{EXaGcvdi@(c{xn6&unu~aIFKAgB~FfUFr(=GG# z4(bbNSv+)(gT}5!i#iJsAhcCWVkcuHIjy;$xC8AW5pYOC%Ol*L@sGcPz!w|{_Z1=t Vxce8|PB#Dm002ovPDHLkV1ka#14{q^ literal 0 HcmV?d00001 diff --git a/docs/html/img47.png b/docs/html/img47.png new file mode 100644 index 0000000000000000000000000000000000000000..8659d7c87c9283fa07b1ff475b1de838a69f17d5 GIT binary patch literal 651 zcmV;60(AX}P)0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*J2}wjjR5*?8RKIH!K@|S>XXbW|dxDrC3L`exd5B#I8Az}Zy!{hS zu!x0nXp_!SFpNTsok^EY!DhiGU~_hMZf7T{t9^3poq;g|-J5 zS&ITzL$bsfhslJcIQVP}eFind@e#){hxPh%;kAc5MPiuv)31M%o{Wo7T#+ew?c z>Irjw+^otYEaq!u-pvtdeT|*2*;0YnNsTTv^mQAo^gKktqvKhiqfx{=k41$!=&L}% zn@5(L3p4b^U9a21zJGLO!h44=IoiAK=(fDLQn=V}tBf9DlD|EDeLK^k|I#24zlP2~ z@HpP0cuCl3!aHBpizk)2MBlw1YFEHJ7`ws`jfszd?a~O0%CzxDjoZEzW3BWYrN!>`UYGY;BpFFz>1*h)z+}YLyn%nK0O>><85<10LyLH z^iney)#x4q%U#@uZRd%kr!(24iF^lsx|9*;fQLYwVNQb`hA|O>GU^T7rd}Rq2>W$c l59TaRF0BC;XFQ{0> literal 0 HcmV?d00001 diff --git a/docs/html/img48.png b/docs/html/img48.png new file mode 100644 index 0000000000000000000000000000000000000000..c151a16708bc6889418f51b00e83c06a49e7dc58 GIT binary patch literal 330 zcmV-Q0k!^#P)RHR400001 zbW%=J06^y0W&i*H$Vo&&R49>SV88_!q4Wg~5Xt%ht0EQ#uy|tvkl^^hzz-H=nt;<# zCXCbz*eyFGF)I_;3TA%H~@5vmjcv^4-5@3(G75auoW0w$c0$UU?h;h z&mah58E~=#J<-4fRm9KmL4Z2$Aq&hmU|^8=h$6(U)4;&2jT*ol92*z{{1reRHR400001 zbW%=J06^y0W&i*JrAb6VR7i>KRy%7HQ562>k<86Zc4rIGbZ$@~DI}w!AfkJX_~^1~ zVoqnO7QtU|#ULrYkC~m>>?0u{Sop!t zJ?EZpzI)D{duA4B2h#(`Bj6RqsIXrWMo#RY5p{hietA<`_W=_&yNF)k?XDS*U%;f) zCrf#A>gpEY6nhHw!L6`k%4%7|p2$xcGw?+EGGO1;A$zF2B8Q-g=Cy`g+8u6sK7zc< z^TJ!xG_s$Z_K0+QY_D@2AEb~W5v<9b8q?k-i>fgaG_4Rt4A?v%?ZJ4CpTtNcjc^i; zp%y8;YJ@K4eB5-!6rJ|d6|=}`T^QP}?XSjv6-4gDZV1BI@cXegJ4vr`xQ*ed%uBa_Y87XJOR!ZVTT<;rJ{JFT(2lHQPo%* zz!epHD!Y7|%cp9jC7Qo_6eqEje#tQrw8!4Sc$WQWnm>V~y@c-RKNDK00F!nw9;D_- lZN5)VDU8L1a8Ja2;t$Idj4nQIBS8QF002ovPDHLkV1nLRaD@N> literal 0 HcmV?d00001 diff --git a/docs/html/img5.png b/docs/html/img5.png new file mode 100644 index 0000000000000000000000000000000000000000..81733c70d1ac2fe10917daec4e7a767517c3702e GIT binary patch literal 648 zcmV;30(bq1P)r001Ne0{{R4)3}dc0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*J21!IgR7i>KRlkcAF%9i)!jm{bX%+2;snbS7H4(S2$rLb zAQmHtSf-F;K*23UY=qOoda<-RuvNI?1nuTOFvTKgb-w(XUpwxI_zUraoxHq!`I5Z6 zyannI+*{k99=?4V)oXe0BUWw6TM=v%&lMQLRiO^qR%JH-j| zq;`Fd*iTbt69dnjmvd^&L50|_GStvLLZ<&5zLjw1|b zRuhr?XkCbKZRpz6uk{;o+>2kcp{pIfi~2)1;nPoXT6+*Cb&iSrA{IVbl@8dr88yR^ zTY{`SmyUxVs~B@-Ig?%I7}~(c6(yu>d_nEDPC~0w7*0~@#JFN~W|(@HVn^Y@$zxeS zLUQozG-T8|r&b|3d*6hq-*XMuu!>=a?_a^6%EKQ<_~^s*)|ZsMlMVMKJ$Wvyed9s0 zGOYyLH_d1dl;uH-sO$0As!(Bi_HC8OMrE|Xoh7zfgLRd(Tjl)Ty(gs#R}7z{Ns}@7 zSgBA7&e4JFJy<&{tT)!GY`Q?*cKr*@;f?Z22gMo{oSCc}t>k9? iod5V6&|k^E1787WRrEz8O1RRHR400001 zbW%=J06^y0W&i*I07*naR49>SU;qM62_W$Uh&dR*;Q#;s5C)LX!pZ;#|NnnLa2y~M z69XQQz`$Vep##X+ssJ+W149!?lo?`n0X7}~|HCcE3N#orVN7;@h7B-w4;RNJUIqcU zGDVQp)CamqY<@8LfuWJ3qY2DrKft^JCeG2o01qlAhlB}mU2H50j2#VN;cJY34aN)z zDWtGv_`rx@b2d=P^_bv49DE?G7$4w=(jNDL1k0}`R8i)52L^_W3utONxEmNm`4b=< zrv45EFvAQOj0U~v<~J~Z3S{_(Cdiz?aFc-@XsoRPLoSAsfTlCBVu<yuDX90tR g0EXyb1OKrB07|1#FNm7QA^-pY07*qoM6N<$g3uO@N&o-= literal 0 HcmV?d00001 diff --git a/docs/html/img51.png b/docs/html/img51.png new file mode 100644 index 0000000000000000000000000000000000000000..e68a72d3eda989d78ca241cdfad5793c96549d2d GIT binary patch literal 324 zcmeAS@N?(olHy`uVBq!ia0vp^3LwnF%)r3-EjT<7$T0};331)LdGm@DE9T6ZGhxDn zmX?-^ii(_^oP>mgkdP1$4-Xp~8v_Fa6%`c;2?-t^9-yXIk*DVYDaMi@zhDN3XE)M- zoI{>2jv*QolM@)2*x7U*Ftblc_*-1_lK&44R1v;Rlw}viEo&kt)AIXDLY|P4w2Yr zXb_*2P{1rb@xUk7#>Y&}`xsrAz3&UP@#g%smiWRdF+*m8Zt|NP{{#sQ1_ow+WnE5P S(Y-+5FnGH9xvXRHR400001 zbW%=J06^y0W&i*Jph-kQR7i>KR=$C$rT<7R|L7@tZqRND-9MFf^KZY z=5z`R?zlX9leaFe5@40}d}avPcpm>0p98GsJQ6n_aLbe}T5-RHOYuHOe>98*L zGiwHQc8uIo;RC_4j*-eg2_rw8v*j})^Lx#?43x;+vEyL} zcUh~BkUbReJP)iWOh2>4I_fC}u?uR0WhV>ro<%i4Es(c=es2IsTrI@R~-3JY+HocDi49Ah`{ z^jO6$kLKtk?9LQhw4gJoQ!OgpbwBTv?tO=Hx<4nO3oR2jw~N+MG{jq6)k|g;<5S(~cfX`2dMlUpa&&qIS1#O>w$fpUT5n-A^}F zfk#bzL!-$O@FIhJIiCrE`UMS&B^rG~3!IuIj!^aaJ}4m%&!&7G0$ayuX#fJ2G>oT;$%LRHR400001 zbW%=J06^y0W&i*IOG!jQR5*>@Qaww=KoEW8Yxk0qc;XL8VIf!;u(3>Gf5Bc%DX1uR zcGD=q=Hl8v(ECV@4zHYYayaWCpli7+I#s`o>+Mt z0LnYgD2_%&Ytw-VE1f&hjbKeWWY$uMsGsC~ALuQAW zIS#tIx#?nOYzd-Gu3PejPU`Ao=Q6}1PxjL5aZf``00000NkvXXu0mjf DBRHR400001 zbW%=J06^y0W&i*I1xZ9fR49>SU;qM62_W&Ifq{Xe0mNna|NlRjX5e68U;!&&fQo-$ zfCC2x!XSZx!Qev&kg-((WZDM?Zm=*f*ldmhEIR)Ghg*&nXfSBPnC$!v8({1nE{;nK z3_M5**;t5hAE`hWiOmltKQJ_MbTon4><5@Pz{G(82@fhJhlB}8&Qf4t@N)nOUt{!Z z;Adb(GB5y%eSjIp&QJMqftsE`0{`LQ17XGZ06&!WxDO;)el?+rGRHeGFl1anQ_I2K zz#z(>0O2t8cPM}vX24)H=tVcbf%#J)!#6ZR<^+bD4D1&e*kXa44s32>{D@7IV*&#c lrl`CE;{*)Vg9`k|1^@;GQf|cz$JGD;002ovPDHLkV1m7)lD7Z= literal 0 HcmV?d00001 diff --git a/docs/html/img55.png b/docs/html/img55.png new file mode 100644 index 0000000000000000000000000000000000000000..5920385fcf8c4359f41d7ffb376cbd9360d79cc5 GIT binary patch literal 1062 zcmV+>1ljwEP)RHR400001 zbW%=J06^y0W&i*Kq)9|UR9J=WS3PJHK@|S>=k{hV7x%PMELTwzWzgoZ2$r!C%UB88Y=}t2#`)RZyG?d4dz!2C zgWG-c=9@Qf_PsYV2c$t#EeAGoU^P1$D$E*C%i~JWuzP3 zk|_mBbJ-<9AiGzPrU;GInG7PBbL?l#MkG`tA=LP18KZ&B zIL|)<*9I$yC4H8h}>si z^n^=`eKTG7T37&wmsn;zhw3wIuH{?bSvLQOTYqZ#_I{kgYbK2P(naR3JC73S_`GCy zXg0Hlcfp>|c#JbC6~RN*vD~&o9jWOqdWGe%<w1_@jYt$Lvo}PcOwE32^alF69 zZq&OmNTGWIM^x0uRi`|E@0BOM^NfwcP*)OBr`@Te=&5qmWnd_hH!Ghb gY=3&A#}R$PZ-Q&jmZ_>M)&Kwi07*qoM6N<$g3Vs>dH?_b literal 0 HcmV?d00001 diff --git a/docs/html/img56.png b/docs/html/img56.png new file mode 100644 index 0000000000000000000000000000000000000000..f064dfa9b8fcd48b43920ddd3233bf7765df8f62 GIT binary patch literal 1320 zcmV+@1=sqCP)RHR400001 zbW%=J06^y0W&i*Lrb$FWR9J=WSWjpiRT%%x&YykR+0Bgqpx~k7LEVCqtx-WJWGq!8 zQZgXD6iNo_AtlC2#GAr1gmz*QyO2u`1@|IKz3ee%LF2*F<5CY6^iWWwHz%={Ed}*^ zGjC>RHnTQq4;Gpa=FNNGeDC{y?|a|--nR?vfx`I3WqX*~XXt5ja5ZM>{>s)~G#1c@ z@yiA*;9bC@_xrJF6R3nVG(7hKjUZi2A?cza^QAm{jGjquF?8Bs)ISgblvLUzfUmQi z${P2!_rFkOC#z~gh$GIcGj|JR>iyyCPe>&4x=kN-N^}$ zHqbZtV>J4PCJTM%sDE>D6EzEFi7Qb&J^v$Z_$H+L<}>(O(u!q2=z8YQ!DG6bEN9Iwmps zN3}Jw%d2AGhE*M*9&0l!r>i$weQk09%=AOWe@TePNVq|vlo-b0Ds1ktV4+3=E}qPQ zbWt228l1QzErcv#?9(GhNpuh9zM`n#y*96iKVV`F2ZyOqZ=jjc)=E!S7bhe?6gK+D zmU8eRY8fxk#zI|0`dL50CWTb4h~5~Tz38;f;<%7rpvKgX7ATqw0y@)ebo(qlJw?nd zB`K#Zcxe(q*&@y`;;w`hkn%_y>(FItXuh;(&{50MkA1M~xr+s?V>5cBaWeUhRwKw_F+<$(4t`Nn27KDRW*O$ANKRFzQ zwkqCJUpthi184WpX6{nMdb}QpB5wei7*76uF3YNa=aRR6S)`gUSV-h6u7puqrc{d; zuev!DuMpE%&Ewq#m8YqhO>T<>n!Ktm(WBkUPgv%_iS3-cGR@htp0T1>b<; z-QF#tl$hmVe99T%w)?8h{Eb?!Z&I<{%<*0p;~3@q3f&5q^U75JV~n%CNB?|<>-ObA zZVV@?Gp5|!7p870UVbTtT_JfZDw6nw{gk$i{1i+)Yg>NQpS$Wn`*z__Pimdp_{>MW z7p%eTbUOJuihMs6sf6=sBpY99=8 z@_B}!?Z}a;?RHR400001 zbW%=J06^y0W&i*Ku}MThR9J=WS50WtKoow-CfUh$w-XN@q=&}hp$Ot0M9@<#C`AvO zi=bXi1&dY01@-J$g=VqUEr<&C(2F8?*<;bm;-U7qUZls02SG3K2dQ{*ev)*vo1|IY z#e;s(?90qIU*61nZ)OS*1&X{`U_t_LqwPfo-2gC*Br*r_;@h>ZmMZ%){UJ~WDOI!M z3uVAMN$AWj#1)>@0lZme71yKP#n4*r!M80mNY@9O^x=6h9qn0SuT>ME9-~r<7avOd za!dg7teMA6p#g*))OcvIfP$Y3$e_bqYMd?8$Hifl56j^_#?v+#3`XF4F3p2KKtlF( z;)Ym)RCX<|_|{%k7X~4TY!&-c%FE8ORNYC}zK}8W3W$=hGqHOIYVgqD_Oj()T&928 zqE8Ak7I`_gEEQ508OJ!9TDO}8YDs?a>cv2-s+j!O1Bdu6LsHqcagsNf&9k%2Bv#Gw z>{dB-a{mA{4=~Bhwqa&FimL_DQ*#sai3lntl6B;h^GFiAxhp4<>p4HNsN{&^(oiC~ zb;J>djGR9kxpa(WL>wI1g5#dx8+mt{LrvX5x|U z7@a|vKuzGPK$2wsBQwso1}2^HV9$iZ8?-u>Kz1qmt9BVP~sB-e)Kd^a^az>5_=g2ca?n3)Gl# zuM$rB47++3hTPh<7uO>#lOL@ixbTxmuldcB;n2JT=tJ+~2`G{1`?>xp)7#Hf-_#;F zGk0q+!tppd*kadG?|mrKJ%Pb5c3@d)GG&Ft(e8!T# z#*XT+PQq#rmAi@^UQya8JdOxUHYU=P2VWHr!$`it8@8E`gY0XKs(Zfn(Hq z$-qc(++Ao$g(|AE3l`tRq(%PUN$7J}?V-43%0aPnPewWSG^IUSZ67uMsSNX*R(@sfS(UHz-Aq@*wneCMLm}xznj4zg to3ivpT$B2h&pzBu>(YAdeUGCCfM3Mh)~JtLRqp@*002ovPDHLkV1h}Q3=RMQ literal 0 HcmV?d00001 diff --git a/docs/html/img58.png b/docs/html/img58.png new file mode 100644 index 0000000000000000000000000000000000000000..f220846e6f3a0b538ba50a77a924fa8e5a3fd902 GIT binary patch literal 1355 zcmV-R1+@B!P)RHR400001 zbW%=J06^y0W&i*L$w@>(R9J=WSWjpiRT%%x|CgOjX01j=gbX4W4<)gPCow}6sfcEa zAU#wwXoWy%2?Z~L_!`>uC3f9~isT~Qi;#-o9z3K3%l4p@o>oMyAT%I~p4`S%#EX7! z-ppoaGP_NpLJ#>MGvE8(`+nb_`QCe97T5u`)r&<>4@L(obVj{& zUs_~k(3@itO>i>U0zQS_MqtK9{~fjaO?f?LT>2ZG^GvKZU?NJ$u@t0JMqLd`X-$j% zoLxKnKT=_<$n#)_n?p80ak_|-LQ^bo3*cPF&Yn%_y(1qLPMKMS`w;O}0%}R&+Vn)3 zGQz29PSNn%9Oa4-1@Rm6;I3!6y09XUN4_otHQYTLgFf2j;|I~x{!ik*^Qccnc2PM; zEBg(f!ayIu^B76txiR;a;z(;$z6W7-Y|YRpkC+ggc7=5?9=nl#0yw4(D8}|=@tnq3 zqGy-^H_wyprrgR}sePb;aM5E5kaHk6jb!iG(&fmtt#ncHX%ZF=)q5v4L` zV$P!yB=<3%a&{m;9m!@dcMtYxkFZ${IftY=(qr1**4=(}NxV9q?7QMr7hb)y=ju2T zb1jK-RxOcu_e2LLhr1HA`UCOA5-Zd^Y3BsaQU2azY@;aUMKxWswIXUv@O_Z0hOpKZGsU9EY$`Jz z_9?ltVahfMF^Dcow(H@=5h>sVMf~6w9eAu8pm$Jx<6gw z_c9t6>XJQq4hSzHO^&~e!)|R?{yjnc$ap0yRsLDhHIJue7=A*Sj>ia`cDxvTqBLw~ zGsW<>jY&V^k6-m+|G=OBMGaA1S`49y1+pUM`4K9M6gIfAei-U=nU_!J_*c!ugNwt6 zS6Fwdclb(Zhr-Rk7 zAYUuulSFh)EMbh=hzg7k33jMgM?vAr$5eWwl94KKtWqIJhol^%6d~0N6bdk8xpu)bL$zwzJ>||zU ztAx4(28>IdFl&2o-ezOlkjcx(>2T>lE3?NYo5U0O2QD0+@KJinTXvT=TRD#u|ArF< zAJ`2ferr2exW@3VVX|IWC3QnzWkXHVhMS@@_8As5Zed{1Jt=jNeO|*vpmP{JUHx3v IIVCg!09Z6yGXMYp literal 0 HcmV?d00001 diff --git a/docs/html/img6.png b/docs/html/img6.png new file mode 100644 index 0000000000000000000000000000000000000000..e87ce05c74de935590dab11f3a086c473e966cba GIT binary patch literal 819 zcmV-31I+x1P)u|J= z@v{|vnS`!ouLcmknn+)}B8Ih!p4^7Paaqsw%^~iB;E4(i4710dWDyLM;bxjq%p9AE z7bec9K}--a_h6_Jf)p-V6)AdLKKUX2wa?G&BjLM#?)mC3f};-hOZV~ zQJO6hEgNOq_yggVa8&sY#Uk7(4i~QzE3FBcy#}lvIRgj1{}cYz_|p#k0*suBntDb{ z)Y=1G{-TVedRKaV?pc6m8)qA&=_P^1rO2-LwLt}F79HfoPn$4TPmzkRD5bZYHMqgg z^k?i5LE$Twl+L0Le1@R$BYTP?=txkHd+jJL#6gx04mFN(g0l?Hhh04n!z@OGkR-ZsL;8wl^g*G-uT}~GzFj_C>(sJjXdGdgb#y|_h`{(=w_rNKY+ROjb^QU8f*1&>-J`TzXfg+JPGT#2 zaj)lt?{b*{JwuEfp31hn(QsTsvpE;Zw9uY19m7%{APPCOg$6u1X^1{|z!YQAEkRiC z-IM?^eVAj7?$6=gcA>>nC$GX8CrhJkR|?enM*0zoCz_@$y?N@A4or^bGexK0XL@sI xmToOuga7t_XjF*Zws_->H~w0@{F3}~`~VNBEv%=#X5s(<002ovPDHLkV1mF8Z(RTY literal 0 HcmV?d00001 diff --git a/docs/html/img60.png b/docs/html/img60.png new file mode 100644 index 0000000000000000000000000000000000000000..1bdd98ba0e23cb922fa9d8e7fd0c7611c12f550b GIT binary patch literal 441 zcmV;q0Y?6bP)RHR400001 zbW%=J06^y0W&i*IH%UZ6R49>SU_b#Z3=9Iue2xGhp~%4S0aY0TBTO|D2g82^V89DF z_`wv<4IsfE#K6D`GzVl`ClK>B5N{3$Fl}MrZGiJ4S$Uu=9R^O2O-&pOKv`i{R){D& zpTP!*-Gogh6Y!()IX*DxIA97hY+wjNsBU0tfI6^&4dg)m21}p|*%BOJh8PM!Lf!}D zkq-wHAi_*+1{1&xW-gHMhXSZ_9%hIFMwB>20spZ9^w^~sFy)e>8Y7I*KrhgLtX~;8 zIyyR<2q|XH*ucQ(aRJk0#>5W{pIJaY?ErxmkQfJ$Z^WN~P{hv9zy*p2My>*m2@C}c z$iR%@3mZc(l7K)vBzrLUGw=(rGoYBRHR400001 zbW%=J06^y0W&i*Hwn;=mR2Y?GU;u#tFv%bw0wOm6F*}<)11jM9z|8-Ffgy$g6I_7O z%-pODKN{FMK|&lH4HgAl0a#Q+K?01y0-@NN8Mqk^v;f5!KR9qR&Jb(>3NARn?99OM z0mw9%!NIUXAOp8~K)~?|i{K|@4r7;UR{{e^0|VoXc7~1#90x$UxEmNhFz^d7>|l`K zU_HRF0Hn|kq^N^|1*DtDfEnzMGXn!-#I@qpK#qEVPl)U0&6`)OSTSeLoCy;q zw6wHTR8%A+B!q;7*x1+@7#OIisPORc0M$BZzUl!|j3q&S!3+-1ZlnP@Hl8kyAsjQ4 z6C4=iI1ci(BphHo!s=in>d9*y@`gdc9H?K)>1V)#Iv$rzISdo$a4KAq*4f9SQ=`zx Z$RPKaeF3L$X&lfT22WQ%mvv4FO#nalGS&b9 literal 0 HcmV?d00001 diff --git a/docs/html/img63.png b/docs/html/img63.png new file mode 100644 index 0000000000000000000000000000000000000000..4f60c79abbe0c8fc8f69c3cad158931e335924d5 GIT binary patch literal 257 zcmeAS@N?(olHy`uVBq!ia0vp^VnD3G!py+HICEP z6IxnYDk>^+a&i(95<)^kJUl#XY-|h+3{+H9BqStwczA%CUPYds2c#HFg8YIR9G=}s z19Iv;T^vIsrY0veG_VHDn$O6#Bd|iFVdg@H-7Fj%>KKAK<)1XF2p?u+?f77H$Lhiv zHfBDKP^N2VPrSLnU^H`KBGUw|gc}8nO41Aq)dVt45)bTUJeTt62Sd8`#+pV$ODn57 zgAGno81I&JHC|^pku=kOqT}P(VAV;1{2y5aSs55U=ZF=Byqxd_=oAJ|S3j3^P6JS0*rSQS`@`y3_lx~7cgg<#dT~{ zIM5g^&i3HPfd@+&jGi+)Gtb!1_{d-zQ!}@gLfb?KrVgVADd`>!uWm9d<)4tie=%Vn zBXjc+cZvSk<&BMz)l7G`%1BEv{Si&Lqcn{_hsRn{!pw08FVB6M2s=ZA#=FO_RQDt* pdf(?|?PC)8{BvsN!z>vFhK*WspWQo*T!0Q{@O1TaS?83{1OV71VMG7` literal 0 HcmV?d00001 diff --git a/docs/html/img65.png b/docs/html/img65.png new file mode 100644 index 0000000000000000000000000000000000000000..c5039cd9fef62904747a45f9810eafdbe67989a6 GIT binary patch literal 325 zcmV-L0lNN)P)RHR400001 zbW%=J06^y0W&i*H!%0LzR49>SV1NQ%1~kCWz#xFk=LVAvUpx&42<8wLh~mwXuNAe)6cfAfx+WX144kKzXgv6hb;gA Xe`F_8j-N-?00000NkvXXu0mjf5*m4q literal 0 HcmV?d00001 diff --git a/docs/html/img66.png b/docs/html/img66.png new file mode 100644 index 0000000000000000000000000000000000000000..55d516c1428b6c6b43caada669b785eae39d94dc GIT binary patch literal 8736 zcmZvCRZtvE)Fti&cXxMpf_J}oFPci;O?^d_TSpthkfY2 zRo&IM?!!6f-mW?^>Z;#9=by@_MLZr+&)ZSk=NXn0&VB%dhial%@KwuhKCbl`$qi70-WLY(h&BT$_?Z z&pb$_^sc(hbnl4{j?C=87qzjPlm0HQb-w%Y_X)_;^1Fqn_Pyu#-{a%s=f#fhu4hA? zt!Mr`dkiEvJ1CzNG#Sfe+P7&wvL|GxnGi|SwbPwp?aDB2<1g6=5o(~=oDU+dn~Lh^ zjOt&1w*_8iGHwH`zQ~+8R;!%Pk023fz9=7Fb8b3^C>627$kgSRkmUE^{dD6NwUCwR znpEBO@#rBCqZw(KSk3*h8Nk~ZoW|girm^>dKK!WVUiF4&QFMlJ7TMINwD4E|tV8F8 zOLX}#yRUS0N6%z-5VQsTxd$Hm^rO7>Vh!e%Jla%_vLg0{>hclP8=0i>@4pL5J~KuEDxEOHTOII?4hXdWy0W3{k2ghvWmCFT_w|q%dpQ zU4xo3+IN`n!({DbAo^H+T5HbZp$N7OT-|D1fXghFIV4pnUsoEq{OQy#yIdS~SK`Q* zz%&3+l{7v}W08WbE34pJeu!zYq<8qqE|?ApgMf%mttN;#=SWe6^E)3Fvxkh`XfR4ZMeu z$|U=P^j~94aqe+-Gl#WK^(iLoN<)F>BZUZ?8wG~Y8t^PV)E5{fAPOnI3IdtLKOFXf zfd$A#g460=g}^A7@&$&p#~{48uPrRMOsUb>TKgA|qa7{ejhn@X5|j$2F8dr5@Yj>j z*Ev;6s*AlMHEde0tgzz0eIjxugLIb|j(|bvX>Br(GfC5gxHFooaC&68$71yy3L0LD z?A9T#msO7SSIcS!-&$un!#|GSF6n&5b`0)=NJLc5qUz=2#~^89jMb13*7^1V>Y6qYmS*uy0GQ}20E1@E%O(|XO3gMeZx_dkEL$_j7p^p)s_gMKjU`%7 z+wd(K{nIagMh*ZzUkT%jkER)TYTR`s*$<2tsCW;fy>P8L29{OY>Rk7jU#_S9jbXD} zVu+RKWkGE{Ai!{eTq9iUG0JeaU)0h{p?A?cyIIGE;bC79fIwzgkl1ikw5Si$nfas`cWjS95w-5 zb8Cu_)p;787lp=>U_cN0g43f3HwN&Nch=3>)1C0eRxM}h9UY|)KxePXs`*`_iI%#I z?bmyf-u#2t`x|xev!HeG(L&0PrBdc@YmDgL>^S{OGEwBhi}a+gC+`jm2;r+Vx+h!n zw+%!nx^FK7fo5ndgMHN;m=wdhZPp^N*G}N0g(RkOjFUZwXiRA&*9~+yXAGIk9o~2$ z7EVDlpeFVpnCiW@%AY5H)I{F$sf#5Q6Dmw z^YBqDg58>MbN2bfQ2ni|amnQ!vgKh52gTgy@r#x7cx~{jF+oZ1uaHH&@298rVbZR9 z1;G=?6k0|qOW2XY_bjKQdqYoq=1HEUelcZy>E)VFvZk5)5?}0%2>7NDLIWtpgNYJr z^&5@2(C|hWpxIHp=UDKXkYixgrO25uXgvR%ny6AVZ)6G6v$B#?pj@+rk|I}DDsCmQfvYq;O74`@*uYJD z5ht4hniz*yt(bxzy5dQIuYI|r>PWHA6hAm%)sF3 z53)T+!Yolue08+II>&1b!p)D_BNG=ICE2rMS5oJOAD_5H)i+n}qyMTF-h4{NnBY#< zz8Occ-}hcp!=wg8Xe}2ToY$eJ@wu<$+#ygOHo6s<7iPy+Nn3<$S zTt)J#x(PhR=-*+~i3#WqPQLrqR`f`bMq48F9o*z(<8eC`=GdK9YMSLTj#*@?vj~?D zH5@m)Ode=CtJn6pr7_sbF#;3=1ZrvQ`eM=^Tf4~`v z!GECNwEE2puV)0Q2Xxpn)z++Hn?AtF7w4Px)6zCb^<%Wl(vD=q8Rh`e-pV4Pe{*9i z$Z;F@UW`DGTraH0nkjVe#ekzm7{}ZXQ0(8(1o68klI|xK3Ma{mIC%t6IlC?6W?B!N zCvirPSP2c$pD`I(BblRMwJY9+L2}GiVKgs4d+}mx@GylmXeowmijEd6@G^3i~+U2$Ju1?n}h=;mUUw8+g9m4g9%;rOZnLyiqo&~@^IFET&zxF52t zSVs+pf`~XvJMfh5`gj@PI#Fx1NfAvO8=jzyMKCK|FV~Fjiez;^xp2*QSMv=p)42rV zHM!pAyUg$m`$Ul``lXex&f2ArQw60Ogm9Fela^52?pu{hWQEa@Y?nkOvC^WBOEqgy zchCH7G9fsvBofr$_$xgecBc#)r(WG39)AcH$<1S}Sj&-D&PC0eTFAynkmM%}2T-jg zCCf5lKrkTR9~<91W`L zdAKe(h}fyP7ZOdNjao}GCgYCy_>m7%g2dX1i9jua-e9-|Dty@Ka3y-A=E`z{bRMX! zZLSGm6!SQjalhuY<(j1^&wEclAOWeyx_5x$IB80NyU}y59UoaFLE5Q_zc$gd8?b00 z)W5FZYSs@K-K3igQ>TM`x1=cLakqAX&(&V6r-|%Bot~3Gzp>RTPSIfcx)$i`x0mzC z#&Zj`_KCLrCPcfg35je>Tl_H2kE2p0y)8}ZDkt94WQCq|_+6=c{3cK9yQEzOIcxd?6$7-jzv3(`B+E`yDs6vjSQ$K;P%3@ ziV^4OFcr--%znp&yrq~YClo_ZuU5d@0nEVa@r@kQe=K?THlUyLeB;$u-PX+1M~|d9 zQuwIT?|trHM7^t4q8wOjJ|&(ClxBm*E9#b#pn~ec_Uh8mW0eo+TM22H)iphX9}wjc zYHmCZE9%rpo+OUWfz}Pv?r2fyXvB=!=Wu`uMQ%2yxXoj@!m&_!1^!=va_u=D;J0QF zTcgn0J6B55EjRlQAr0i5Iy=l|3RW!a%h5@}HIGo*EMGt)7&*&99qAu#k{l!fPAvnT zdH6Yr=V{KRfg=XsV6xy7EG}c`C zfaE~pO!9fyB9)QzRP3YO>|fu`VHhT%PPyh|bC8@nrmE+E8HCr~V=+2RCNx5(B#9#|TbA*T5cHG+yalO{7g_QB z=v${9UHD7&kfHfmNP6f zFSq2YW!V?$dp1V?Q+9t~#hLJ;gs#;|1;r>HMw@i7g-WcH0h|CBNMPVAp|68KpnnD;&a*`nn;6F%Q(34{LbemG;w1W z%Vc3`Z}f9N|3S}2d8W?7tI>zSO z)$Kt0@pS-8M%cKG3KBxznCXDz<5{?P8TNPqk=aK?7<#bdUMgbpu7yJPEA8-dzo!P7iN7&qY&AE9K zNnd4N3A^5alCNF$AAp93l8G~anuCujR7kq`ICXaOQV@rUEfGPM<@Dibot#y-5=?oS zKjzPvobC_-%6-Z)X5W#R-FA`W`aS_lwnCm2FNP%7q|a2eH<=Di;Lo$eo@+`1`=8J}&2$9V^N=TxGGd6& zex8sues#D-!9o+f`X@ynO9q9TI4!_SEWa3EQv!^Jm$(4aywjL=g_b{2V}>m~aDkY7 zb{b9g`s~)NYmrhvvM3`I=dWO6XnQabwvNa$^u=efm~XF++^6(wR*~38KB|#7oORkL zK^q(g_X6LVoV3*iG02ZS=}W_C4Iy(H^3C06SBMWS ziWykV+N@8NM2pIw9BX$U1Wl-RR23x|HT$cMb82O?0PA?JeXd#KS8@{WpP>M9aVMw@Et^07jF+i#Q(DERoWT1>NEgYFb-h$NV{rN~+Q{%eNet9Ky??r%kV; znRJ20o#&IJ5|k^e@tfM!)5GeN27RHdz^?rQZ|;PmJ*Yz_N8kLb#1Z8ZQ*I{-_wx{* zhcEMKEzQuRHea=UaHxp|R4RWjV2La=L9vvuZr5j1!|JOSK%ScutQ*tpkDa&F33gY}7MO7%fTC((uc6$w0P^ zKOQ@vU&}5Da52r{N(SeYQTNsBHeEMgBWMh+l1bNLDdG8|e|`beeF>e~ynWEnY2m|J z)AwB8QDK2tL8TfxWoi3m`dH@P+g;lQ@W1gq_0eF0$ZZgJGkaf6mL0oeFaP_st)f*t z6+S*`%7ojxS@qlE6Ms8{WOJuXJ?JdAuKxVPjdvE1KhAKH;`&7b5BBjm+PZn>SHqqm zTRk&5NIpe0)l+z@q9oC<5o#PEP-fS(cpcuW1wXn4%=yjuA=73`?v zCl8tyXTV`*CLAG6x>{1xj|k*S`%xaS?@sjVN69YnEmG*yhrkck_{QBv>VG-SQ(0b*|98=|9vQn|(QrX}!XV5`PD~#4qWrp{jFyiS2QJ+@OSGdUlrQvXb z)db~fV|b;QMpsJuZj(nI&{`b(PO`m;xYtNVoY9fW4ZsPz4-s>=vSFfdhJkmivTk4K zG|-V{+pg$Iv@xrHA3N7zThoC0mKm13sS8)Fs#(XvBG40DdR^Tr%>JB!nhRH z{s!IRCz-zqHTkAwb@o;MZOH6v$(ZC5V$jEYVD|NM%MAzdVb=k3jG3?n$!8de5%a80oWTDgD?c!>8kFCsQXGJ3d}RK7)iXN^%*iG9rs z$#7(|sfn5_x{=$+7LVeP_JD`n6%JZncFZVB|DXq+uYM|gI9Ge8AR~XmjmycJ8aZx_ zFP5wI+Qn;A(LUBZEGr&;dU+>S`485%7vjB-2XhF?i)@0?+9lCr&88W;#eLkmt@b5-z&QMl5Re51Fl21HF zK-Dl%nQfZ=BRzF@xFLq~)8qwnqnOt%Yi$rlLAr?ua!1djsAvE`YseFVcSzb&;1^>vA(pN2XH$Nq?zMJ$VoF?;^Xu$EN!m9$TF&{(uds#)ka9zP~ z;+-)(mOmE}-53K`eu*|00XOeqlEd=0f8?R&LzAi8Q-!D0O0oTS18Q3B5f!>W4P9k_ z4Pp_9y5bS}g#Tzm18w>6dB2cb{?4yrVOij7JO}9gY~63`aeX!Wgb$yE3_?-M{!@fy z`ZQ!WvpF6%?Mqp~+ZH@dJ3tSMz(SX_(0607Qa{y~_k$EF5;r?EPt&8~I4&)7{xfhaS)Y$j<}Z7XPgz z4K(VROaW+cg#64?_t7Lf2Yag+QTMoE(IW=G%FtKq-*Gmhfi(R`a(qWtGocTy*9I~r z4Nwf&%j5f7fImp-yDN1B-C+}OKdsHi`?DHn<<^Co6?p}v7JrF^zTP-BGK22xKjDuL zGLuUG!4(6B(TN{|ad~R~-#g7wYUf{Ewp^Kh4XR@@b4Tlx1~@KHp@kVy1fGO@Tt`>*@V~il z1k9w$WcB(ZT5=7(%9JKMBLd4(9}3~8xT{jWM_RvKt3ka}h^ER(lT@E7Qq$`Ir_2LQ zI$;z1d#%4GoiI3MoP^Q?A7>sJ21;kQP)!n>314w3iJyEqU)=&8>r-z3#MO~sH;k>u z3ru6|kO;@E<#eMY_=_RNA5&dfAB~QU88r$gx9E`WTk6bte;H+kB`Bs_-k7Ofwp#Vr zLH~GPH~p`l<#D+2LE!bG@w*&;N-U4>B>b#2i*V^32YJ4$7`K1RtpBIbj}fHDk+EmX zmMo5LS3W}R3|r56K;vL_&c$7x#y@Evn=1^SLf<7>S%=Ss32VPKUKQ^=UptyR|M@LM zT9(tG>FpMk$PaA;<+cw4dcCdapLuN|S|W z%v7k?%RA|qf&wWAo|xl5W4(+DxpqE&DO%CS43zLt1W$OVi5`a(P6D_l3_6 z5=LO=gKEPZ*|x{ZLs*y&NPJ{RtDyFqPhs{fe9c1Co@NVxCC?;0JmzMq!d`j}<~!T& z0t=lLg!1vy_v7E$L9P3?$1`E6I^{KPxxorMbA9lf@%0}f*BFcK_=4d#AFKlja$XcB zMKd>+!u%Z+m-De>P+N0%@G1`{ zewSM(y>L!nZm>uQT*b2ay;&%peuLsx1akJcExUm1f3PsW%G_E@XLA;Ud93EoO6wit zr`|&2wjtBwbA{;eU!Jg-Eqsz~Nl^Wr6%5DafSX*!1ITSm`cl1vg5z&%NL#D0F+{cG zB@KLKC!1aVLB*e89rv&N^;`>1G-#s!jYCrQ5+RQ2Bs0bJqt;f%PP8NFcKNDyR!44J z3Jk5}KkULBRf~EhKpAex{+I0QJ7vC+PCfva3i?~lE*#pmG?Al$Uka9E zH#R1F&989W5lK~?mZ;JobT{k3xl@cJSycJW32dz1Jy#%mUXuh>4D{EAbww7@(8HLg z!#R^8EyBTt4GzeB;F#qTau1QYCKkEZp3)G`sj%ATW5=i5dikPx3d%UuGPC(UlXON3 zhtlO=$oPUw{@A74J_c^ZBA?65(L|+{aX8lhw-m{?nI z^^Cmm4S!>OPCj`{gLpac0?WRy8w@${?Yi5(N|zcH`cvw@+eH2)^B0Y+mMrA8jK$*H zOJ8^Q9Ke6{zI7&f!^MEkIbX32{_gvLXzZE7JW~7E5edUMda-TQer_IIw+gK}{a1 zLCM1n-2?X=*CSI-=TQJFM9Y;iPQASANe=yYl7fw5fG0g)Kbd z_po6lOxOlQO}9#ku^H9#URr^X`+?)Gl0WGD9HmSD$&f)=(}vT}y7aWC?)h`18{g9{ z!*}H)SCO!>(v1~G5}*uRF;Wm!BGW@*Pd>Fg*w2gSF-) zl!6G5RqtIkd>{W^mUV&BkX^Yl=1bx%maettk^C@m!92zCjw|QYtDb(-M6-}Z2_oK9 zm?OXS#)(YbhDo!+30lIZ{DZG^*RtkoWcqGG@5&o!4nvi?Za%MZMfKa+BvpDv4MEBO z>Il2s6m7Cktn@RJ$`_*{tddSF?G>wy+R(NkEo>8^XXw|<3L`*o;BMKN!&T(^Wbv#r z@;T$XnQB)5P9Xz|@GO~FM$unQgx(ZZy)s*H*63V5s@slN2HaVqY06zPYY@FILQRkL z#do%$%1;lI4W5B71VpA1xBuYlh@00R$V~r1WG7upqQL&7d;bxf>n}4`=FEEPq#kN6 zgXh)v4YKwA*d}e)vLjn+w1xvU-jxOUb1RT;?)Wi5=kJUml5<ZV(%evkj2vd_e!VB_5D)>$<9$#Ss%LFl)tNHESCo2p*T2n;Z z5>%n-3J4M^{6mPxcNUTN&liyLpBEtfdBo(r76wP;SbIIUatkVd$-mqOL?N!DWWZ8NGI$ipD`uS1*`!n{A@x|XWoXy!8lROX~*V%WU`Ff9g z(M;@1Nz<&XTY1mh85`!WsF&liScIDsO7PFo%-UAzL(n)3>g{V^Hf>PYf1M&tF2UXz zK+xF!o%zYu$90a!xD+-Hl zm}Mn*n>Y0ONH4cy2o+}yWn$Hz?s>>iLgc>|0Q2+_!^aH?iuBX}XWM{MlvR~!kTMPZ EU(2i&2LJ#7 literal 0 HcmV?d00001 diff --git a/docs/html/img67.png b/docs/html/img67.png new file mode 100644 index 0000000000000000000000000000000000000000..3be36af806d12a4bf22e191d4dc243c4b8f6087b GIT binary patch literal 292 zcmeAS@N?(olHy`uVBq!ia0vp^vOuiB!py+Hm>m~)6UZ?L@Ck9K=#Yb5>G84?3d7>E>R!de$>M09=P!KMMnU`=W=6%y2ONiXAUTEUi{bE_?EkQALE%V`^5QrcF+3C mDj^{}A@}7QjRiCL3xJ-El4E*Y&w3f?S_V&7KbLh*2~7az5NcZh literal 0 HcmV?d00001 diff --git a/docs/html/img68.png b/docs/html/img68.png new file mode 100644 index 0000000000000000000000000000000000000000..f37f62402d3e8a5640f5bce0271de9defe78d2e9 GIT binary patch literal 355 zcmeAS@N?(olHy`uVBq!ia0vp^vOuiC!py+H*v@-r3y@zGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VxHZ}$Z1}Z8l5)u+TJUl>6uOd&+15%77L4Lsu4$p3+ z0XYvnT^vI+CME;5Jz!2sV`GUpa9}>e^8ynCgDnNkGr4#q7BF`xPV!YKW^wS6F_@aj z)DbDaLqe`0qpXcz;9*@mpWF-~JvQb&ZhzVv_#;$xt)vc=9Ap=`d*EmQ!?rf*H~w~R z?D7)~^p%gS&Cy}CacDPKn_zM4fB-|GQES**pOo(QadSK7>gMlHd+Qm0TxU~T2Sq4v6KbLh*2~7aM?0e|| literal 0 HcmV?d00001 diff --git a/docs/html/img69.png b/docs/html/img69.png new file mode 100644 index 0000000000000000000000000000000000000000..1842512df08d0530d8ead9841bf012aebac3856a GIT binary patch literal 265 zcmeAS@N?(olHy`uVBq!ia0vp^Qb4T0!py+H*xBT|0LU>2@Ck98?cxGmhv!S)iU~(ew#D>&;Ow8EP z6IxnYDk>^+a&i(95<)^kJUl#XY-|h+3{+H9BqStwczA%CUPYds2c#HFg8YIR9G=}s z19H+lT^vI=W+o>zH1YHBu=4QK)Fkj3%QJHYq(5NOOnl2QX^t%Cib)PTeH4B+G;!3;OXk;vd$@?2>{?PP167X literal 0 HcmV?d00001 diff --git a/docs/html/img70.png b/docs/html/img70.png new file mode 100644 index 0000000000000000000000000000000000000000..5b68e6d910b44d40edbea4a539a58e6e1abd3a41 GIT binary patch literal 374 zcmV-+0g3*JP)d0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*H^hrcPR49>SU;qIQ26iCH&43IV1U3Lk0c0WGv;$z8pN#=8X!_8= zz-FMp!0?%Yft6tc1M3HnD7OQCU6??63j@Ofeue-bQ-+a&2PE`?pAkeQFfcHIoc4hm zk9Mj7{f3il7a+{)4ZvV(0J&lE1aN?HGq|uYFt8;QfTcOu*c^ZqR52ScV1eKOBxqS2 zxL^iWZ=i>>sSEfU7&w6O*oZ8~d<>F4xHm9pegUT;V7#OpDRk=?{)ymeQ;#>0ZUB!5VIyhxhy{z7)}~MIUP{@wnFI%3=E5?MiOw*UYD07*qoM6N<$f>~&YH~;_u literal 0 HcmV?d00001 diff --git a/docs/html/img71.png b/docs/html/img71.png new file mode 100644 index 0000000000000000000000000000000000000000..b7d510e1613cb98f20f29e8d6aefc61f425e9ccb GIT binary patch literal 1387 zcmV-x1(f=UP)RHR400001 zbW%=J06^y0W&i*L=}AOER9J=WSY3!4RTMsx`N?D^*%@%rBE@DwmiU7PL=b$L2P@k? zn0a252CA@V!93RD!*qq3?Y1;1zO^v5h++}1=+@%;lSjdqJSg@t)tB}ybX%-Ni09lp zlgvz#Nir<$3LePZpL5Q4zI*Q9OaP{d)$jKQjiLo67G2(8`11hdq6uadS}pf<{whfN zRK%1(E>#@ftWp3MJ4`p|B4k-+ph62f8LW&zxDm9uK3{^I)muUf5p`nc_5+ZUDG2|I^&=?G0 z3*SN|#5OS>?vFO)JBUn(o(#|th#n#;h^1dBQrgh`ifa`70_x5aVt(>qBB60sm!eZ=0Z1B+q-%qwJ88=-zDL582Zct?ZfyCp5RfkzhaO6u9?hml?9Bqu)Ix6) z!8Nomlmfs*Sp3{EFsKQ2n$4mmG?s{G!7-f!>d@4G2moC=LO9@#<_H2kcmMheRrJU) zkaK0|xnNqle9idS$vda?7M(2!=pf)ycn%Hs^=J+m@oYvGnZlC=)ZPcZNDY}pT0_&@(8d? zI9e>fN%55TA}z7gOn#JBs!d4Fay{ld(>hE_;6z8?@&sKbz`1pqoU)wQnNIotWpBvm z_bJY*pUuy@Z|}%QvbpUd!6_T*!4ve;)zb)8esbW@-%hf748gNEoRxpP+?VTN2aBoW zEofc}D#nN^?vo(+dr&@89w6NUWrSah;3Jo}8(8RFQ0~I;^COkuTkuLy^JgMRHU6b? zJ0uWt(&56G?|R|3uZiCm@RTjO@;!KcJGdLq1fcJ{Klt+GEDnDl8d?X=iJHMxQuEYc zVEZ=Si27J=lHkVCjcSx&k-ap+PaHBknvc(R(5Kwa+h?N}E`yq_d&3r&C%)n1Z%B8+ zAQYdg&OkAo5}ir6Vm?RQ2*D?>gZ6McZ-Ws6p9Hu`bvs5-<#(d;MIvBq-{09Z`>vs5kX1yA@2oS)i{|zS&bO#4UoE` zUuFjUfv=@wc5!TzNMqxU5S%2b$BdBPWL2n05d1AD571maKRNh=yXv0f&&Q{^?fJXd t@OPC(irmZSr)GL%pIeO7zZCuh@-HeuIp%20`04-v002ovPDHLkV1nB9lC=N; literal 0 HcmV?d00001 diff --git a/docs/html/img72.png b/docs/html/img72.png new file mode 100644 index 0000000000000000000000000000000000000000..f88736e714e5ebbfdbfecaadf1f957e2eb2d5cce GIT binary patch literal 445 zcmV;u0Yd(XP)RHR400001 zbW%=J06^y0W&i*IJ4r-AR5*>@ld(?2Fc60SBv$2Op=4u&?ks(Tya9QHh#jeqkO2WL zNM(S9nE|PbN2D$pJN6L*D~kstM)28jo75>%rHX-n@SVT>x%g}cXo)Y-p`_$`%*%-T z&j=NWGa=FObi0@ezyPJw!N-W3j3c08YL_~``UiDVEP<)XUT@L2i!FfIAXQluq|%{1 z>U&eW^>mn;!1U63nMnl?6NJyuq{$fLaMe%4h9~sZ_5HHsA={y(U zbhM|5t21?XZteNPNufiD?H;BuqbOINGvIEc&YQ^5`WC+r-*MgYIIY%fn_ai*tA^*l ndH7{>#;&?N|3u!c^Z(@^guaM>0A3tB00000NkvXXu0mjfeVW9S literal 0 HcmV?d00001 diff --git a/docs/html/img73.png b/docs/html/img73.png new file mode 100644 index 0000000000000000000000000000000000000000..fc5ad6bb37652fd14b90a4cee6bde4f55cf08962 GIT binary patch literal 195 zcmeAS@N?(olHy`uVBq!ia0vp^Ahr+-GXn$T^La_{fE@JzpAgs0n>Vjmv0~1gIV~+M z6%`dZIXMXl2_YdN9v&VxHa03MDiRVBK($+so{|Pqj3q&S!3+-1ZlnP@UY;(FAsjQ4 z6BwF|9dZs7FdTWpA{fJC6A-A8!1kz&WqPBmmd=3#2X-)?@L+tzw4l$JT_7t);LIns q33Ass6}Fj1JXs*+^Nxpufngg5pWK`+PnQEtW$<+Mb6Mw<&;$Uo*F8f3 literal 0 HcmV?d00001 diff --git a/docs/html/img74.png b/docs/html/img74.png new file mode 100644 index 0000000000000000000000000000000000000000..77ba92a4ddb8f2794bc813a22d23112d06d19daa GIT binary patch literal 342 zcmV-c0jd6pP)RHR400001 zbW%=J06^y0W&i*H)Ja4^R49>SV88(U3=Awt+zAW}90{1J;Ie!S4M05tAdSpmAr731 zp`g#@2Ui2wCbkU>3@#u>K_debOgaa~AYjmcD8MDp*a#$Ua2(Lrgh4E=1#hW$2R$aetJmtg`M85lgU o*=lqFO@LRGG-p#6{6_^J07n@>E-6&6Pyhe`07*qoM6N<$f>iB!lmGw# literal 0 HcmV?d00001 diff --git a/docs/html/img75.png b/docs/html/img75.png new file mode 100644 index 0000000000000000000000000000000000000000..8d6fa2fd07d0da43f0a0424afbba060e0387ed9e GIT binary patch literal 501 zcmV001Zi0{{R4GY2ZW0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*Ib4f%&R5*?8RJ%^YFcdwh)4WP)SHzM(Xazz72Cx{IJ2G~I3574f zu;6x}u$7G;K zYFhP*SXyjSkGd!ow7V)}#1u^8zZLXl;j-CWW|wLLj`5U^KpTJP&wNyg9gdIahk$Rv00000NkvXXu0mjf$K2GW literal 0 HcmV?d00001 diff --git a/docs/html/img76.png b/docs/html/img76.png new file mode 100644 index 0000000000000000000000000000000000000000..d7d7589462fc3cae06e27a25524d5f42df00fcd8 GIT binary patch literal 517 zcmV+g0{Z=lP)RHR400001 zbW%=J06^y0W&i*IgGod|R5*?8Q!z^eF%&<<{PaCE4H z6c=$9^onp+EnGnaoopvvgd&3AfrwLAXBU5ho1Lu5HP?!5iU>jxKX~LN@A2N3FE2nB zHt>Go049MFCR{k`a33e!Qo=DtWp(;^RcBFbqXt5FJ>BJdpBoGLg50OR!)8=tb&}pb z=sKQP1T@+UG=v;TW4%4@w zrnXmx<;*4->JU22AST{r8P`^EvcR-hm~U4Ap^UK`NvVgUW=ezImsnt)o2WBk(5(Sd zyzd`FXDCMei(f;mq>jA-XP>qd&yM+&xI3+b+@!OldU*(x@(VKh0$d4aaV^|yE}x+D z%%f2QrgA_M8{k8c=w{n4RttP(*{HZ*+0VvZ%L7Yc9UfW*E{BZzGAS7ZftUqa_R;=A zHocOUUKC*&c|{zdrMiB#U6iimO)4%nkJY05V@xspPbu&LJ6D-&G*Bp|00000NkvXX Hu0mjfZ4%kf literal 0 HcmV?d00001 diff --git a/docs/html/img77.png b/docs/html/img77.png new file mode 100644 index 0000000000000000000000000000000000000000..e6be141f1d247b185c4bcc939a15a3a2b9050151 GIT binary patch literal 1471 zcmV;w1wi_VP)RHR400001 zbW%=J06^y0W&i*MJxN4CR9J=WSxsykMHGI!Ua!aNxa(FNsuIAJA`}h~gFr;$&_#_z z5eHjBh@c+2TmV&-Y7mETn?itf(vq#X6pF+~pr*jZJ(L3+vIh>mVWa{Tr<6(+2q8@y zQ>8gEGyDHzXYJZj5BU`D&YOAr&F7gnGjAP$;h?gMh@b+10TZXP!LJhin6~GLBacz{ zb3}N)GGwn_7cK~>3dpQrAh4l=BAu1ktdB2w7J_Dx%9y90x4xlM$T)d}$;L?w@3eYs^Un;%gncFiSOY@3a~gDP&`uh2 z*;fT)LLd01QB(GlJ4JjE@(9+hU?Y9ir6F%+cHKoUh&#K4V2!F+hV6rj>~H*17%tk4R<4R*LvDvnPd`7{_VgPn!#?zlM~9kMTC##FR?vjv7?SjN+L05=dZD(5m2jc)VppRDX+7x#+e zW8yt#jfr?zD8s%E3Qu)*b{Yn%<=my^6lpSs@?n-9osK+$=@v!5OO_Xpdr$;Y`e222 zqX*p|fJ$u;_3?#Ke??tTH9A4Bvo<87{779n#g!^uH;l{C zs?|_AhexLf*4X>A?C0xSG=e6Z@K8LEesE$ez$Emxc2p!TZ6$vvJhDBta)I8Bv&=f+ zIebmWqmxWyr7pl1ks9haZ!LW4TKVYD5s$4de3ho?ST^Btu%X)RQ~3Nj3>Mtb~4Te9? z_G)>e70<9eMJxO-4mxm!FO917Q47OahbpkXh&Zc^47K3tEpJFYwX} z*HT7xbc&EE{+Vc0uy6xr_BNR!x@rm)riiZEHdAyRri*4cR!6MpKEkLrq!A)zE8oR< Z@IQ&9L1*;0I;{Wz002ovPDHLkV1j^jr7{2j literal 0 HcmV?d00001 diff --git a/docs/html/img78.png b/docs/html/img78.png new file mode 100644 index 0000000000000000000000000000000000000000..1b4149348adaa4d3d21dec2614efeb685424f174 GIT binary patch literal 279 zcmeAS@N?(olHy`uVBq!ia0vp^(m<@h!py+HnC75256CeH@Ck9gR^HBa4q|3Ey4Gp@uv*W8i!jgjq1mdwKwBM=#|{qIWGnyx literal 0 HcmV?d00001 diff --git a/docs/html/img79.png b/docs/html/img79.png new file mode 100644 index 0000000000000000000000000000000000000000..cf3b348af1ca389a534a7f60916e07d64726552b GIT binary patch literal 222 zcmeAS@N?(olHy`uVBq!ia0vp^LO{&V!py+Hn6rMdHMX&V{Wu3_F>!7VXkUPEN%)2Dm_rPmXsZpbxhGU%MRHR400001 zbW%=J06^y0W&i*H@<~KNR49?vQ9BC4KoET~t1L#))-E}KkONqxwK7NWC@Dl^m(s!_ zAc%G;Y(xu>;1N8+7WV7x2V5muh>eeB=Ivwl?aVGf=;8q>r6HvNdX5$nDbP*Pbjw{d zD}VzG4M0GbpOw*@a_uXncoBV@uVjT}LSavK>dunff*8o6w~pVzuT0L#ykn>rmq0rO zE7VLGaG^d~Wq3%9U`T@!kLZm?v@Nds9RG1^F60BB%GfNd)u+$f90T*cL8ju?{xuWe z`Z-#~$q0v7B`(w=Y%sPC{wj5Jfw^@!CKSD!HSRC;dA74%@#XsSn12CT3vmamT34<1 S8N}WI0000@P)RHR400001 zbW%=J06^y0W&i*IWJyFpR5*=eV1NL2P6kFG#Vx>q1u%0n7#c8aV35Nm2?eD<+>b~8 zKOEptz{vo#fnSh|1IYfs0Co)s9N>mCNdR!mKHyT(kp!kVGSYygK?9h>=Ku@=AkEUi zV#O0M!9n2|NR9y_$;01Dv%Fo%s{0t4gf0)~bS7WRA$ zhZ!0k00nt~SP_U>K5(-!Gm0`CFa~m%)&nB|NT+{jK$z*k4~i)uKo)EegJ@rn(2nK; zphZIw{Ko`1(-L(7Q#v+LX#<8{BrXTTZ3FI$ti3C{7#O!mI51QL8DQ|0fx!$!+a!Xy z%niUyIbR`*A(MeY(is@d3Yidf`Tw_qC{72Mf&Crr4h#<&P6%)cFr+d>Fq}w$%J_ql z5Z~_IySIasHTE<7z~a0XpgIMRc?wWZFmyAVz@l#3j4ntbgu0Khqk$oBGM>;F1vCU$ c5;-;i0MApBSqDB>pa1{>07*qoM6N<$g1R!aKL7v# literal 0 HcmV?d00001 diff --git a/docs/html/img81.png b/docs/html/img81.png new file mode 100644 index 0000000000000000000000000000000000000000..f661a49f2cae91aae13bdb5e162b832a47b34049 GIT binary patch literal 456 zcmV;(0XP1MP)RHR400001 zbW%=J06^y0W&i*IMoC0LR5*>zQ$0(>KoEVmx#V(wC17QjP7n(l`z!4(rRCK&27580 z9D@kPMy{~1v#<$>AX@knywcJiAb8+uW#P!l_0Y!36T_h6_=LD_-n@CmiWPI_%$YD@ zLQ6|aMMXtUPEJBXLP$u6hlhuajg5hUfr^TXgoFeS4-Zh&tH{&yfD~g%kY6x^!?PP{ zKu)r!i(?4K%;bcG2k8vV+-!Vm0%uPgIIyj;@gSoT*A!ERNjkz35@p+r6qxhcxOsTi z@Nhb)#w&6)&T?=$#w1e8(<3W8lS|>42^*XDh7-~=9{Pm-XLi`a8BopKv9Y=FqXaWE ZL*{M1WluSFSpltM@O1TaS?83{1OUt>M2P?Z literal 0 HcmV?d00001 diff --git a/docs/html/img83.png b/docs/html/img83.png new file mode 100644 index 0000000000000000000000000000000000000000..d2d4988d2c157991d1ce165b8ebeedb816135615 GIT binary patch literal 554 zcmV+_0@eMAP)RHR400001 zbW%=J06^y0W&i*Is7XXYR5*?8RXtC_Kp1|ol^#@}y910QE({JXh7LyE;1`(2&B=~# zT-3z+35ooGuEwRK34lMBk3R3mU3&pYfKI{y z6Do8MZwU-TDifT3F2_nznQ8c~A-<@ujhY3eJgimS3eVmyJWGBWv;oAI#e;pGWw|55V?P7AVEMs?&92 zfrF3J*_?}!bIFMtx!Xr#EmWXc@%fVOfKEN?m1zHLPpJCs%y>NNDI|TMVNN~BSl80n zczlWHw_{!~+ct1ds#S}`*U<`;Mly`&kD`tSr99%T~llC|Ovo#nR*3*Sa^| sD+75COZ{k^i|w2t9n$_!?5E7f7wG(1PH213>;M1&07*qoM6N<$f<&VFT>t<8 literal 0 HcmV?d00001 diff --git a/docs/html/img84.png b/docs/html/img84.png new file mode 100644 index 0000000000000000000000000000000000000000..f34aa7f1c59e09e4a26618b4f1bb64c3e7bbc0c9 GIT binary patch literal 200 zcmeAS@N?(olHy`uVBq!ia0vp^0zk~i!py+HxR`CDK9Hju;1lAydGqEKD^^UHFrlTT zrJ|xDCnqN%At59r#KXhG#>U3Lz(7SsMM6S?hldBK<9znncp$}C666=m;PC858j$1Z z>Eal|F*7-Vp*ca|;KdUR>~B~Lp0O$9ITR#1G%7N{an^LB{Ts5%nvzS literal 0 HcmV?d00001 diff --git a/docs/html/img85.png b/docs/html/img85.png new file mode 100644 index 0000000000000000000000000000000000000000..822e77fbdf1f1a3d3eb8d04798eb18cb0e189579 GIT binary patch literal 345 zcmeAS@N?(olHy`uVBq!ia0vp^MnEje!py+H*tmbfEFi}qz$e6Y^XAPfR;-vaXU>EP z6IxnYDk>^+a&i(95<)^kJUl#XY-|h+3{+H9BqStwczA%CUPYds2c#HFg8YIR9G=}s z19Gl=x;TbtOiWH-V2opB6FG43K<^>*gam=KgdhBD@)8#qj9s{`CnO|3V4w8nPQcO^ zS~u%T6nIh+bP_TcUS%gFlrw$$aWJY;p@BJ8T99GY^v2?&Y#RB@H>Cdv$h~IY!TZm_ z+R?^t#=I8(gsEBq`x`2Fdw3J%gl~w5e30i%Xkqa?Amn}Fslb6>osEgC%FVdQ&MBb@032a=%m4rY literal 0 HcmV?d00001 diff --git a/docs/html/img86.png b/docs/html/img86.png new file mode 100644 index 0000000000000000000000000000000000000000..f2a18b21213c8823872450308b3f7f56eb9380a2 GIT binary patch literal 303 zcmeAS@N?(olHy`uVBq!ia0vp^xFf)G1Idic?&4i0?#EL)j!H+!DR3Iwr9EJ()}7w?n0eDD{(yhwY(Lp_ x9_h$Sgegn&KPi@BFqA7&UtqC#vZH?^BZKNit^1Q1zJY>+!PC{xWt~$(69E3TV)6h0 literal 0 HcmV?d00001 diff --git a/docs/html/img87.png b/docs/html/img87.png new file mode 100644 index 0000000000000000000000000000000000000000..c1c56e363700ae42ef8078c1738e99dde3d70ac9 GIT binary patch literal 210 zcmeAS@N?(olHy`uVBq!ia0vp^f^GJUl=hf3lAN^)oP*1o;IsI6S+N2IK^L zx;Tb#%uG&jU_5iqKc)I$ztaD0e F0svkVKqvqJ literal 0 HcmV?d00001 diff --git a/docs/html/img88.png b/docs/html/img88.png new file mode 100644 index 0000000000000000000000000000000000000000..da04492277b863bf7d01d3c7d489dd56b19b777d GIT binary patch literal 280 zcmeAS@N?(olHy`uVBq!ia0vp^3P3E+!py+H$Xx$O6UfmG@Ck9Qts#Mkw0hhu?`WbkzLb6Mw<&;$UcD_Ac8 literal 0 HcmV?d00001 diff --git a/docs/html/img89.png b/docs/html/img89.png new file mode 100644 index 0000000000000000000000000000000000000000..0d021da2308dc0c4bc27a4c68eda8be08d5af88b GIT binary patch literal 190 zcmeAS@N?(olHy`uVBq!ia0vp^+(697!py+HSmSZp0Lak_@Ck9d&cdHCk`+$Wb3m3Jo9c(E6_9sPgg&ebxsLQ01#3*HUIzs literal 0 HcmV?d00001 diff --git a/docs/html/img9.png b/docs/html/img9.png new file mode 100644 index 0000000000000000000000000000000000000000..bee88229d851003ac9a29bd4c8d55d90605965f9 GIT binary patch literal 213 zcmeAS@N?(olHy`uVBq!ia0vp@K+Mm=%)r37i!0+2kYf@x5)wQ-JU~saB2Ui)Qj8@*e!&b5&u*jv zIl-PTjv*W~lM@miq%|=8V-q-e@W261(F`U*g@deo4o-&{w9ZUoIN~size8OnA;IGZ zLyCxj!I=~Xwu5E~k0p{8{F$>p;nZ|Rd7t_wFP$Wt69*U=_B!zDSO1+>3N)U<)78&q Iol`;+0Qs9lD*ylh literal 0 HcmV?d00001 diff --git a/docs/html/img90.png b/docs/html/img90.png new file mode 100644 index 0000000000000000000000000000000000000000..5a5301f39fb08ed0f2611f3b7bf9c0ff7eccc664 GIT binary patch literal 370 zcmV-&0ge8NP)RHR400001 zbW%=J06^y0W&i*H@JU2LR5*=eU;qIo1_uy<4X^+)M>jSZ?%fOw4J=qSK>-I4H!yI6 z2$1>>5SojD!6Lu|pFTW*7icEi1`sO&Vgt}f2RN6TMF7f$0R_^n_>TgJ(Xj*SHYj(4 zAkdKLOw*kcc0O#)BEr84|0LeDMxnR9q6ZjZ7esIG~26`UkO$3(# ziAxhedT0;?K=)d9G(gxgaObnm-n|hl$+3XJP5>Ttw0H{D?{C2qr Qb^rhX07*qoM6N<$f_wCXEdT%j literal 0 HcmV?d00001 diff --git a/docs/html/img91.png b/docs/html/img91.png new file mode 100644 index 0000000000000000000000000000000000000000..c266352ec4860c3453473840e4f9e573cff1ae82 GIT binary patch literal 223 zcmeAS@N?(olHy`uVBq!ia0vp@K+Mm=%)r37i!0+2kfR&m6XLpg^X3&RR?L|*XTpRD zEiEk-6%{!-ISB~~At50i9v(I}HUO}I`xC}G$X zE_A6~{6oW6w41D^cQ{yKZ RCjcGC;OXk;vd$@?2>{b?S1kYl literal 0 HcmV?d00001 diff --git a/docs/html/img93.png b/docs/html/img93.png new file mode 100644 index 0000000000000000000000000000000000000000..fb6b7f9cead5d6bd428a5978d231a459559f2097 GIT binary patch literal 634 zcmV-=0)_pFP)RHR400001 zbW%=J06^y0W&i*I_(?=TR7i>KRljf3KotJ$T%2=jVlPN#bJ-{$B1R^U6-zU*WbxQ; z5o4Dg6ePD25QGHXNdJSZ-7JupEhMClNJyQprRs*@J)f<(B(jV|6$U=(?)~$*Fcukn#oSV%*(*|!yKCE|la^Daw!K9}6r%2WOFpFE*M*$d(zGE* zOeL5ixT5@<<7XZ86)bpnt~QVw4?{kAb4uc&rJ-c<)W@>XDBDnX{CZbFPTHKQ4*@(; zko}&qrlL*NcZR*P`i>+^I?j0!4r6Za{U9#aS*7u{@C`@VNTBC-j405ZD56p6o0k|SCX8pqxXRAdQ82(~_N3F+-w2JX{VEAzr}V{O|2kg^OAb3DRB(dU`OQ=8 zfUS>(c5rkl9nFvQmokxVSXozSc*<4QIX-~@6Bm&n-tXXT@+RN!cUR4n=^*!tX7p%U=h^k literal 0 HcmV?d00001 diff --git a/docs/html/img94.png b/docs/html/img94.png new file mode 100644 index 0000000000000000000000000000000000000000..a6754f48c035fca8ea45d27b2b04e5bfa9122f39 GIT binary patch literal 257 zcmeAS@N?(olHy`uVBq!ia0vp^Vn8gFVdQ&MBb@0O@HutpET3 literal 0 HcmV?d00001 diff --git a/docs/html/img96.png b/docs/html/img96.png new file mode 100644 index 0000000000000000000000000000000000000000..2c3a36e81383d14899a041603e8ffe1ac743f2b1 GIT binary patch literal 216 zcmeAS@N?(olHy`uVBq!ia0vp^d_XME!py+H81(w07m%YH;1lAydGqEKD^|>zGiSnt z2`w!x6%`dZIXMXl2_YdN9v&VB1_mlBDiRVBJUl!=9nOsVcLOQLk|4ie28U-i(tw;u zPZ!4!j+w~`3`}_f2PYgTXk?Ur5X~^@FyoEN2A1bcF_&gEOl*|(FkxYs$#2Hc$)j*E z!fj988-*mMX3hyo!gmjR;5hQU?7<9%MU|{?L=?2r8cvGJrbzHH1nuQ{%j{os6=(^A Mr>mdKI;Vst0NN}?4gdfE literal 0 HcmV?d00001 diff --git a/docs/html/img97.png b/docs/html/img97.png new file mode 100644 index 0000000000000000000000000000000000000000..a9d84a65494ef7a0d8b94a7d8bab70544847e698 GIT binary patch literal 648 zcmV;30(bq1P)RHR400001 zbW%=J06^y0W&i*J21!IgR7i>KRljf4FckjoE|+t!cjN|G!9!Is-hhf=Doov)p+X2G zK7&N`T2X# z&-Swe6mUh-hXHf+021{e&U=Xuq{R?F!S^XXy-0w7#EF~68j$zVA+)luKMmkzgn>?# zM|#M^)y`%qr>&;4YHQDkg{&oyFsWZd>?;IjcxEkg5-GApW1H9Rb%A#4vL$E2SB+iE zP+isy!1}_@%ZlNfJeu)pOdAFDAH!iC{=k^)WkX(34X^|e^db+fX$0&Sm_2k95*EpT z)C>%sI2%c$j^#rSOtqAW(YB0pgR8lJa;Zrh*c^xMfskQfHIK)VHXj=vcNpSTKUcX_ zV-FjP-K?39f<1pqkH4j7lCFX|^)dVo;}}K!jXM2ZoG%-w$d+ciD7VQt-I?!5xv(=0 zfk!2$`(vuY^ammC>M&=P(GEl*1Pfi(WAa-2y7~Pq%}a#OZNEQyLWfAF zv=V7(TZd0@ay~y+w+_r``*drb+Q9=8QLE&M7oaiiC!kcim zTkJ1oaR<)?w%xhm;?oc}qStyYycchg_@lJg?XJb`1HOW-F9H>OG-O`wsP4#YRO$k? ib#aXU6t(wSExrPC5%2_(rmHCc0000l0000mP)t-sv$M0P zsHmKroRE-^goK26czA4VY+ztuR8&+*NJu<9JTNdYBqSsl7#Iu;3;+NC>RHR400001 zbW%=J06^y0W&i*JBuPX;R7i>KRljQ#K@|RWcHNu1i`gq;mtrl1q{@OCtjv{GCW39q zmKF+ES}2TH$V75*{s%b|Fj`$BSYDAoAOsY|!t`mDaD)&9eKY$jvpLyCG#2LLcHi4K z-@N%|-pm}3!+EVuK#vCqRKy8A5!%=ltXhXFF9F^Hb>UNv1oz<5V0HTb^WZ|8AVQqp z(!sB*_~4@pF4Z)rDI~x1NHsv=sMXPFJ{p@MyIY~2^tv|K2Dl;UD^NSS)+LVAVsV!Nrw)w;jX z6rP0Yfu%|@ol}ykB-+dB@kIpdrrOItsJ&*lTUz(H`B?Qg&4mG))q2 zk7<+l^zN2E?xx}OSHb+?=@z!h=S_iYUWiNyoPreb5!T9a`t>%k8^E~p3CsE*F4CC| zdPXm^f_C@}H~F5K7|s!D2kr>(HCxz64{&S{%p@F3H(Ht04EuEKulDOgO~(%L1vO)w z!gLmii|5508jsa$c4E_1Yhw63_~D8&g9%N=5?|sHzm4*L|MENbCq1+Hu&ny59RL6T M07*qoM6N<$g2F~V0RR91 literal 0 HcmV?d00001 diff --git a/docs/html/img99.png b/docs/html/img99.png new file mode 100644 index 0000000000000000000000000000000000000000..321efb07dbe0dd29699d3f01ba644c597e805cee GIT binary patch literal 372 zcmeAS@N?(olHy`uVBq!ia0vp^20*ON!py+Hc;?45Mvy>&Pl)U0&6`)OSTSeLoCy;q zw6wHTR8-{T@*cccXsHmt&NJ#MT@BlTviab3JNHLZK`2{mLJiCzw zwL6VIF81jc3j94FbD zZV5KLWoE8tzGJ!OjGsW_f@I4I;RR_*l4lQiG~M)gU@xTLRH--P$&CXS4l;1@GAo?? z*O0V2Nm<$oNEl4|64FHD5{6Xo!DRV Q8t8ilPgg&ebxsLQ0Dw<_WdHyG literal 0 HcmV?d00001 diff --git a/docs/html/index.html b/docs/html/index.html new file mode 100644 index 00000000..18ed4357 --- /dev/null +++ b/docs/html/index.html @@ -0,0 +1,266 @@ + + + + + +userhtml + + + + + + + + + + + + + + + + +next +up +previous + +contents +
+ Next: Contents +   Contents +
+
+ + +

+ +MLD2P4 User's and Reference Guidetitle + +
+ + +
+
+MLD2P4 +
+
+User's and Reference Guide + +
+
+
+
A guide for the Multi-Level Domain Decomposition
+
+Parallel Preconditioners Package +based on PSBLAS + +
+ +

+
+ + +
+
+Pasqua D'Ambra +
ICAR-CNR, Naples, Italy +
+
+
+
Daniela di Serafino +
Second University of Naples, Italy +
+
+
+
Salvatore Filippone +
University of Rome ``Tor Vergata'', Italy + +
+ +

+
+ + +
+
+Software version: 1.0 +
+July 22, 2008 + +
+ +

+
+ +
+ +

+ +

+ +

Abstract:

+
+MLD2P4 (MULTI-LEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON +PSBLAS) is a package of parallel algebraic multi-level preconditioners. +It implements various versions of one-level additive and of multi-level additive +and hybrid Schwarz algorithms. In the multi-level case, a purely algebraic approach +is applied to generate coarse-level corrections, so that no geometric background is needed +concerning the matrix to be preconditioned. The matrix is required to be square, real +or complex, with a symmetric sparsity pattern. + +

+MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the +context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) +computational framework and can be used in conjuction with the Krylov solvers +available in this framework. MLD2P4 enables the user to easily specify different aspects +of a generic algebraic multilevel Schwarz preconditioner, thus allowing to search +for the ``best'' preconditioner for the problem at hand. + +

+The package has been designed employing object-oriented techniques, +using Fortran 95, with interfaces to additional third party libraries +such as UMFPACK, SuperLU and SuperLU_Dist, that +can be exploited in building multi-level preconditioners. The parallel +implementation is based on a Single Program Multiple Data (SPMD) +paradigm for distributed-memory architectures; the inter-process data +communication is based on MPI and is managed mainly through PSBLAS. + +

+This guide provides a brief description of the functionalities and +the user interface of MLD2P4. +

+

+ +

+ +

+ + + + + +
+ + +next +up +previous + +contents +
+ Next: Contents +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/internals.pl b/docs/html/internals.pl new file mode 100644 index 00000000..df38b3cf --- /dev/null +++ b/docs/html/internals.pl @@ -0,0 +1,190 @@ +# LaTeX2HTML 2002-2-1 (1.71) +# Associate internals original text with physical files. + + +$key = q/cite_PSBLASGUIDE/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precinit/; +$ref_files{$key} = "$dir".q|node16.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precset/; +$ref_files{$key} = "$dir".q|node18.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_dd2_96/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_Saad_book/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_CAI_SARKIS/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:conventions/; +$ref_files{$key} = "$dir".q|node3.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_SUPERLUDIST/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_dd1_94/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_TUMINARO_TONG/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precdescr/; +$ref_files{$key} = "$dir".q|node26.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_psblas_00/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/eq:tent_prol/; +$ref_files{$key} = "$dir".q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:overview/; +$ref_files{$key} = "$dir".q|node2.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:multilevel/; +$ref_files{$key} = "$dir".q|node11.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_SUPERLU/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_StubenGMD69_99/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:mlhpost_alg/; +$ref_files{$key} = "$dir".q|node11.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:userinterface/; +$ref_files{$key} = "$dir".q|node15.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:background/; +$ref_files{$key} = "$dir".q|node10.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_VANEK_MANDEL_BREZINA/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/system1/; +$ref_files{$key} = "$dir".q|node2.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_3la/; +$ref_files{$key} = "$dir".q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:license/; +$ref_files{$key} = "$dir".q|node29.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:errors/; +$ref_files{$key} = "$dir".q|node28.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_default/; +$ref_files{$key} = "$dir".q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_UMFPACK/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_apnum_07/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:started/; +$ref_files{$key} = "$dir".q|node13.html|; +$noresave{$key} = "$nosave"; + +$key = q/eq:jac_smoother/; +$ref_files{$key} = "$dir".q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_3lh/; +$ref_files{$key} = "$dir".q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precaply/; +$ref_files{$key} = "$dir".q|node22.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_BREZINA_VANEK/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_Cai_Widlund_92/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_para_04/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_EFSTATHIOU/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:aggregation/; +$ref_files{$key} = "$dir".q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:examples/; +$ref_files{$key} = "$dir".q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_MPI1/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_aaecc_07/; +$ref_files{$key} = "$dir".q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:building/; +$ref_files{$key} = "$dir".q|node5.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:distribution/; +$ref_files{$key} = "$dir".q|node4.html|; +$noresave{$key} = "$nosave"; + +$key = q/eq:smoothed_prol/; +$ref_files{$key} = "$dir".q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_1l/; +$ref_files{$key} = "$dir".q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precbld/; +$ref_files{$key} = "$dir".q|node20.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precfree/; +$ref_files{$key} = "$dir".q|node24.html|; +$noresave{$key} = "$nosave"; + +1; + diff --git a/docs/html/labels.pl b/docs/html/labels.pl new file mode 100644 index 00000000..1cf53c81 --- /dev/null +++ b/docs/html/labels.pl @@ -0,0 +1,197 @@ +# LaTeX2HTML 2002-2-1 (1.71) +# Associate labels original text with physical files. + + +$key = q/cite_PSBLASGUIDE/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precinit/; +$external_labels{$key} = "$URL/" . q|node16.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precset/; +$external_labels{$key} = "$URL/" . q|node18.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_dd2_96/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_Saad_book/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_CAI_SARKIS/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:conventions/; +$external_labels{$key} = "$URL/" . q|node3.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_SUPERLUDIST/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_dd1_94/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_TUMINARO_TONG/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precdescr/; +$external_labels{$key} = "$URL/" . q|node26.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_psblas_00/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/eq:tent_prol/; +$external_labels{$key} = "$URL/" . q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:overview/; +$external_labels{$key} = "$URL/" . q|node2.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:multilevel/; +$external_labels{$key} = "$URL/" . q|node11.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_SUPERLU/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_StubenGMD69_99/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:mlhpost_alg/; +$external_labels{$key} = "$URL/" . q|node11.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:userinterface/; +$external_labels{$key} = "$URL/" . q|node15.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:background/; +$external_labels{$key} = "$URL/" . q|node10.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_VANEK_MANDEL_BREZINA/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/system1/; +$external_labels{$key} = "$URL/" . q|node2.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_3la/; +$external_labels{$key} = "$URL/" . q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:license/; +$external_labels{$key} = "$URL/" . q|node29.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:errors/; +$external_labels{$key} = "$URL/" . q|node28.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_default/; +$external_labels{$key} = "$URL/" . q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_UMFPACK/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_apnum_07/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:started/; +$external_labels{$key} = "$URL/" . q|node13.html|; +$noresave{$key} = "$nosave"; + +$key = q/eq:jac_smoother/; +$external_labels{$key} = "$URL/" . q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_3lh/; +$external_labels{$key} = "$URL/" . q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precaply/; +$external_labels{$key} = "$URL/" . q|node22.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_BREZINA_VANEK/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_Cai_Widlund_92/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_para_04/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_EFSTATHIOU/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:aggregation/; +$external_labels{$key} = "$URL/" . q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:examples/; +$external_labels{$key} = "$URL/" . q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_MPI1/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/cite_aaecc_07/; +$external_labels{$key} = "$URL/" . q|node30.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:building/; +$external_labels{$key} = "$URL/" . q|node5.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:distribution/; +$external_labels{$key} = "$URL/" . q|node4.html|; +$noresave{$key} = "$nosave"; + +$key = q/eq:smoothed_prol/; +$external_labels{$key} = "$URL/" . q|node12.html|; +$noresave{$key} = "$nosave"; + +$key = q/fig:ex_1l/; +$external_labels{$key} = "$URL/" . q|node14.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precbld/; +$external_labels{$key} = "$URL/" . q|node20.html|; +$noresave{$key} = "$nosave"; + +$key = q/sec:precfree/; +$external_labels{$key} = "$URL/" . q|node24.html|; +$noresave{$key} = "$nosave"; + +1; + + +# LaTeX2HTML 2002-2-1 (1.71) +# labels from external_latex_labels array. + + +1; + diff --git a/docs/html/node1.html b/docs/html/node1.html new file mode 100644 index 00000000..a35b336f --- /dev/null +++ b/docs/html/node1.html @@ -0,0 +1,129 @@ + + + + + +Contents + + + + + + + + + + + + + + + + + + + +next + +up + +previous +
+ Next: General Overview + Up: userhtml + Previous: userhtml +
+
+ +
+ +

+Contents +

+ + + + + +

+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node10.html b/docs/html/node10.html new file mode 100644 index 00000000..d8ca4205 --- /dev/null +++ b/docs/html/node10.html @@ -0,0 +1,190 @@ + + + + + +Multi-level Domain Decomposition Background + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Multi-level Schwarz Preconditioners + Up: userhtml + Previous: Example and test programs +   Contents +
+
+ + +

+
+Multi-level Domain Decomposition Background +

+ +

+Domain Decomposition (DD) preconditioners, coupled with Krylov iterative +solvers, are widely used in the parallel solution of large and sparse linear systems. +These preconditioners are based on the divide and conquer technique: the matrix +to be preconditioned is divided into submatrices, a ``local'' linear system +involving each submatrix is (approximately) solved, and the local solutions are used +to build a preconditioner for the whole original matrix. This process +often corresponds to dividing a physical domain associated to the original matrix +into subdomains, e.g. in a PDE discretization, to (approximately) solving the +subproblems corresponding to the subdomains and to building an approximate +solution of the original problem from the local solutions +[6,7,15]. + +

+Additive Schwarz preconditioners are DD preconditioners using overlapping +submatrices, i.e. with some common rows, to couple the local information +related to the submatrices (see, e.g., [15]). +The main motivation for choosing Additive Schwarz preconditioners is their +intrinsic parallelism. A drawback of these +preconditioners is that the number of iterations of the preconditioned solvers +generally grows with the number of submatrices. This may be a serious limitation +on parallel computers, since the number of submatrices usually matches the number +of available processors. Optimal convergence rates, i.e. iteration numbers +independent of the number of submatrices, can be obtained by correcting the +preconditioner through a suitable approximation of the original linear system +in a coarse space, which globally couples the information related to the single +submatrices. + +

+Two-level Schwarz preconditioners are obtained +by combining basic (one-level) Schwarz preconditioners with a coarse-level +correction. In this context, the one-level preconditioner is often +called `smoother'. Different two-level preconditioners are obtained by varying the +choice of the smoother and of the coarse-level correction, and the +way they are combined [15]. The same reasoning can be applied starting +from the coarse-level system, i.e. a coarse-space correction can be built +from this system, thus obtaining multi-level preconditioners. + +

+It is worth noting that optimal preconditioners do not necessarily correspond +to minimum execution times. Indeed, to obtain effective multi-level preconditioners +a tradeoff between optimality of convergence and the cost of building and applying +the coarse-space corrections must be achieved. The choice of the number of levels, +i.e. of the coarse-space corrections, also affects the effectiveness of the +preconditioners. One more goal is to get convergence rates as less sensitive +as possible to variations in the matrix coefficients. + +

+Two main approaches can be used to build coarse-space corrections. The geometric approach +applies coarsening strategies based on the knowledge of some physical grid associated +to the matrix and requires the user to define grid transfer operators from the fine +to the coarse levels and vice versa. This may result difficult for complex geometries; +furthermore, suitable one-level preconditioners may be required to get efficient +interplay between fine and coarse levels, e.g. when matrices with highly varying coefficients +are considered. The algebraic approach builds coarse-space corrections using only matrix +information. It performs a fully automatic coarsening and enforces the interplay between +the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine +interpolation [17]. + +

+MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices +starting from the original matrix. The algebraic approach is based on the smoothed +aggregation algorithm [1,19]. A decoupled version +of this algorithm is implemented, where the smoothed aggregation is applied locally +to each submatrix [18]. In the next two subsections we provide +a brief description of the multi-level Schwarz preconditioners and of the smoothed +aggregation technique as implemented in MLD2P4. For further details the user +is referred to [2,3,4,15]. + +

+

+ +Subsections + + + +
+ + +next + +up + +previous + +contents +
+ Next: Multi-level Schwarz Preconditioners + Up: userhtml + Previous: Example and test programs +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node11.html b/docs/html/node11.html new file mode 100644 index 00000000..18e0525c --- /dev/null +++ b/docs/html/node11.html @@ -0,0 +1,774 @@ + + + + + +Multi-level Schwarz Preconditioners + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Smoothed Aggregation + Up: Multi-level Domain Decomposition Background + Previous: Multi-level Domain Decomposition Background +   Contents +
+
+ + +

+
+Multi-level Schwarz Preconditioners +

+ +

+The Multilevel preconditioners implemented in MLD2P4 are obtained by combining +AS preconditioners with coarse-space corrections; therefore +we first provide a sketch of the AS preconditioners. + +

+Given the linear system , +where +$A=(a_{ij}) \in \Re^{n \times n}$ is a +nonsingular sparse matrix with a symmetric nonzero pattern, +let $G=(W,E)$ be the adjacency graph of $A$, where +$W=\{1, 2, \ldots, n\}$ +and +$E=\{(i,j) : a_{ij} \neq 0\}$ are the vertex set and the edge set of $G$, +respectively. Two vertices are called adjacent if there is an edge connecting +them. For any integer $\delta > 0$, a $\delta$-overlap +partition of $W$ can be defined recursively as follows. +Given a 0-overlap (or non-overlapping) partition of $W$, +i.e. a set of $m$ disjoint nonempty sets +$W_i^0 \subset W$ such that + +$\cup_{i=1}^m W_i^0 = W$, a $\delta$-overlap +partition of $W$ is obtained by considering the sets + +$W_i^\delta \supset W_i^{\delta-1}$ obtained by including the vertices that +are adjacent to any vertex in +$W_i^{\delta-1}$. + +

+Let $n_i^\delta$ be the size of $W_i^\delta$ and +$R_i^{\delta} \in +\Re^{n_i^\delta \times n}$ the restriction operator that maps +a vector $v \in \Re^n$ onto the vector +$v_i^{\delta} \in \Re^{n_i^\delta}$ +containing the components of $v$ corresponding to the vertices in +$W_i^\delta$. The transpose of $R_i^{\delta}$ is a +prolongation operator from +$\Re^{n_i^\delta}$ to $\Re^n$. +The matrix +$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in +\Re^{n_i^\delta \times n_i^\delta}$ can be considered +as a restriction of $A$ corresponding to the set $W_i^{\delta}$. + +

+The classical one-level AS preconditioner is defined by +

+
+ + +\begin{displaymath} +M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T +(A_i^\delta)^{-1} R_i^{\delta}, +\end{displaymath} +
+
+

+where $A_i^\delta$ is assumed to be nonsingular. Its application +to a vector $v \in \Re^n$ within a Krylov solver requires the following +three steps: + +
    +
  1. restriction of $v$ as +$v_i = R_i^{\delta} v$, $i=1,\ldots,m$; +
    2. +
  2. solution of the linear systems +$A_i^\delta w_i = v_i$, + $i=1,\ldots,m$; +
    3. +
  3. prolongation and sum of the $w_i$'s, i.e. +$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$. +
    4. +
+Note that the linear systems at step 2 are usually solved approximately, +e.g. using incomplete LU factorizations such as ILU($p$), MILU($p$) and +ILU($p,t$) [14, Chapter 10]. + +

+A variant of the classical AS preconditioner that outperforms it +in terms of convergence rate and of computation and communication +time on parallel distributed-memory computers is the so-called Restricted AS +(RAS) preconditioner [5,10]. It +is obtained by zeroing the components of $w_i$ corresponding to the +overlapping vertices when applying the prolongation. Therefore, +RAS differs from classical AS by the prolongation operators, +which are substituted by +$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$, +where $\tilde{R}_i^0$ is obtained by zeroing the rows of $R_i^\delta$ +corresponding to the vertices in +$W_i^\delta \backslash W_i^0$: +

+
+ + +\begin{displaymath} +M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T +(A_i^\delta)^{-1} R_i^{\delta}. +\end{displaymath} +
+
+

+Analogously, the AS variant called AS with Harmonic extension (ASH) +is defined by +

+
+ + +\begin{displaymath}M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T +(A_i^\delta)^{-1} \tilde{R}_i^0. +\end{displaymath} +
+
+

+We note that for $\delta=0$ the three variants of the AS preconditioner are +all equal to the block-Jacobi preconditioner. + +

+As already observed, the convergence rate of the one-level Schwarz +preconditioned iterative solvers deteriorates as the number $m$ of partitions +of $W$ increases [7,15]. To reduce the dependency +of the number of iterations on the degree of parallelism we may +introduce a global coupling among the overlapping partitions by defining +a coarse-space approximation $A_C$ of the matrix $A$. +In a pure algebraic setting, $A_C$ is usually built with +a Galerkin approach. Given a set $W_C$ of coarse vertices, +with size $n_C$, and a suitable restriction operator + +$R_C \in \Re^{n_C \times n}$, $A_C$ is defined as +

+
+ + +\begin{displaymath} +A_C=R_C A R_C^T +\end{displaymath} +
+
+

+and the coarse-level correction matrix to be combined with a generic +one-level AS preconditioner $M_{1L}$ is obtained as +

+
+ + +\begin{displaymath} +M_{C}^{-1}= R_C^T A_C^{-1} R_C, +\end{displaymath} +
+
+

+where $A_C$ is assumed to be nonsingular. The application of $M_{C}^{-1}$ +to a vector $v$ corresponds to a restriction, a solution and +a prolongation step; the solution step, involving the matrix $A_C$, +may be carried out also approximately. + +

+The combination of $M_{C}$ and $M_{1L}$ may be +performed in either an additive or a multiplicative framework. +In the former case, the two-level additive Schwarz preconditioner +is obtained: +

+
+ + +\begin{displaymath} +M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. +\end{displaymath} +
+
+

+Applying $M_{2L-A}^{-1}$ to a vector $v$ within a Krylov solver +corresponds to applying $M_{C}^{-1}$ +and $M_{1L}^{-1}$ to $v$ independently and then summing up +the results. + +

+In the multiplicative case, the combination can be +performed by first applying the smoother $M_{1L}^{-1}$ and then +the coarse-level correction operator $M_{C}^{-1}$: +

+
+ + +\begin{displaymath} +\begin{array}{l} +w = M_{1L}^{-1} v, \\ +z = w + M_{C}^{-1} (v-Aw); +\end{array}\end{displaymath} +
+
+

+this corresponds to the following two-level hybrid pre-smoothed +Schwarz preconditioner: +

+
+ + +\begin{displaymath} +M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. +\end{displaymath} +
+
+

+On the other hand, by applying the smoother after the coarse-level correction, +i.e. by computing +

+
+ + +\begin{displaymath} +\begin{array}{l} +w = M_{C}^{-1} v , \\ +z = w + M_{1L}^{-1} (v-Aw) , +\end{array}\end{displaymath} +
+
+

+the two-level hybrid post-smoothed +Schwarz preconditioner is obtained: +

+
+ + +\begin{displaymath} +M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. +\end{displaymath} +
+
+

+One more variant of two-level hybrid preconditioner is obtained by applying +the smoother before and after the coarse-level correction. In this case, the +preconditioner is symmetric if $A$, $M_{1L}$ and $M_{C}$ are symmetric. + +

+As previously noted, on parallel computers the number of submatrices usually matches +the number of available processors. When the size of the system to be preconditioned +is very large, the use of many processors, i.e. of many small submatrices, often +leads to a large coarse-level system, whose solution may be computationally expensive. +On the other hand, the use of few processors often leads to local sumatrices that +are too expensive to be processed on single processors, because of memory and/or +computing requirements. Therefore, it seems natural to use a recursive approach, +in which the coarse-level correction is re-applied starting from the current +coarse-level system. The corresponding preconditioners, called multi-level +preconditioners, can significantly reduce the computational cost of preconditioning +with respect to the two-level case (see [15, Chapter 3]). +Additive and hybrid multilevel preconditioners +are obtained as direct extensions of the two-level counterparts. +For a detailed descrition of them, the reader is +referred to [15, Chapter 3]. +The algorithm for the application of a multi-level hybrid +post-smoothed preconditioner $M$ to a vector $v$, i.e. for the +computation of $w=M^{-1}v$, is reported, for +example, in Figure [*]. Here the number of levels +is denoted by $nlev$ and the levels are numbered in increasing order starting +from the finest one, i.e. the finest level is level 1; the coarse matrix +and the corresponding basic preconditioner at each level $l$ are denoted by $A_l$ and +$M_l$, respectively, with $A_1=A$. + +

+ + + +
Figure: +Application of the multi-level hybrid post-smoothed preconditioner.
+
+ +\framebox{ +\begin{minipage}{.85\textwidth} {\small +\begin{tabbing} +\quad \=\quad... +...= y_l+r_l$\\ +\textbf{endfor} \ [1mm] +$w = y_1$; +\end{tabbing}} +\end{minipage}} + +
+
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: Smoothed Aggregation + Up: Multi-level Domain Decomposition Background + Previous: Multi-level Domain Decomposition Background +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node12.html b/docs/html/node12.html new file mode 100644 index 00000000..2842f66b --- /dev/null +++ b/docs/html/node12.html @@ -0,0 +1,328 @@ + + + + + +Smoothed Aggregation + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Getting Started + Up: Multi-level Domain Decomposition Background + Previous: Multi-level Schwarz Preconditioners +   Contents +
+
+ + +

+
+Smoothed Aggregation +

+ +

+In order to define the restriction operator $R_C$, which is used to compute +the coarse-level matrix $A_C$, MLD2P4 uses the smoothed aggregation +algorithm described in [1,19]. +The basic idea of this algorithm is to build a coarse set of vertices +$W_C$ by suitably grouping the vertices of $W$ into disjoint subsets +(aggregates), and to define the coarse-to-fine space transfer operator $R_C^T$ by +applying a suitable smoother to a simple piecewise constant +prolongation operator, to improve the quality of the coarse-space correction. + +

+Three main steps can be identified in the smoothed aggregation procedure: + +

    +
  1. coarsening of the vertex set $W$, to obtain $W_C$; +
    2. +
  2. construction of the prolongator $R_C^T$; +
    3. +
  3. application of $R_C$ and $R_C^T$ to build $A_C$. +
    4. +
+ +

+To perform the coarsening step, we have implemented the aggregation algorithm sketched +in [4]. According to [19], a modification of +this algorithm has been actually considered, +in which each aggregate $N_r$ is made of vertices of $W$ that are strongly coupled +to a certain root vertex $r \in W$, i.e.

+
+ + +\begin{displaymath}N_r = \left\{s \in W: \vert a_{rs}\vert > \theta \sqrt{\vert a_{rr}a_{ss}\vert} \right\} +\cup \left\{ r \right\} , +\end{displaymath} +
+
+

+for a given +$\theta \in [0,1]$. +Since this algorithm has a sequential nature, a decoupled version of +it has been chosen, where each processor $i$ independently applies the algorithm to +the set of vertices $W_i^0$ assigned to it in the initial data distribution. This +version is embarrassingly parallel, since it does not require any data communication. +On the other hand, it may produce non-uniform aggregates near boundary vertices, +i.e. near vertices adjacent to vertices in other processors, and is strongly +dependent on the number of processors and on the initial partitioning of the matrix $A$. +Nevertheless, this algorithm has been chosen for the implementation in MLD2P4, +since it has been shown to produce good results in practice +[3,4,18]. + +

+The prolongator $P_C=R_C^T$ is built starting from a tentative prolongator + +$P \in \Re^{n \times n_C}$, defined as +
+

+ + + + + +
\begin{displaymath} +P=(p_{ij}), \quad p_{ij}= +\left\{ \begin{array}{ll} +1 & \qu... +...\in V^j_C \\ +0 & \quad \mbox{otherwise} +\end{array} \right. . +\end{displaymath} +(2)
+

+$P_C$ is obtained by +applying to $P$ a smoother +$S \in \Re^{n \times n}$: +
+
+ + + + + +
\begin{displaymath} +P_C = S P, +\end{displaymath} +(3)
+

+in order to remove oscillatory components from the range of the prolongator +and hence to improve the convergence properties of the multi-level +Schwarz method [1,17]. +A simple choice for $S$ is the damped Jacobi smoother: +
+
+ + + + + +
\begin{displaymath} +S = I - \omega D^{-1} A , +\end{displaymath} +(4)
+

+where the value of $\omega$ can be chosen +using some estimate of the spectral radius of $D^{-1}A$ [1]. + +

+

+ + +next + +up + +previous + +contents +
+ Next: Getting Started + Up: Multi-level Domain Decomposition Background + Previous: Multi-level Schwarz Preconditioners +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node13.html b/docs/html/node13.html new file mode 100644 index 00000000..c19e6216 --- /dev/null +++ b/docs/html/node13.html @@ -0,0 +1,258 @@ + + + + + +Getting Started + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Examples + Up: userhtml + Previous: Smoothed Aggregation +   Contents +
+
+ + +

+
+Getting Started +

+ +

+We describe the basics for building and applying MLD2P4 one-level and multi-level +Schwarz preconditioners with the Krylov solvers included in PSBLAS [11]. +The following steps are required: + +

    +
  1. Declare the preconditioner data structure. It is a derived data type, + mld_xprec_type, where x may be s, d, c + or z, according to the basic data type of the sparse matrix + (s = real single precision; d = real double precision; + c = complex single precision; z = complex double precision). + This data structure is accessed by the user only through the MLD2P4 routines, + following an object-oriented approach. +
    2. +
  2. Allocate and initialize the preconditioner data structure, according to + a preconditioner type chosen by the user. This is performed by the routine + mld_precinit, which also sets defaults for each preconditioner + type selected by the user. The defaults associated to each preconditioner + type are given in Table [*], where the strings used by + mld_precinit to identify the preconditioner types are also given. + Note that these strings are valid also if uppercase letters are substituted by + corresponding lowercase ones. +
    3. +
  3. Modify the selected preconditioner type, by properly setting + preconditioner parameters. This is performed by the routine mld_precset. + This routine must be called only if the user wants to modify the default values + of the parameters associated to the selected preconditioner type, to obtain a variant + of the preconditioner. Examples of use of mld_precset are given in + Section [*]; a complete list of all the + preconditioner parameters and their allowed and default values is provided in + Section [*], Tables [*]-[*]. +
    4. +
  4. Build the preconditioner for a given matrix. This is performed by + the routine mld_precbld. +
    5. +
  5. Apply the preconditioner at each iteration of a Krylov solver. + This is performed by the routine mld_precaply. When using the PSBLAS Krylov solvers, + this step is completely transparent to the user, since mld_precaply is called + by the PSBLAS routine implementing the Krylov solver (psb_krylov). +
    6. +
  6. Free the preconditioner data structure. This is performed by + the routine mld_precfree. This step is complementary to step 1 and should + be performed when the preconditioner is no more used. +
    7. +
+A detailed description of the above routines is given in Section [*]. +Examples showing the basic use of MLD2P4 are reported in Section [*]. + +

+Note that the Fortran 95 module mld_prec_mod, containing the definition of the +preconditioner data type and the interfaces to the routines of MLD2P4, +must be used in any program calling such routines. +The modules psb_base_mod, for the sparse matrix and communication descriptor +data types, and psb_krylov_mod, for interfacing with the +Krylov solvers, must be also used (see Section [*]). + +

+ +
Remark 1. The coarsest-level solver used by the default two-level +preconditioner has been chosen by taking into account that, on parallel +machines, it often leads to the smallest execution time when applied to +linear systems coming from finite-difference discretizations of basic +elliptic PDE problems, considered as standard tests for multi-level Schwarz +preconditioners [3,4]. However, this solver does +not necessarily correspond to the smallest number of iterations of the +preconditioned Krylov method, which is usually obtained by applying +a direct solver to the coarsest-level system, e.g. based on the LU +factorization (see Section [*] +for the coarsest-level solvers available in MLD2P4). + +

+ +
Remark 2. The include path for MLD2P4 must override +those for PSBLAS, e.g. the latter must come first in the sequence +passed to the compiler, as the MLD2P4 version of the Krylov solver +interfaces must override that of PSBLAS. This will change in the future +when the support for the class statement becomes widespread in Fortran +compilers. + +

+

+
+ + + +
Table: +Preconditioner types, corresponding strings and default choices. +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
TYPESTRINGDEFAULT PRECONDITIONER
No preconditioner'NOPREC'Considered only to use the PSBLAS + Krylov solvers with no preconditioner.
Diagonal'DIAG'--
Block Jacobi'BJAC'Block Jacobi with ILU(0) on the local blocks.
Additive Schwarz'AS'Restricted Additive Schwarz (RAS), + with overlap 1 and ILU(0) on the local blocks.
Multilevel'ML'Multi-level hybrid preconditioner (additive on the + same level and multiplicative through the levels), + with post-smoothing only. + Number of levels: 2. + Post-smoother: RAS with overlap 1 and ILU(0) + on the local blocks. + Aggregation: smoothed aggregation with + threshold $\theta = 0$. + Coarsest matrix: distributed among the processors. + Coarsest-level solver: + 4 sweeps of the block-Jacobi solver, + with LU factorization of the blocks + (UMFPACK for the double precision versions and + SuperLU for the single precision ones)
+
+ +

+

+

+
+ +

+

+ +Subsections + + + +
+ + +next + +up + +previous + +contents +
+ Next: Examples + Up: userhtml + Previous: Smoothed Aggregation +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node14.html b/docs/html/node14.html new file mode 100644 index 00000000..2cd3505f --- /dev/null +++ b/docs/html/node14.html @@ -0,0 +1,341 @@ + + + + + +Examples + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: User Interface + Up: Getting Started + Previous: Getting Started +   Contents +
+
+ + +

+
+Examples +

+ +

+The code reported in Figure [*] shows how to set and apply the default +multi-level preconditioner available in the real double precision version +of MLD2P4 (see Table [*]). This preconditioner is chosen +by simply specifying 'ML' as second argument of mld_precinit +(a call to mld_precset is not needed) and is applied with the BiCGSTAB +solver provided by PSBLAS. As previously observed, the modules psb_base_mod, +mld_prec_mod and psb_krylov_mod must be used by the example program. + +

+The part of the code concerning the +reading and assembling of the sparse matrix and the right-hand side vector, performed +through the PSBLAS routines for sparse matrix and vector management, is not reported +here for brevity; the statements concerning the deallocation of the PSBLAS +data structure are neglected too. +The complete code can be found in the example program file mld_dexample_ml.f90, +in the directory examples/fileread of the MLD2P4 tree (see +Section [*]). +For details on the use of the PSBLAS routines, see the PSBLAS User's +Guide [11]. + +

+The setup and application of the default multi-level +preconditioners for the real single precision and the complex, single and double +precision, versions are obtained with straightforward modifications of the previous +example (see Section [*] for details). If these versions are installed, +the corresponding Fortran 95 codes are available in examples/fileread/. + +

+ +

+ + + +
Figure: +Setup and application of the default multi-level Schwarz preconditioner. +
+
+
+ +
+
+  use psb_base_mod
+  use mld_prec_mod
+  use psb_krylov_mod
+... ...
+!
+! sparse matrix
+  type(psb_dspmat_type) :: A
+! sparse matrix descriptor
+  type(psb_desc_type)   :: desc_A
+! preconditioner
+  type(mld_dprec_type)  :: P
+! right-hand side and solution vectors
+  real(kind(1.d0))      :: b(:), x(:)
+... ...
+!
+! initialize the parallel environment
+  call psb_init(ictxt)
+  call psb_info(ictxt,iam,np)
+... ...
+!
+! read and assemble the matrix A and the right-hand side b 
+! using PSBLAS routines for sparse matrix / vector management 
+... ...
+!
+! initialize the default multi-level preconditioner, i.e. hybrid
+! Schwarz, using RAS (with overlap 1 and ILU(0) on the blocks) 
+! as post-smoother and 4 block-Jacobi sweeps (with UMFPACK LU
+! on the blocks) as distributed coarse-level solver
+  call mld_precinit(P,'ML',info)
+!
+! build the preconditioner
+  call mld_precbld(A,desc_A,P,info)
+!
+! set the solver parameters and the initial guess
+  ... ...
+!
+! solve Ax=b with preconditioned BiCGSTAB
+  call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info)
+  ... ...
+!
+! deallocate the preconditioner
+  call mld_precfree(P,info)
+!
+! deallocate other data structures
+  ... ...
+!
+! exit the parallel environment
+  call psb_exit(ictxt)
+  stop
+
+
+
+ +
+
+ +

+Different versions of multi-level preconditioners can be obtained by changing +the default values of the preconditioner parameters. The code reported in +Figure [*] shows how to set a three-level hybrid Schwarz +preconditioner, which uses block Jacobi with ILU(0) on the +local blocks as post-smoother, has a coarsest matrix replicated on the processors, +and solves the coarsest-level system with the LU factorization from UMFPACK [8]. +The number of levels is specified by using mld_precinit; the other +preconditioner parameters are set by calling mld_precset. Note that +the type of multilevel framework (i.e. multiplicative among the levels +with post-smoothing only) is not specified since it is the default +set by mld_precinit. + +

+Figure [*] shows how to +set a three-level additive Schwarz preconditioner, +which uses RAS, with overlap 1 and ILU(0) on the blocks, +as pre- and post-smoother, and applies five block-Jacobi sweeps, with +the UMFPACK LU factorization on the blocks, as distributed coarsest-level +solver. Again, mld_precset is used only to set +non-default values of the parameters (see Tables [*]-[*]). +In both cases, the construction and the application of the preconditioner +are carried out as for the default multi-level preconditioner. +The code fragments shown in in Figures [*]-[*] are +included in the example program file mld_dexample_ml.f90 too. + +

+Finally, Figure [*] shows the setup of a one-level +additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding +example program is available in mld_dexample_1lev.f90. + +

+For all the previous preconditioners, example programs where the sparse matrix and +the right-hand side are generated by discretizing a PDE with Dirichlet +boundary conditions are also available in the directory examples/pdegen. + +

+ +

+ + + +
Figure: +Setup of a hybrid three-level Schwarz preconditioner.
+
+
+ +
+
+... ...
+! set a three-level hybrid Schwarz preconditioner, which uses 
+! block Jacobi (with ILU(0) on the blocks) as post-smoother,
+! a coarsest matrix replicated on the processors, and the 
+! LU factorization from UMFPACK as coarse-level solver
+  call mld_precinit(P,'ML',info,nlev=3)
+  call_mld_precset(P,mld_smoother_type_,'BJAC',info)
+  call mld_precset(P,mld_coarse_mat_,'REPL',info)
+  call mld_precset(P,mld_coarse_solve_,'UMF',info)
+... ...
+
+
+
+
+

+

+
+
+ +

+ +

+ + + +
Figure: +Setup of an additive three-level Schwarz preconditioner.
+
+
+ +
+
+... ...
+! set a three-level additive Schwarz preconditioner, which uses 
+! RAS (with overlap 1 and ILU(0) on the blocks) as pre- and 
+! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
+! on the blocks) as distributed coarsest-level solver
+  call mld_precinit(P,'ML',info,nlev=3)
+  call mld_precset(P,mld_ml_type_,'ADD',info)
+  call_mld_precset(P,mld_smoother_pos_,'TWOSIDE',info)
+  call mld_precset(P,mld_coarse_sweeps_,5,info)
+... ...
+
+
+
+
+

+

+
+
+ +

+ +

+ + + +
Figure: +Setup of a one-level Schwarz preconditioner.
+
+
+ +
+
+... ...
+! set RAS with overlap 2 and ILU(0) on the local blocks
+  call mld_precinit(P,'AS',info)
+  call mld_precset(P,mld_sub_ovr_,2,info)
+... ...
+
+
+
+ +
+
+ +

+ +
Remark 3. Any PSBLAS-based program using the basic preconditioners +implemented in PSBLAS 2.0, i.e. the diagonal and block-Jacobi ones, +can use the diagonal and block-Jacobi preconditioners +implemented in MLD2P4 without any change in the code. +The PSBLAS-based program must be only recompiled +and linked to the MLD2P4 library. + +

+

+ + +next + +up + +previous + +contents +
+ Next: User Interface + Up: Getting Started + Previous: Getting Started +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node15.html b/docs/html/node15.html new file mode 100644 index 00000000..cc90b4c5 --- /dev/null +++ b/docs/html/node15.html @@ -0,0 +1,196 @@ + + + + + +User Interface + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precinit + Up: userhtml + Previous: Examples +   Contents +
+
+ + +

+
+User Interface +

+ +

+The basic user interface of MLD2P4 consists of six routines. The four routines mld_precinit, +mld_precset, mld_precbld and mld_precaply encapsulate all the functionalities +for the setup and the application of any one-level and multi-level +preconditioner implemented in the package. +The routine mld_precfree deallocates the preconditioner data structure, while +mld_precdescr prints a description of the preconditioner setup by the user. + +

+For each routine, the same user interface is overloaded with +respect to the real/complex case and the single/double precision; +arguments with appropriate data types must be passed to the routine, +i.e. + +

    +
  • the sparse matrix data structure, containing the matrix to be + preconditioned, must be of type mld_xspmat_type + with x = s for real single precision, x = d + for real double precision, x = c for complex single precision, + x = z for complex double precision; +
    • +
  • the preconditioner data structure must be of type + mld_xprec_type, with x = + s, d, c, z, according to the sparse + matrix data structure; +
    • +
  • the arrays containing the vectors $v$ and $w$ involved in + the preconditioner application $w=M^{-1}v$ must be of type + type(kind_parameter), with type = + real, complex and kind_parameter = kind(1.e0), + kind(1.d0), according to the sparse matrix and preconditioner + data structure; note that the PSBLAS module psb_base_mod + provides the constants psb_spk_ + = kind(1.e0) and psb_dpk_ = kind(1.d0); +
    • +
  • real parameters defining the preconditioner must be declared + according to the precision of the sparse matrix and preconditioner + data structures (see Section [*]). +
    • +
+A description of each routine is given in the remainder of this section. + +

+

+ +Subsections + + + +
+ + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precinit + Up: userhtml + Previous: Examples +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node16.html b/docs/html/node16.html new file mode 100644 index 00000000..51e59573 --- /dev/null +++ b/docs/html/node16.html @@ -0,0 +1,90 @@ + + + + + +Subroutine mld_precinit + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Arguments + Up: User Interface + Previous: User Interface +   Contents +
+
+ + +

+
+Subroutine mld_precinit +

+ +

+

+mld_precinit(p,ptype,info) +
mld_precinit(p,ptype,info,nlev) +
+
+ +

+This routine allocates and initializes the preconditioner data structure, +according to the preconditioner type chosen by the user. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node17.html b/docs/html/node17.html new file mode 100644 index 00000000..4cc27ced --- /dev/null +++ b/docs/html/node17.html @@ -0,0 +1,106 @@ + + + + + +Arguments + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precset + Up: Subroutine mld_precinit + Previous: Subroutine mld_precinit +   Contents +
+
+ + +

+Arguments +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ptype(mld_xprec_type), intent(inout).
 The preconditioner data structure. Note that x + must be chosen according to the real/complex, single/double + precision version of MLD2P4 under use.
ptypecharacter(len=*), intent(in).
 The type of preconditioner. Its values are specified + in Table [*].
 Note that the strings are case insensitive.
infointeger, intent(out).
 Error code. If no error, 0 is returned. See Section [*] for details.
nlevinteger, optional, intent(in).
 The number of levels of the multilevel preconditioner. + If nlev is not present and ptype='ML', 'ml', + then nlev=2 is assumed. Otherwise, nlev is ignored.
+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node18.html b/docs/html/node18.html new file mode 100644 index 00000000..d6651557 --- /dev/null +++ b/docs/html/node18.html @@ -0,0 +1,90 @@ + + + + + +Subroutine mld_precset + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Arguments + Up: User Interface + Previous: Arguments +   Contents +
+
+ + +

+
+Subroutine mld_precset +

+ +

+

+mld_precset(p,what,val,info) +
+
+ +

+This routine sets the parameters defining the preconditioner. More +precisely, the parameter identified by what is assigned the value +contained in val. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node19.html b/docs/html/node19.html new file mode 100644 index 00000000..f67181fd --- /dev/null +++ b/docs/html/node19.html @@ -0,0 +1,433 @@ + + + + + +Arguments + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precbld + Up: Subroutine mld_precset + Previous: Subroutine mld_precset +   Contents +
+
+ + +

+Arguments +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + +
ptype(mld_xprec_type), intent(inout).
 The preconditioner data structure. Note that x must + be chosen according to the real/complex, single/double precision + version of MLD2P4 under use.
whatinteger, intent(in).
 The number identifying the parameter to be set. + A mnemonic constant has been associated to each of these + numbers, as reported in Tables [*]-[*].
val integer or character(len=*) or + real(psb_spk_) or real(psb_dpk_), + intent(in).
 The value of the parameter to be set. The list of allowed + values and the corresponding data types is given in + Tables [*]-[*]. + When the value is of type character(len=*), + it is also treated as case insensitive.
infointeger, intent(out).
 Error code. If no error, 0 is returned. See Section [*] + for details.
+ +

+ +
+A variety of (one-level and multi-level) preconditioners can be obtained +by a suitable setting of the preconditioner parameters. These parameters +can be logically divided into four groups, i.e. parameters defining + +

    +
  1. the type of multi-level preconditioner; +
    2. +
  2. the one-level preconditioner used as smoother; +
    3. +
  3. the aggregation algorithm; +
    4. +
  4. the coarse-space correction at the coarsest level. +
    5. +
+A list of the parameters that can be set, along with their allowed and +default values, is given in Tables [*]-[*]. +For a detailed description of the meaning of the parameters, please +refer to Section [*]. + +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + +
whatDATA TYPEvalDEFAULTCOMMENTS
mld_ml_type_character(len=*)'ADD' 'MULT''MULT'Basic multi-level framework: additive or multiplicative + among the levels (always additive inside a level).
mld_smoother_type_character(len=*)'DIAG' 'BJAC' 'AS''AS'Basic one-level preconditioner (i.e. smoother): diagonal, + block Jacobi, AS
mld_smoother_pos_character(len=*)'PRE' 'POST' 'TWOSIDE''POST'``Position'' of the smoother: pre-smoother, post-smoother, + pre- and post-smoother.
+
+ +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
whatDATA TYPEvalDEFAULTCOMMENTS
mld_sub_ovr_integerany integer number $\ge 0$1Number of overlap layers.
mld_sub_restr_character(len=*)'HALO' 'NONE''HALO'Type of restriction operator: + 'HALO' for taking into account the overlap, 'NONE' + for neglecting it.
mld_sub_prol_character(len=*)'SUM' 'NONE''NONE'Type of prolongator operator: + 'SUM' for adding the contributions from the overlap, 'NONE' + for neglecting them.
mld_sub_solve_character(len=*)'ILU' 'MILU' 'ILUT' + 'UMF' 'SLU''UMF'Local solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU + (plus triangular solve).
mld_sub_fillin_integerAny int. num. $\ge 0$0Fill-in level $p$ of the incomplete LU factorizations.
mld_sub_iluthrs_real(kind_parameter)Any real num. $\ge 0$0.e0 (or 0.d0)Drop tolerance $t$ in the ILU($p,t$) factorization.
mld_sub_ren_character(len=*)'RENUM_NONE' 'RENUM_GLOBAL' 'RENUM_NONE'Row and column reordering of the local submatrices: no reordering, + reordering according to the global numbering of the rows and columns of + the whole matrix.
+
+ +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
whatDATA TYPEvalDEFAULTCOMMENTS
mld_aggr_alg_character(len=*)'DEC''DEC'Aggregation algorithm. Currently, only the decoupled aggregation is available.
mld_aggr_kind_character(len=*)'SMOOTH' 'RAW''SMOOTH'Type of aggregation: smoothed or raw, i.e. using the tentative prolongator.
mld_aggr_thresh_real(kind_parameter)Any real num. $\in [0, 1]$0.e0 (or 0.d0)The threshold $\theta$ in the aggregation algorithm.
mld_aggr_eig_character(len=*)'A_NORMI''A_NORMI'Estimate of the maximum eigenvalue of $D^{-1}A$ + for the smoothed aggregation. Currently, only the infinity norm of + the matrix is available.
mld_aggr_damp_real(kind_parameter)Any real num. $>0$4.e0/3.e0 (or 4.d0/3.d0)The damping parameter $\omega$ in the aggregation algorithm.
+
+ +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
whatDATA TYPEvalDEFAULTCOMMENTS
mld_coarse_mat_character(len=*)'DISTR' 'REPL''DISTR'Coarsest matrix: distributed among the processors or replicated on each of them.
mld_coarse_solve_character(len=*)'BJAC' 'UMF' 'SLU' + 'SLUDIST''BJAC'Solver used at the coarsest level: block Jacobi, sequential LU from UMFPACK, + sequential LU from SuperLU, distributed LU from SuperLU_Dist. + If the coarsest matrix is distributed, only 'BJAC' and 'SLUDIST' + can be chosen; if it is replicated, only 'BJAC' or 'SLUDIST' can + be selected.
mld_coarse_subsolve_character(len=*)'ILU' 'MILU' 'ILUT' + 'UMF' 'SLU''UMF'Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver + is chosen as coarsest-level solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, + LU from SuperLU, plus triangular solve.
mld_coarse_sweeps_integerAny int. num. $>0$4Number of Block-Jacobi sweeps when 'BJAC' is used as coarsest-level solver.
mld_coarse_fillin_integerAny int. num. $\ge 0$0Fill-in level $p$ of the incomplete LU factorizations.
mld_coarse_iluthrs_real(kind_parameter)Any real. num. $\ge 0$0.d0 (or 0.e0)Drop tolerance $t$ in the ILU($p,t$) factorization.
+
+ +

+ +

+ + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precbld + Up: Subroutine mld_precset + Previous: Subroutine mld_precset +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node2.html b/docs/html/node2.html new file mode 100644 index 00000000..c243d11a --- /dev/null +++ b/docs/html/node2.html @@ -0,0 +1,213 @@ + + + + + +General Overview + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Notational Conventions + Up: userhtml + Previous: Contents +   Contents +
+
+ + +

+
+General Overview +

+ +

+The MULTI-LEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON +PSBLAS (MLD2P4) provides multi-level Schwarz preconditioners [15], +to be used in the iterative solutions of sparse linear systems: +
+

+ + + + + +
\begin{displaymath} +Ax=b, +\end{displaymath} +(1)
+

+where $A$ is a square, real or complex, sparse matrix with a symmetric sparsity pattern. +These preconditioners have the following general features: + +
    +
  • both additive and hybrid multilevel variants are implemented, +i.e. variants that are additive among the levels and inside each level, and variants +that are multiplicative among the levels and additive inside each level; +the basic Additive Schwarz (AS) preconditioners are obtained by considering only one level; +
    • +
  • a purely algebraic approach is used to +generate a sequence of coarse-level corrections to a basic AS preconditioner, without +explicitly using any information on the geometry of the original problem (e.g. the +discretization of a PDE). The smoothed aggregation technique is applied +as algebraic coarsening strategy [1,19]. +
    • +
+ +

+The package is written in Fortran 95, following an +object-oriented approach through the exploitation of features +such as abstract data type creation, functional +overloading and dynamic memory management. +The parallel implementation is based +on a Single Program Multiple Data (SPMD) paradigm for distributed-memory architectures. +Single and double precision implementations of MLD2P4 are available for both the +real and the complex case, that can be used through a single interface. + +

+MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners +in the context of the PSBLAS (Parallel Sparse BLAS) +computational framework [12]. +PSBLAS is a library originally developed to address the parallel implementation of +iterative solvers for sparse linear system, by providing basic linear algebra +operators and data management facilities for distributed sparse matrices; it +also includes parallel Krylov solvers, built on the top of the basic PSBLAS kernels. +The preconditioners available in MLD2P4 can be used with these Krylov solvers. +The choice of PSBLAS has been mainly motivated by the need of having +a portable and efficient software infrastructure implementing ``de facto'' standard +parallel sparse linear algebra kernels, to pursue goals such as performance, +portability, modularity ed extensibility in the development of the preconditioner +package. On the other hand, the implementation of MLD2P4 has led to some +revisions and extentions of the PSBLAS kernels, leading to the +recent PSBLAS 2.0 version [11]. The inter-process comunication required +by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where +MPI [16] is explicitly called. Therefore, MLD2P4 can be run on any parallel +machine where PSBLAS and MPI implementations are available. + +

+MLD2P4 has a layered and modular software architecture where three main layers can be identified. +The lower layer consists of the PSBLAS kernels, the middle one implements +the construction and application phases of the preconditioners, and the upper one +provides a uniform and easy-to-use interface to all the preconditioners. +This architecture allows for different levels of use of the package: +few black-box routines at the upper layer allow non-expert users to easily +build any preconditioner available in MLD2P4 and to apply it within a PSBLAS Krylov solver. +On the other hand, the routines of the middle and lower layer can be used and extended +by expert users to build new versions of multi-level Schwarz preconditioners. +We provide here a description of the upper-layer routines, but not of the +medium-layer ones. + +

+This guide is organized as follows. The notational conventions used in +the guide and in the naming of the MLD2P4 routines are reported in +Section [*]. Information on the distribution of the source code and the +related license is given in Section [*], while details on the configuration +and installation of package are given in Section [*]. A description of +multi-level Schwarz preconditioners based on smoothed aggregation is provided +in Section [*], to help the users in choosing among the different preconditioners +implemented in MLD2P4. The basics for building and applying the preconditioners +with the Krylov solvers implemented in PSBLAS are reported in Section [*], where the +Fortran 95 codes of a few sample programs are also shown. A reference guide for +the upper-layer routines of MLD2P4, that are the user interface, is provided +in Section [*]. The error handling mechanism used by the package is briefly described +in Section [*]. The copyright terms concerning the distribution and modification +of MLD2P4 are reported in Appendix [*]. + +

+

+ + +next + +up + +previous + +contents +
+ Next: Notational Conventions + Up: userhtml + Previous: Contents +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node20.html b/docs/html/node20.html new file mode 100644 index 00000000..09431593 --- /dev/null +++ b/docs/html/node20.html @@ -0,0 +1,89 @@ + + + + + +Subroutine mld_precbld + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Arguments + Up: User Interface + Previous: Arguments +   Contents +
+
+ + +

+
+Subroutine mld_precbld +

+ +

+

+mld_precbld(a,desc_a,p,info) +
+
+ +

+This routine builds the preconditioner according to the requirements made by +the user through the routines mld_precinit and mld_precset. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node21.html b/docs/html/node21.html new file mode 100644 index 00000000..1ce719b8 --- /dev/null +++ b/docs/html/node21.html @@ -0,0 +1,106 @@ + + + + + +Arguments + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precaply + Up: Subroutine mld_precbld + Previous: Subroutine mld_precbld +   Contents +
+
+ + +

+Arguments +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + +
atype(psb_xspmat_type), intent(in).
 The sparse matrix structure containing the local part of the + matrix to be preconditioned. Note that x must be chosen according + to the real/complex, +single/double precision version of MLD2P4 under use. + See the PSBLAS User's Guide for details [11].
desc_atype(psb_desc_type), intent(in).
 The communication descriptor of a. See the PSBLAS User's Guide for + details [11].
ptype(mld_xprec_type), intent(inout).
 The preconditioner data structure. Note that x must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
infointeger, intent(out).
 Error code. If no error, 0 is returned. See Section [*] for details.
+ +

+ +

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node22.html b/docs/html/node22.html new file mode 100644 index 00000000..d7b78022 --- /dev/null +++ b/docs/html/node22.html @@ -0,0 +1,107 @@ + + + + + +Subroutine mld_precaply + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Arguments + Up: User Interface + Previous: Arguments +   Contents +
+
+ + +

+
+Subroutine mld_precaply +

+ +

+

+mld_precaply(p,x,y,desc_a,info) +
mld_precaply(p,x,y,desc_a,info,trans,work) +
+
+ +

+This routine computes +$y = op(M^{-1}) x$, where $M$ is a previously built +preconditioner, stored into p, and $op$ +denotes the preconditioner itself or its transpose, according to +the value of trans. +Note that, when MLD2P4 is used with a Krylov solver from PSBLAS, +mld_precaply is called within the PSBLAS routine mld_krylov +and hence it is completely transparent to the user. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node23.html b/docs/html/node23.html new file mode 100644 index 00000000..7e7ce7bd --- /dev/null +++ b/docs/html/node23.html @@ -0,0 +1,188 @@ + + + + + +Arguments + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precfree + Up: Subroutine mld_precaply + Previous: Subroutine mld_precaply +   Contents +
+
+ + +

+Arguments +

+ +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ptype(mld_xprec_type), intent(inout).
 The preconditioner data structure, containing the local part of $M$. + Note that x must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
xtype(kind_parameter), dimension(:), intent(in).
 The local part of the vector $x$. Note that type and + kind_parameter must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
ytype(kind_parameter), dimension(:), intent(out).
 The local part of the vector $y$. Note that type and + kind_parameter must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
desc_atype(psb_desc_type), intent(in).
 The communication descriptor associated to the matrix to be + preconditioned.
infointeger, intent(out).
 Error code. If no error, 0 is returned. See Section [*] for details.
transcharacter(len=1), optional, intent(in).
 If trans = 'N','n' then +$op(M^{-1}) = M^{-1}$; + if trans = 'T','t' then +$op(M^{-1}) = M^{-T}$ + (transpose of $M^{-1})$; if trans = 'C','c' then +$op(M^{-1}) = M^{-C}$ + (conjugate transpose of $M^{-1})$.
worktype(kind_parameter), dimension(:), optional, target.
 Workspace. Its size should be at + least 4 * psb_cd_get_local_cols(desc_a) (see the PSBLAS User's Guide). + Note that type and kind_parameter must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precfree + Up: Subroutine mld_precaply + Previous: Subroutine mld_precaply +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node24.html b/docs/html/node24.html new file mode 100644 index 00000000..d9639c22 --- /dev/null +++ b/docs/html/node24.html @@ -0,0 +1,88 @@ + + + + + +Subroutine mld_precfree + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Arguments + Up: User Interface + Previous: Arguments +   Contents +
+
+ + +

+
+Subroutine mld_precfree +

+ +

+

+mld_precfree(p,info) +
+
+ +

+This routine deallocates the preconditioner data structure. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node25.html b/docs/html/node25.html new file mode 100644 index 00000000..cae28244 --- /dev/null +++ b/docs/html/node25.html @@ -0,0 +1,86 @@ + + + + + +Arguments + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Subroutine mld_precdescr + Up: Subroutine mld_precfree + Previous: Subroutine mld_precfree +   Contents +
+
+ + +

+Arguments +

+ +

+ + + + + + + + + + + + + +
ptype(mld_xprec_type), intent(inout).
 The preconditioner data structure. Note that x must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
infointeger, intent(out).
 Error code. If no error, 0 is returned. See Section [*] for details.
+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node26.html b/docs/html/node26.html new file mode 100644 index 00000000..9879008b --- /dev/null +++ b/docs/html/node26.html @@ -0,0 +1,89 @@ + + + + + +Subroutine mld_precdescr + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Arguments + Up: User Interface + Previous: Arguments +   Contents +
+
+ + +

+
+Subroutine mld_precdescr +

+ +

+

+mld_precdescr(p,info) +
mld_precdescr(p,info,iout) +
+
+ +

+This routine prints a description of the preconditioner +to the standard output or to a file. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node27.html b/docs/html/node27.html new file mode 100644 index 00000000..f9432f78 --- /dev/null +++ b/docs/html/node27.html @@ -0,0 +1,93 @@ + + + + + +Arguments + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Error Handling + Up: Subroutine mld_precdescr + Previous: Subroutine mld_precdescr +   Contents +
+
+ + +

+Arguments +

+ +

+ + + + + + + + + + + + + + + + + + + +
ptype(mld_xprec_type), intent(in).
 The preconditioner data structure. Note that x must be chosen according + to the real/complex, single/double precision version of MLD2P4 under use.
infointeger, intent(out).
 Error code. If no error, 0 is returned. See Section [*] for details.
ioutinteger, intent(in), optional.
 The id of the file where the preconditioner description + will be printed; the default is the standard output.
+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node28.html b/docs/html/node28.html new file mode 100644 index 00000000..d7b07c27 --- /dev/null +++ b/docs/html/node28.html @@ -0,0 +1,84 @@ + + + + + +Error Handling + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: License + Up: userhtml + Previous: Arguments +   Contents +
+
+ + +

+
+Error Handling +

+ +

+The error handling in MLD2P4 is based on the PSBLAS version 2 error +handling. Error conditions are signaled via an integer argument +info; whenever an error condition is detected, an error trace +stack is built by the library up to the top-level, user-callable +routine. This routine will then decide, according to the user +preferences, whether the error should be handled by terminating the +program or by returning the error condition to the user code, which +will then take action, and whether +an error message should be printed. These options may be set by using +the PSBLAS error handling routines; for further details see the PSBLAS +user's guide. + +

+ +

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node29.html b/docs/html/node29.html new file mode 100644 index 00000000..7a139726 --- /dev/null +++ b/docs/html/node29.html @@ -0,0 +1,111 @@ + + + + + +License + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Bibliography + Up: userhtml + Previous: Error Handling +   Contents +
+
+ + +

+
+License +

+ +

+The MLD2P4 is freely distributable under the following copyright +terms: 

 
+                         MLD2P4  version 1.0
+MultiLevel Domain Decomposition Parallel Preconditioners Package
+           based on PSBLAS (Parallel Sparse BLAS version 2.3)
+
+(C) Copyright 2008
+
+                    Salvatore Filippone  University of Rome Tor Vergata       
+                    Alfredo Buttari      University of Rome Tor Vergata
+                    Pasqua D'Ambra       ICAR-CNR, Naples
+                    Daniela di Serafino  Second University of Naples
+
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+  1. Redistributions of source code must retain the above copyright
+     notice, this list of conditions and the following disclaimer.
+  2. Redistributions in binary form must reproduce the above copyright
+     notice, this list of conditions, and the following disclaimer in the
+     documentation and/or other materials provided with the distribution.
+  3. The name of the MLD2P4 group or the names of its contributors may
+     not be used to endorse or promote products derived from this
+     software without specific written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
+BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.
+
+ + +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node3.html b/docs/html/node3.html new file mode 100644 index 00000000..e17062f4 --- /dev/null +++ b/docs/html/node3.html @@ -0,0 +1,75 @@ + + + + + +Notational Conventions + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Code Distribution + Up: userhtml + Previous: General Overview +   Contents +
+
+ + +

+
+Notational Conventions +

+ +

+- caratteri tipografici usati nella guida (vedi guida ML recente e guida Aztec) +
- convenzioni sui nomi di routine (anche differenza nei nomi tra high-level e + medium-level?), strutture dati, moduli, costanti, etc. (vedi guida psblas) +
- versione reale e complessa, singola e doppia precisione +
+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node30.html b/docs/html/node30.html new file mode 100644 index 00000000..539409a7 --- /dev/null +++ b/docs/html/node30.html @@ -0,0 +1,179 @@ + + + + + +Bibliography + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: About this document ... + Up: userhtml + Previous: License +   Contents +

+ + +

+Bibliography +

1 +
+M. Brezina, P. Vanek, +A Black-Box Iterative Solver Based on a Two-Level Schwarz Method, +Computing, 63, 1999, 233-263. +

2 +
+A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, +Extending PSBLAS to Build Parallel Schwarz Preconditioners, +in , J. Dongarra, K. Madsen, J. Wasniewski, editors, +Proceedings of PARA 04 Workshop on State of the Art +in Scientific Computing, Lecture Notes in Computer Science, +Springer, 2005, 593-602. +

3 +
A. Buttari, P. D'Ambra, D. di Serafino, S. Filippone, +2LEV-D2P4: a package of high-performance preconditioners +for scientific and engineering applications, +Applicable Algebra in Engineering, Communications and Computing, +18, 3, 2007, 223-239. +

4 +
P. D'Ambra, S. Filippone, D. di Serafino, +On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners, +Applied Numerical Mathematics, Elsevier Science, +57, 11-12, 2007, 1181-1196. + +

+

5 +
+X. C. Cai, M. Sarkis, +A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems, +SIAM Journal on Scientific Computing, 21, 2, 1999, 792-797. +

6 +
+X. C. Cai, O. B. Widlund, +Domain Decomposition Algorithms for Indefinite Elliptic Problems, +SIAM Journal on Scientific and Statistical Computing, 13, 1, 1992, 243-258. +

7 +
+T. Chan and T. Mathew, +Domain Decomposition Algorithms, +in A. Iserles, editor, Acta Numerica 1994, 61-143. +Cambridge University Press. +

8 +
+T.A. Davis, +Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal +Method with a Column Pre-ordering Strategy, +ACM Transactions on Mathematical Software, 30, 2004, 196-199. +(See also http://www.cise.ufl.edu/ davis/) +

9 +
+J.W. Demmel, S.C. Eisenstat, J.R. Gilbert, X.S. Li and J.W.H. Liu, +A supernodal approach to sparse partial pivoting, +SIAM Journal on Matrix Analysis and Applications, 20, 3, 1999, 720-755. +

10 +
+E. Efstathiou, J. G. Gander, +Why Restricted Additive Schwarz Converges Faster than Additive Schwarz, +BIT Numerical Mathematics, 43, 2003, 945-959. +

11 +
+S. Filippone, A. Buttari, +PSBLAS-2.3 User's Guide. A Reference Guide for the Parallel Sparse BLAS Library, +available from http://www.ce.uniroma2.it/psblas/. +

12 +
+S. Filippone, M. Colajanni, +PSBLAS: A Library for Parallel Linear Algebra +Computation on Sparse Matrices, +ACM Transactions on Mathematical Software, 26, 4, 2000, 527-550. +

13 +
+X. S. Li, J. W. Demmel, SuperLU_DIST: A Scalable Distributed-memory +Sparse Direct Solver for Unsymmetric Linear Systems, +ACM Transactions on Mathematical Software, 29, 2, 2003, 110-140. +

14 +
+Y. Saad, +Iterative methods for sparse linear systems, 2nd edition, +SIAM, 2003 + +

+

15 +
+B. Smith, P. Bjorstad, W. Gropp, +Domain Decomposition: Parallel Multilevel Methods for Elliptic +Partial Differential Equations, +Cambridge University Press, 1996. +

16 +
+M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, +MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, +MIT Press, 1998. +

17 +
+K. Stüben, +Algebraic Multigrid (AMG): an Introduction with Applications, +in A. Schüller, U. Trottenberg, C. Oosterlee, editors, Multigrid, +Academic Press, 2000. +

18 +
+R. S. Tuminaro, C. Tong, +Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines, +in J. Donnelley, editor, Proceedings of SuperComputing 2000, Dallas, 2000. +

19 +
+P. Vanek, J. Mandel and M. Brezina, +Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems, +Computing, 56, 1996, 179-196. + +

+

+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node31.html b/docs/html/node31.html new file mode 100644 index 00000000..0743e8ba --- /dev/null +++ b/docs/html/node31.html @@ -0,0 +1,77 @@ + + + + + +About this document ... + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Up: userhtml + Previous: Bibliography +   Contents +
+
+ + +

+About this document ... +

+

+This document was generated using the +LaTeX2HTML translator Version 2002-2-1 (1.71) +

+Copyright © 1993, 1994, 1995, 1996, +Nikos Drakos, +Computer Based Learning Unit, University of Leeds. +
+Copyright © 1997, 1998, 1999, +Ross Moore, +Mathematics Department, Macquarie University, Sydney. +

+The command line arguments were:
+ latex2html -dir ../html userhtml.tex +

+The translation was initiated by Salvatore Filippone on 2008-07-22 +

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node4.html b/docs/html/node4.html new file mode 100644 index 00000000..ba0ac76f --- /dev/null +++ b/docs/html/node4.html @@ -0,0 +1,85 @@ + + + + + +Code Distribution + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Configuring and Building MLD2P4 + Up: userhtml + Previous: Notational Conventions +   Contents +
+
+ + +

+
+Code Distribution +

+ +

+MLD2P4 is available from our project web site +

+http://www.mld2p4.it + +
+where you will also find contact points for further information and +bug reports. + +

+The software is available under a modified BSD license, as specified +in appendix [*]; please note that some of the optional +third party libraries may be licensed under a different and more +stringent license, most notably the GPL, and this should be taken into +account when treating derived works. +

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node5.html b/docs/html/node5.html new file mode 100644 index 00000000..dcd7940b --- /dev/null +++ b/docs/html/node5.html @@ -0,0 +1,103 @@ + + + + + +Configuring and Building MLD2P4 + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Prerequisites + Up: userhtml + Previous: Code Distribution +   Contents +
+
+ + +

+
+Configuring and Building MLD2P4 +

+ +To build MLD2P4 it is necessary to set up a Makefile with appropriate +values for your system; this is done by means of the configure +script. The distribution also includes the autoconf and automake +sources employed to generate the script, but this should not normally +be needed to build the software. + +

+MLD2P4 is implemented almost entirely in Fortran 95, with some +interfaces to external libraries in C; we require the Fortran compiler +to support the Fortran 95 standard plus the extension TR15581, which +enhances the usability of ALLOCATABLE variables. Most modern +Fortran compilers support this language level. In particular, this is +supported by the GNU Fortran compiler as of version 4.2.0; however we +recommend to use the latest available release (4.3.1 at the time of +this writing§). +The software defines data types and interfaces for +real and complex data, in both single and double precision. + +

+

+ +Subsections + + + +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node6.html b/docs/html/node6.html new file mode 100644 index 00000000..f9f9e8ee --- /dev/null +++ b/docs/html/node6.html @@ -0,0 +1,137 @@ + + + + + +Prerequisites + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Optional third party libraries + Up: Configuring and Building MLD2P4 + Previous: Configuring and Building MLD2P4 +   Contents +
+
+ + +

+Prerequisites +

+The following base libraries are needed: +
+
BLAS
+
The Basic Linear Algebra subprograms. Many vendors provide + optimized versions; if no vendor version is available for a given + platform, the ATLAS software http://www.netlib.org/atlas + may be employed. The reference BLAS from Netlib + http://www.netlib.org/blas are meant to define the standard + behaviour of the BLAS interface, so they not optimized for any + particular plaftorm, and should only be used as a last + resort. Note that BLAS computation form a relatively small part of + the MLD2P4/PSBLAS computations; they are however critical when using + preconditioners based on the UMFPACK or SuperLU third party + libraries. +
+
MPI
+
A version of MPI is available on most high performance + computing system; we only require version 1.1. +
+
BLACS
+
The Basic Linear Algebra Communication Subroutines are + available in source form from http://www.netlib.org/blacs; + some vendors include them in their parallel computing + support libraries. +
+
+ +

+The MLD2P4 software requires PSBLAS version 2.3 (at least), available +from http://www.ce.uniroma2.it/psblas; indeed, all the +prerequisites listed so far are also prerequisites of PSBLAS. Please +note that to build the MLD2P4 library it is necessary to get access to +the source PSBLAS directory used to build the version under use; after +the build process completes, only the compiled form of the library is +necessary to build user applications. + +

+Please note that all the libraries listed so fare (BLAS, MPI, BLACS, +PSBLAS) must have Fortran interfaces compatible with the MLD2P4; +usually this means that they should all be built with the same +compiler. + +

+

+ + +next + +up + +previous + +contents +
+ Next: Optional third party libraries + Up: Configuring and Building MLD2P4 + Previous: Configuring and Building MLD2P4 +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node7.html b/docs/html/node7.html new file mode 100644 index 00000000..f4b5f2e4 --- /dev/null +++ b/docs/html/node7.html @@ -0,0 +1,97 @@ + + + + + +Optional third party libraries + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Configuration options + Up: Configuring and Building MLD2P4 + Previous: Prerequisites +   Contents +
+
+ + +

+Optional third party libraries +

+ +

+We provide interfaces to the following third-party software libraries; +note that these are optional, but if you enable them some defaults +for multilevel preconditioners may change to reflect their presence. + +

+

+
UMFPACK
+
A sparse direct factorization package available from +
http://www.cise.ufl.edu/research/sparse/umfpack/; + provides serial factorization and solution for double + precision real and complex double precision data. We have tested + versions 4.4 and 5.1; +
+
SuperLU
+
A sparse direct factorization package available from +
http://crd.lbl.gov/~xiaoye/SuperLU/; provides serial + factorization and solution for single and double precision real and + complex data. We have tested versions 3.0 and 3.1. +
+
SuperLU_Dist
+
A sparse direct factorization package available + from the same site as SuperLU; provides parallel factorization and + solution for real and complex double precision data. We have tested + version 2.1. +
+
+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node8.html b/docs/html/node8.html new file mode 100644 index 00000000..6a9dce9b --- /dev/null +++ b/docs/html/node8.html @@ -0,0 +1,212 @@ + + + + + +Configuration options + + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Example and test programs + Up: Configuring and Building MLD2P4 + Previous: Optional third party libraries +   Contents +
+
+ + +

+Configuration options +

+ +

+To build MLD2P4 the first step is to use the configure script +in the main directory to generate the necessary makefile(s). + +

+As a minimal example consider the following: +

+./configure --with-psblas=/home/user/PSBLAS/psblas-2.3
+
+This assumes that the various MPI compilers and support libraries are +available in the standard directories on the system. Note that the +PSBLAS build directory must be specified with an absolute path. +The full set of options may be looked at by issuing the command +./configure --help, which produces: +
+$ ./configure --help
+`configure' configures MLD2P4 1.0 to adapt to many kinds of systems.
+
+Usage: ./configure [OPTION]... [VAR=VALUE]...
+
+To assign environment variables (e.g., CC, CFLAGS...), specify them as
+VAR=VALUE.  See below for descriptions of some of the useful variables.
+
+Defaults for the options are specified in brackets.
+
+Configuration:
+  -h, --help              display this help and exit
+      --help=short        display options specific to this package
+      --help=recursive    display the short help of all the included packages
+  -V, --version           display version information and exit
+  -q, --quiet, --silent   do not print `checking...' messages
+      --cache-file=FILE   cache test results in FILE [disabled]
+  -C, --config-cache      alias for `--cache-file=config.cache'
+  -n, --no-create         do not create output files
+      --srcdir=DIR        find the sources in DIR [configure dir or `..']
+
+Installation directories:
+  --prefix=PREFIX         install architecture-independent files in PREFIX
+			  [/usr/local]
+  --exec-prefix=EPREFIX   install architecture-dependent files in EPREFIX
+			  [PREFIX]
+
+By default, `make install' will install all the files in
+`/usr/local/bin', `/usr/local/lib' etc.  You can specify
+an installation prefix other than `/usr/local' using `--prefix',
+for instance `--prefix=$HOME'.
+
+For better control, use the options below.
+
+Fine tuning of the installation directories:
+  --bindir=DIR           user executables [EPREFIX/bin]
+  --sbindir=DIR          system admin executables [EPREFIX/sbin]
+  --libexecdir=DIR       program executables [EPREFIX/libexec]
+  --sysconfdir=DIR       read-only single-machine data [PREFIX/etc]
+  --sharedstatedir=DIR   modifiable architecture-independent data [PREFIX/com]
+  --localstatedir=DIR    modifiable single-machine data [PREFIX/var]
+  --libdir=DIR           object code libraries [EPREFIX/lib]
+  --includedir=DIR       C header files [PREFIX/include]
+  --oldincludedir=DIR    C header files for non-gcc [/usr/include]
+  --datarootdir=DIR      read-only arch.-independent data root [PREFIX/share]
+  --datadir=DIR          read-only architecture-independent data [DATAROOTDIR]
+  --infodir=DIR          info documentation [DATAROOTDIR/info]
+  --localedir=DIR        locale-dependent data [DATAROOTDIR/locale]
+  --mandir=DIR           man documentation [DATAROOTDIR/man]
+  --docdir=DIR           documentation root [DATAROOTDIR/doc/mld2p4]
+  --htmldir=DIR          html documentation [DOCDIR]
+  --dvidir=DIR           dvi documentation [DOCDIR]
+  --pdfdir=DIR           pdf documentation [DOCDIR]
+  --psdir=DIR            ps documentation [DOCDIR]
+
+Optional Packages:
+  --with-PACKAGE[=ARG]    use PACKAGE [ARG=yes]
+  --without-PACKAGE       do not use PACKAGE (same as --with-PACKAGE=no)
+  --with-psblas           The source directory for PSBLAS, for example,
+                          --with-psblas=/opt/packages/psblas-2.2
+  --with-libs             List additional link flags here. For example,
+                          --with-libs=-lspecial_system_lib or
+                          --with-libs=-L/path/to/libs
+  --with-clibs            additional CLIBS flags to be added: will prepend
+                          to CLIBS
+  --with-flibs            additional FLIBS flags to be added: will prepend
+                          to FLIBS
+  --with-library-path     additional LIBRARYPATH flags to be added: will
+                          prepend to LIBRARYPATH
+  --with-include-path     additional INCLUDEPATH flags to be added: will
+                          prepend to INCLUDEPATH
+  --with-module-path      additional MODULE_PATH flags to be added: will
+                          prepend to MODULE_PATH
+  --with-umfpack=LIBNAME  Specify the library name for UMFPACK library.
+                          Default: "-lumfpack -lamd"
+  --with-umfpackdir=DIR   Specify the directory for UMFPACK library and
+                          includes.
+  --with-superlu=LIBNAME  Specify the library name for SUPERLU library.
+                          Default: "-lslu"
+  --with-superludir=DIR   Specify the directory for SUPERLU library and
+                          includes.
+  --with-superludist=LIBNAME
+                          Specify the libname for SUPERLUDIST library.
+                          Requires you also specify SuperLU. Default: "-lslud"
+  --with-superludistdir=DIR
+                          Specify the directory for SUPERLUDIST library and
+                          includes.
+
+Some influential environment variables:
+  FC          Fortran compiler command
+  FCFLAGS     Fortran compiler flags
+  LDFLAGS     linker flags, e.g. -L<lib dir> if you have libraries in a
+              nonstandard directory <lib dir>
+  LIBS        libraries to pass to the linker, e.g. -l<library>
+  CC          C compiler command
+  CFLAGS      C compiler flags
+  CPPFLAGS    C/C++/Objective C preprocessor flags, e.g. -I<include dir> if
+              you have headers in a nonstandard directory <include dir>
+  CPP         C preprocessor
+  MPICC       MPI C compiler command
+
+Use these variables to override the choices made by `configure' or to help
+it to find libraries and programs with nonstandard names/locations.
+
+Report bugs to <bugreport@mld2p4.it>.
+
+Thus, a sample build with libraries in installation +directories specifics to the GNU 4.3 compiler suite might be as +follows, specifying only the UMFPACK external package: +
+ ./configure --with-psblas=/home/user/psblas-2.3/ \
+ --with-libs="-L/usr/local/BLAS/gnu43 -L/usr/local/BLACS/gnu43" \
+ --with-blacs=-lmpiblacs  --with-umfpackdir=/usr/local/UMFPACK/gnu43
+
+Once the configure script has completed execution, it will have +generated the file Make.inc which will then be used by all +Makefiles in the directory tree. + +

+To build the library the user will now enter +

+make
+
+followed (optionally) by +
+make install
+
+ +

+

+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/node9.html b/docs/html/node9.html new file mode 100644 index 00000000..dbf041ff --- /dev/null +++ b/docs/html/node9.html @@ -0,0 +1,87 @@ + + + + + +Example and test programs + + + + + + + + + + + + + + + + + + +next + +up + +previous + +contents +
+ Next: Multi-level Domain Decomposition Background + Up: Configuring and Building MLD2P4 + Previous: Configuration options +   Contents +
+
+ + +

+Example and test programs +

+The package contains the examples and tests directories; +both of them are further divided into fileread and +pargen subdirectories. Their purpose is as follows: +
+
examples
+
contains a set of simple example programs with a + predefined choice of preconditioners, selectable via integer + values. These are intended to get an acquaintance with the + multilevel preconditioners. +
+
test
+
contains a set of more sophisticated examples that + will allow the user, via the input files in the runs + subdirectories, to experiment with the full range of preconditioners + implemented in the library. +
+
+The fileread directories contain sample programs that read +sparse matrices from files, according to the Matrix Market storage +format; the pargen instead generate matrices in full parallel +mode from the discretization of a sample PDE. +
+
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/html/userhtml.css b/docs/html/userhtml.css new file mode 100644 index 00000000..d1824aff --- /dev/null +++ b/docs/html/userhtml.css @@ -0,0 +1,30 @@ +/* Century Schoolbook font is very similar to Computer Modern Math: cmmi */ +.MATH { font-family: "Century Schoolbook", serif; } +.MATH I { font-family: "Century Schoolbook", serif; font-style: italic } +.BOLDMATH { font-family: "Century Schoolbook", serif; font-weight: bold } + +/* implement both fixed-size and relative sizes */ +SMALL.XTINY { font-size : xx-small } +SMALL.TINY { font-size : x-small } +SMALL.SCRIPTSIZE { font-size : smaller } +SMALL.FOOTNOTESIZE { font-size : small } +SMALL.SMALL { } +BIG.LARGE { } +BIG.XLARGE { font-size : large } +BIG.XXLARGE { font-size : x-large } +BIG.HUGE { font-size : larger } +BIG.XHUGE { font-size : xx-large } + +/* heading styles */ +H1 { } +H2 { } +H3 { } +H4 { } +H5 { } + +/* mathematics styles */ +DIV.displaymath { } /* math displays */ +TD.eqno { } /* equation-number cells */ + + +/* document-specific styles come next */ diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html new file mode 100644 index 00000000..18ed4357 --- /dev/null +++ b/docs/html/userhtml.html @@ -0,0 +1,266 @@ + + + + + +userhtml + + + + + + + + + + + + + + + + +next +up +previous + +contents +
+ Next: Contents +   Contents +
+
+ + +

+ +MLD2P4 User's and Reference Guidetitle + +
+ + +
+
+MLD2P4 +
+
+User's and Reference Guide + +
+
+
+
A guide for the Multi-Level Domain Decomposition
+
+Parallel Preconditioners Package +based on PSBLAS + +
+ +

+
+ + +
+
+Pasqua D'Ambra +
ICAR-CNR, Naples, Italy +
+
+
+
Daniela di Serafino +
Second University of Naples, Italy +
+
+
+
Salvatore Filippone +
University of Rome ``Tor Vergata'', Italy + +
+ +

+
+ + +
+
+Software version: 1.0 +
+July 22, 2008 + +
+ +

+
+ +
+ +

+ +

+ +

Abstract:

+
+MLD2P4 (MULTI-LEVEL DOMAIN DECOMPOSITION PARALLEL PRECONDITIONERS PACKAGE BASED ON +PSBLAS) is a package of parallel algebraic multi-level preconditioners. +It implements various versions of one-level additive and of multi-level additive +and hybrid Schwarz algorithms. In the multi-level case, a purely algebraic approach +is applied to generate coarse-level corrections, so that no geometric background is needed +concerning the matrix to be preconditioned. The matrix is required to be square, real +or complex, with a symmetric sparsity pattern. + +

+MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the +context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms) +computational framework and can be used in conjuction with the Krylov solvers +available in this framework. MLD2P4 enables the user to easily specify different aspects +of a generic algebraic multilevel Schwarz preconditioner, thus allowing to search +for the ``best'' preconditioner for the problem at hand. + +

+The package has been designed employing object-oriented techniques, +using Fortran 95, with interfaces to additional third party libraries +such as UMFPACK, SuperLU and SuperLU_Dist, that +can be exploited in building multi-level preconditioners. The parallel +implementation is based on a Single Program Multiple Data (SPMD) +paradigm for distributed-memory architectures; the inter-process data +communication is based on MPI and is managed mainly through PSBLAS. + +

+This guide provides a brief description of the functionalities and +the user interface of MLD2P4. +

+

+ +

+ +

+ + + + + +
+ + +next +up +previous + +contents +
+ Next: Contents +   Contents + +
+Salvatore Filippone +2008-07-22 +
+ + diff --git a/docs/pdf/building.tex b/docs/pdf/building.tex index eda217f0..ed6ffc89 100644 --- a/docs/pdf/building.tex +++ b/docs/pdf/building.tex @@ -91,6 +91,7 @@ PSBLAS build directory must be specified with an {\em absolute} path. The full set of options may be looked at by issuing the command \verb|./configure --help|, which produces: \begin{verbatim} +$ ./configure --help `configure' configures MLD2P4 1.0 to adapt to many kinds of systems. Usage: ./configure [OPTION]... [VAR=VALUE]... @@ -150,9 +151,9 @@ Optional Packages: --without-PACKAGE do not use PACKAGE (same as --with-PACKAGE=no) --with-psblas The source directory for PSBLAS, for example, --with-psblas=/opt/packages/psblas-2.2 - --with-libs List additional libraries here. For example, - --with-libs=-lsuperlu or - --with-libs=/path/libsuperlu.a + --with-libs List additional link flags here. For example, + --with-libs=-lspecial_system_lib or + --with-libs=-L/path/to/libs --with-clibs additional CLIBS flags to be added: will prepend to CLIBS --with-flibs additional FLIBS flags to be added: will prepend @@ -194,7 +195,7 @@ Some influential environment variables: Use these variables to override the choices made by `configure' or to help it to find libraries and programs with nonstandard names/locations. -Report bugs to . +Report bugs to . \end{verbatim} Thus, a sample build with libraries in installation directories specifics to the GNU 4.3 compiler suite might be as diff --git a/docs/userguide.pdf b/docs/userguide.pdf index 29685624..ea3faa28 100644 --- a/docs/userguide.pdf +++ b/docs/userguide.pdf @@ -1,4 +1,5 @@ %PDF-1.4 +%ÐÔÅØ 5 0 obj << /S /GoTo /D (title.0) >> endobj @@ -132,7 +133,7 @@ endobj (8 Error Handling) endobj 93 0 obj -<< /S /GoTo /D (section.A) >> +<< /S /GoTo /D (appendix.A) >> endobj 96 0 obj (A License) @@ -141,9225 +142,4996 @@ endobj << /S /GoTo /D [98 0 R /Fit ] >> endobj 100 0 obj << -/Length 1831 +/Length 1172 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 g 1 G 0 g 0 G -1 g 1 G 0 g 0 G -0 g 0 G -0 g 0 G -1 g 1 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -0.25 g 0.25 G -0 g 0 G -0.5 g 0.5 G -0 g 0 G -1 0 0 1 295.4835 -96.2627 cm -0 g 0 G -0 g 0 G -1 0 0 1 -389.4013 -618.8325 cm BT -/F19 24.7871 Tf 394.8558 618.8325 Td[(MLD2)-1(P)1(4)]TJ -229.0594 -27.0226 Td[(Us)1(e)-1(r')-1(s)-374(and)-375(Re)-1(f)1(e)-1(re)-1(nce)-375(Gui)-1(de)]TJ +/F17 24.7871 Tf 394.856 618.833 Td [(MLD2P4)]TJ -229.06 -27.023 Td [(User's)-375(and)-375(Reference)-375(Guide)]TJ ET -1 0 0 1 93.9178 573.5637 cm -0 0 412.4511 4.9813 re f -1 0 0 1 -93.9178 -573.5637 cm +q +1 0 0 1 93.918 573.564 cm +0 0 412.451 4.981 re f +Q BT -/F21 14.3462 Tf 192.4501 548.5855 Td[(A)-350(guide)-350(for)-349(the)-350(Multi-L)49(evel)-350(Domain)-350(D)-1(e)50(c)50(omp)50(osition)]TJ -5.5128 -17.2553 Td[(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioner)1(s)-350(P)-1(ackage)-350(b)50(ase)50(d)-350(on)-350(PSB)-1(LAS)]TJ -ET -1 0 0 1 400.127 451.9414 cm +/F19 14.3462 Tf 192.45 548.586 Td [(A)-350(guide)-350(for)-350(the)-350(Multi-L)50(evel)-350(Domain)-350(De)50(c)50(omp)50(osition)]TJ -5.513 -17.256 Td [(Par)50(al)-50(lel)-350(Pr)50(e)50(c)50(onditioners)-350(Package)-350(b)50(ase)50(d)-350(on)-350(PSBLAS)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -400.127 -451.9414 cm -BT -/F19 11.9552 Tf 405.5816 451.9414 Td[(P)32(asqua)-375(D'Am)31(br)-1(a)]TJ/F39 11.9552 Tf -31.5954 -13.9477 Td[(ICAR-C)-1(NR)1(,)-327(Na)1(ples)-1(,)-326(Ita)1(ly)]TJ/F19 11.9552 Tf 20.4345 -29.3898 Td[(Dani)-1(ela)-375(di)-376(Ser)-1(a)1(\014no)]TJ/F39 11.9552 Tf -62.7836 -13.9477 Td[(Second)-326(Univ)27(ersit)27(y)-326(o)1(f)-327(Na)1(ple)-1(s,)-326(Italy)]TJ/F19 11.9552 Tf 60.715 -29.3898 Td[(Salv)62(a)1(t)-1(or)-1(e)-375(Fi)-1(li)-1(pp)-31(o)-1(ne)]TJ/F39 11.9552 Tf -93.3271 -13.9477 Td[(Univ)27(ersit)28(y)-326(of)-327(R)1(ome)-326(\134T)82(or)-326(V)81(erg)1(ata)1(",)-326(Italy)]TJ -ET -1 0 0 1 393.8697 272.3948 cm +/F17 11.9552 Tf 218.645 -79.389 Td [(P)31(asqua)-375(D'Am)31(bra)]TJ/F37 11.9552 Tf -31.596 -13.947 Td [(ICAR-CNR,)-326(Naples,)-327(Italy)]TJ/F17 11.9552 Tf 20.435 -29.39 Td [(Daniela)-375(di)-375(Sera\014no)]TJ/F37 11.9552 Tf -62.784 -13.948 Td [(Second)-326(Univ)27(ersit)27(y)-326(of)-326(Naples,)-327(Italy)]TJ/F17 11.9552 Tf 60.715 -29.39 Td [(Salv)62(a)1(tore)-375(Filipp)-32(one)]TJ/F37 11.9552 Tf -93.327 -13.947 Td [(Univ)27(ersit)27(y)-326(of)-326(Rome)-327(\134)1(T)81(or)-326(V)81(ergata")1(,)-327(Italy)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -393.8697 -272.3948 cm -BT -/F39 11.9552 Tf 399.3242 272.3948 Td[(Soft)28(w)27(are)-326(v)27(ersion:)-435(1)1(.0)]TJ 38.9245 -13.9477 Td[(July)-326(20)1(,)-327(2)1(00)1(8)]TJ -ET -1 0 0 1 93.9178 91.6329 cm + 100.299 -78.924 Td [(Soft)27(w)27(a)1(re)-327(v)27(ersion:)-435(1.0)]TJ 38.925 -13.948 Td [(July)-326(22,)-327(2008)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj 98 0 obj << /Type /Page /Contents 100 0 R /Resources 99 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 112 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 106 0 R >> endobj 101 0 obj << -/D [98 0 R /XYZ 93.9178 740.0018 null] +/D [98 0 R /XYZ 93.918 740.002 null] >> endobj 102 0 obj << -/D [98 0 R /XYZ 93.9178 715.0952 null] +/D [98 0 R /XYZ 93.918 715.095 null] >> endobj 6 0 obj << -/D [98 0 R /XYZ 93.9178 715.0952 null] +/D [98 0 R /XYZ 93.918 715.095 null] >> endobj 99 0 obj << -/Font << /F19 105 0 R /F21 108 0 R /F39 111 0 R >> +/Font << /F17 103 0 R /F19 104 0 R /F37 105 0 R >> /ProcSet [ /PDF /Text ] >> endobj -115 0 obj << -/Length 136 +109 0 obj << +/Length 32 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G -1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -114 0 obj << +108 0 obj << /Type /Page -/Contents 115 0 R -/Resources 113 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 112 0 R +/Contents 109 0 R +/Resources 107 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 106 0 R >> endobj -116 0 obj << -/D [114 0 R /XYZ 141.7385 740.0018 null] +110 0 obj << +/D [108 0 R /XYZ 141.738 740.002 null] >> endobj -113 0 obj << +107 0 obj << /ProcSet [ /PDF ] >> endobj -119 0 obj << -/Length 5005 +113 0 obj << +/Length 3800 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G -1 0 0 1 -93.9178 -740.0018 cm BT -/F15 10.9091 Tf 503.3386 740.0018 Td[(i)]TJ -ET -1 0 0 1 506.3689 740.0018 cm +/F15 10.9091 Tf 503.339 740.002 Td [(i)]TJ 0 g 0 G -1 0 0 1 -233.5985 -35.8655 cm 0 g 0 G 0 g 0 G -1 0 0 1 -272.7704 -704.1363 cm -BT -/F41 9.9626 Tf 278.225 704.1363 Td[(Abstract)]TJ -ET -1 0 0 1 108.8618 685.9545 cm +/F39 9.9626 Tf -225.114 -35.866 Td [(Abstract)]TJ 0 g 0 G -1 0 0 1 21.8182 0 cm 0 g 0 G -1 0 0 1 -130.68 -685.9545 cm -BT -/F42 9.9626 Tf 136.1346 685.9545 Td[(MLD2P4)-514(\050Mul)66(ti-Level)-515(Dom)1(a)-1(in)-514(D)-1(e)1(c)-1(o)1(mpo)1(sition)-515(P)88(ara)-1(llel)-515(P)1(r)-1(e)1(c)-1(o)1(nd)-1(i-)]TJ -14.944 -11.9552 Td[(tioners)-400(P)88(a)22(cka)22(ge)-399(ba)-1(s)1(ed)-400(on)-400(P)1(SBL)-1(AS)]TJ/F15 9.9626 Tf 178.6755 0 Td[(\051)-354(is)-354(a)-355(p)1(ac)27(k)56(age)-355(of)-353(paral)1(le)-1(l)-354(al)1(ge)-1(b)1(raic)-354(m)27(u)1(lti-)]TJ -178.6755 -11.9552 Td[(lev)28(e)-1(l)-400(p)1(rec)-1(on)1(diti)1(oners.)-645(It)-401(i)1(m)-1(p)1(lem)-1(en)28(ts)-401(v)56(ar)1(ious)-400(v)28(e)-1(rsion)1(s)-401(of)-400(on)1(e)-1(-lev)28(e)-1(l)-400(ad)1(diti)1(v)28(e)-401(and)-399(of)]TJ 0 -11.9551 Td[(m)27(u)1(lti-lev)28(e)-1(l)-233(ad)1(dit)1(iv)28(e)-234(an)1(d)-233(h)28(yb)1(rid)-233(S)1(c)27(h)28(w)28(arz)-233(algorith)1(ms)-1(.)-411(In)-233(th)1(e)-234(m)28(ulti)1(-)-1(lev)28(el)-233(c)-1(ase)-1(,)-253(a)-233(pu)1(rely)]TJ 0 -11.9552 Td[(algebr)1(aic)-376(ap)1(proac)28(h)-375(is)-375(app)1(lied)-375(to)-375(generate)-375(c)-1(oar)1(s)-1(e-)-1(l)1(e)-1(v)28(el)-375(correc)-1(ti)1(ons,)-386(so)-375(that)-374(no)-375(ge)-1(o-)]TJ 0 -11.9552 Td[(me)-1(tr)1(ic)-470(b)1(ac)27(kgr)1(oun)1(d)-469(is)-469(needed)-469(conce)-1(rn)1(in)1(g)-469(the)-469(m)-1(atr)1(ix)-469(to)-469(b)-27(e)-469(precondi)1(tioned.)-851(Th)1(e)]TJ 0 -11.9551 Td[(matrix)-398(i)1(s)-399(requ)1(ired)-398(to)-398(b)-27(e)-399(squar)1(e)-1(,)-414(real)-398(or)-398(com)-1(p)1(lex,)-414(with)-398(a)-398(symm)-1(etric)-398(s)-1(p)1(arsit)28(y)-398(pat-)]TJ 0 -11.9552 Td[(tern.)]TJ 14.944 -11.9552 Td[(MLD2P)1(4)-291(has)-291(b)-28(een)-291(designed)-291(to)-291(p)1(ro)28(vid)1(e)-292(sc)-1(al)1(able)-291(and)-290(e)-1(asy-to-)-1(u)1(s)-1(e)-291(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)]TJ -14.944 -11.9551 Td[(in)-290(th)1(e)-292(con)28(text)-290(of)-291(t)1(he)-291(PS)1(B)-1(LAS)-290(\050P)29(arallel)-290(Spar)1(s)-1(e)-291(Bas)-1(i)1(c)-291(Linear)-291(Al)1(ge)-1(b)1(ra)-291(S)1(ub)1(progr)1(am)-1(s\051)]TJ 0 -11.9552 Td[(com)-1(p)1(utati)1(onal)-400(f)1(rame)-1(w)28(ork)-399(and)-399(can)-400(b)-27(e)-400(use)-1(d)-399(in)-399(conju)1(c)-1(t)1(ion)-400(wit)1(h)-400(th)1(e)-400(Kryl)1(o)27(v)-399(s)-1(ol)1(v)28(e)-1(r)1(s)]TJ 0 -11.9552 Td[(a)28(v)56(ailabl)1(e)-397(in)-395(this)-396(fr)1(am)-1(ew)27(or)1(k.)-633(M)1(LD2P4)-396(enabl)1(e)-1(s)-396(the)-396(use)-1(r)-396(to)-396(eas)-1(i)1(ly)-396(sp)-28(ec)-1(if)1(y)-396(di)1(\013)-1(eren)28(t)]TJ 0 -11.9551 Td[(asp)-28(ec)-1(ts)-383(of)-382(a)-382(ge)-1(n)1(e)-1(ri)1(c)-383(alge)-1(b)1(raic)-383(m)28(ulti)1(le)-1(v)28(el)-382(Sc)27(h)29(w)27(arz)-383(p)1(rec)-1(on)1(diti)1(oner,)-395(th)29(us)-383(allo)28(win)1(g)-383(to)]TJ 0 -11.9552 Td[(se)-1(arc)28(h)-333(for)-333(th)1(e)-334(\134b)-27(e)-1(st")-333(precondi)1(tioner)-333(for)-333(th)1(e)-334(p)1(robl)1(e)-1(m)-334(at)-333(h)1(and)1(.)]TJ 14.944 -11.9552 Td[(The)-493(pac)28(k)55(age)-493(h)1(as)-494(b)-27(e)-1(en)-493(d)1(e)-1(sign)1(e)-1(d)-492(e)-1(mpl)1(o)27(y)1(ing)-493(ob)-55(j)1(e)-1(ct-orien)28(ted)-493(tec)27(h)1(niqu)1(e)-1(s,)-533(u)1(s)-1(i)1(ng)]TJ -14.944 -11.9551 Td[(F)84(ortran)-341(95,)-343(with)-341(in)29(te)-1(r)1(face)-1(s)-342(to)-341(add)1(ition)1(al)-342(t)1(hir)1(d)-341(part)28(y)-341(lib)1(rar)1(ie)-1(s)-342(suc)28(h)-341(as)-342(UMFP)84(A)28(CK,)]TJ 0 -11.9552 Td[(Su)1(p)-27(e)-1(rLU)-266(an)1(d)-266(Su)1(p)-28(erLU)]TJ +/F40 9.9626 Tf -142.09 -18.181 Td [(MLD2P4)-514(\050Mul)66(ti-Level)-514(Domain)-514(Decomposition)-514(P)87(arallel)-514(Precondi-)]TJ -14.944 -11.956 Td [(tioners)-400(P)88(a)22(cka)22(ge)-399(based)-400(on)-400(PSBLAS)]TJ/F15 9.9626 Tf 178.675 0 Td [(\051)-354(is)-354(a)-354(pac)27(k)56(age)-354(of)-354(parallel)-355(algebr)1(a)-1(i)1(c)-355(m)28(ulti-)]TJ -178.675 -11.955 Td [(lev)28(el)-400(preconditioners.)-645(It)-401(implemen)28(ts)-400(v)55(ari)1(ous)-401(v)28(ersions)-400(of)-400(one-lev)27(el)-400(additiv)28(e)-400(and)-400(of)]TJ 0 -11.955 Td [(m)28(ulti-lev)28(el)-234(additiv)28(e)-233(and)-233(h)28(ybrid)-234(S)1(c)27(h)28(w)28(arz)-233(algorithms.)-411(In)-234(the)-233(m)28(ulti-lev)28(el)-234(case,)-253(a)-233(purely)]TJ 0 -11.955 Td [(algebraic)-375(approac)28(h)-375(is)-375(applied)-375(to)-375(generate)-375(coarse-lev)27(el)-375(corrections,)-385(so)-375(that)-375(no)-375(geo-)]TJ 0 -11.955 Td [(metric)-469(bac)28(kground)-469(is)-469(needed)-469(concerning)-469(the)-469(matrix)-469(to)-469(b)-27(e)-469(preco)-1(n)1(ditioned.)-852(The)]TJ 0 -11.956 Td [(matrix)-398(is)-398(required)-398(to)-398(b)-28(e)-398(square,)-415(real)-398(or)-398(complex,)-414(with)-398(a)-398(symme)-1(tr)1(ic)-399(sparsit)28(y)-398(pat-)]TJ 0 -11.955 Td [(tern.)]TJ 14.944 -11.955 Td [(MLD2P4)-291(has)-291(b)-28(een)-291(designed)-291(to)-291(pro)28(vide)-291(scalable)-291(and)-291(easy-to-use)-291(preconditioners)]TJ -14.944 -11.955 Td [(in)-291(th)1(e)-291(con)28(text)-291(of)-291(the)-290(PSBLAS)-291(\050P)28(arallel)-291(Sp)1(arse)-291(Basic)-291(Linear)-290(A)-1(l)1(ge)-1(b)1(ra)-291(Subprograms\051)]TJ 0 -11.955 Td [(computational)-400(framew)28(ork)-400(and)-399(can)-400(b)-28(e)-399(used)-400(in)-400(conjuction)-399(with)-400(the)-400(Krylo)28(v)-400(solv)28(ers)]TJ 0 -11.955 Td [(a)28(v)55(ailable)-396(in)-396(this)-396(framew)28(ork.)-633(MLD2P4)-396(enables)-396(the)-396(user)-396(to)-397(easily)-396(sp)-28(ecify)-396(di\013eren)28(t)]TJ 0 -11.956 Td [(asp)-28(ects)-383(of)-382(a)-383(generic)-382(algebraic)-383(m)28(ultilev)28(el)-383(Sc)28(h)28(w)27(arz)-382(preconditioner,)-395(th)28(us)-383(allo)28(wing)-383(to)]TJ 0 -11.955 Td [(searc)28(h)-334(for)-333(the)-333(\134b)-28(est")-333(preconditioner)-334(for)-333(the)-333(problem)-333(at)-334(hand.)]TJ 14.944 -11.955 Td [(The)-493(pac)28(k)55(age)-492(has)-493(b)-28(een)-493(designed)-493(emplo)28(ying)-493(ob)-56(ject-orien)28(ted)-493(tec)28(hniques,)-533(using)]TJ -14.944 -11.955 Td [(F)83(ortran)-341(95,)-343(with)-342(in)28(terfaces)-342(to)-341(additional)-341(third)-342(part)28(y)-341(libraries)-342(suc)28(h)-341(as)-342(UMFP)84(A)27(CK,)]TJ 0 -11.955 Td [(Sup)-28(erLU)-266(and)-266(Sup)-28(erLU)]TJ ET -1 0 0 1 220.9631 494.6718 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 220.963 494.871 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -220.9631 -494.6718 cm BT -/F15 9.9626 Tf 223.9519 494.6718 Td[(Dist,)-279(that)-266(can)-266(b)-28(e)-266(e)-1(xp)1(loited)-266(in)-265(bui)1(ldi)1(ng)-266(m)27(u)1(lti-lev)28(e)-1(l)-266(p)1(re)-1(cond)1(i-)]TJ -102.7613 -11.9552 Td[(tion)1(e)-1(r)1(s)-1(.)-497(The)-351(paral)1(le)-1(l)-350(im)-1(p)1(lem)-1(en)28(tation)-350(is)-351(base)-1(d)-350(on)-351(a)-351(Si)1(ngle)-351(Progr)1(am)-352(M)1(ult)1(iple)-351(Data)]TJ 0 -11.9551 Td[(\050S)1(PMD\051)-494(parad)1(igm)-496(f)1(or)-495(di)1(s)-1(tr)1(ibu)1(te)-1(d)1(-m)-1(em)-1(or)1(y)-495(arc)27(h)1(itec)-1(tu)1(res)-1(;)-576(t)1(he)-496(i)1(n)28(ter-pro)-27(c)-1(es)-1(s)-495(data)]TJ 0 -11.9552 Td[(com)-1(m)28(un)1(ic)-1(ati)1(on)-333(is)-334(b)1(as)-1(ed)-333(on)-333(MP)1(I)-334(an)1(d)-333(is)-334(managed)-333(mainl)1(y)-334(t)1(hrou)1(gh)-333(PS)1(B)-1(LAS)1(.)]TJ 14.944 -11.9552 Td[(This)-314(guid)1(e)-315(pr)1(o)28(vides)-315(a)-314(br)1(ie)-1(f)-313(des)-1(crip)1(tion)-314(of)-314(th)1(e)-315(fu)1(nction)1(alities)-315(an)1(d)-314(the)-315(u)1(s)-1(er)-314(in)28(t)1(e)-1(r-)]TJ -14.944 -11.9551 Td[(face)-334(of)-333(M)1(LD2P4.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F15 9.9626 Tf 223.952 494.672 Td [(Dist,)-280(that)-266(can)-266(b)-28(e)-266(exploited)-266(in)-267(b)1(uilding)-267(m)28(ulti-lev)28(el)-266(precondi-)]TJ -102.761 -11.955 Td [(tioners.)-498(The)-351(parall)1(e)-1(l)-351(implemen)28(tation)-351(is)-351(based)-351(on)-351(a)-351(Single)-351(Program)-351(Multiple)-351(Data)]TJ 0 -11.956 Td [(\050SPMD\051)-495(paradigm)-495(for)-495(distributed-memory)-495(arc)28(hitectures;)-576(the)-496(in)28(ter-pro)-28(cess)-495(data)]TJ 0 -11.955 Td [(comm)28(unication)-334(is)-333(based)-333(on)-334(M)1(PI)-334(and)-333(is)-333(managed)-334(mainly)-333(through)-333(PSBLAS.)]TJ 14.944 -11.955 Td [(This)-314(guide)-315(pro)28(vides)-314(a)-314(brief)-315(description)-314(of)-314(the)-315(f)1(unctionalities)-315(and)-314(the)-314(user)-315(in)28(ter-)]TJ -14.944 -11.955 Td [(face)-333(of)-334(MLD2P4.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -118 0 obj << +112 0 obj << /Type /Page -/Contents 119 0 R -/Resources 117 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 112 0 R +/Contents 113 0 R +/Resources 111 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 106 0 R >> endobj -120 0 obj << -/D [118 0 R /XYZ 93.9178 740.0018 null] +114 0 obj << +/D [112 0 R /XYZ 93.918 740.002 null] >> endobj -117 0 obj << -/Font << /F15 123 0 R /F41 126 0 R /F42 129 0 R >> +111 0 obj << +/Font << /F15 115 0 R /F39 116 0 R /F40 117 0 R >> /ProcSet [ /PDF /Text ] >> endobj -132 0 obj << -/Length 225 +120 0 obj << +/Length 82 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(ii)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(ii)]TJ 0 g 0 G -1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -131 0 obj << +119 0 obj << /Type /Page -/Contents 132 0 R -/Resources 130 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 112 0 R +/Contents 120 0 R +/Resources 118 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 106 0 R >> endobj -133 0 obj << -/D [131 0 R /XYZ 141.7385 740.0018 null] +121 0 obj << +/D [119 0 R /XYZ 141.738 740.002 null] >> endobj -130 0 obj << -/Font << /F15 123 0 R >> +118 0 obj << +/Font << /F15 115 0 R >> /ProcSet [ /PDF /Text ] >> endobj -136 0 obj << -/Length 12224 +146 0 obj << +/Length 6033 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G -1 0 0 1 -93.9178 -740.0018 cm BT -/F15 10.9091 Tf 497.278 740.0018 Td[(iii)]TJ -ET -1 0 0 1 506.3689 740.0018 cm +/F15 10.9091 Tf 497.278 740.002 Td [(iii)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(Co)-1(n)31(te)-1(n)32(t)-1(s)]TJ -ET -1 0 0 1 93.9178 679.678 cm +/F17 14.3462 Tf -403.36 -35.866 Td [(Con)31(ten)32(ts)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -679.678 cm -BT -/F41 10.9091 Tf 93.9178 679.678 Td[(1)-925(General)-384(O)1(v)32(e)-1(r)1(vi)-1(ew)]TJ -ET -1 0 0 1 209.0763 679.678 cm +/F39 10.9091 Tf 0 -24.458 Td [(1)-925(General)-383(Ov)32(erview)]TJ 0 g 0 G -1 0 0 1 -209.0763 -679.678 cm -BT -/F41 10.9091 Tf 500.0962 679.678 Td[(1)]TJ -ET -1 0 0 1 93.9178 655.2197 cm + [-26677(1)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -655.2197 cm -BT -/F41 10.9091 Tf 93.9178 655.2197 Td[(2)-925(Notati)-1(onal)-384(C)1(on)32(v)32(en)32(ti)-1(ons)]TJ -ET -1 0 0 1 239.873 655.2197 cm + 0 -24.458 Td [(2)-925(Notational)-383(Con)32(v)31(en)32(tions)]TJ 0 g 0 G -1 0 0 1 -239.873 -655.2197 cm -BT -/F41 10.9091 Tf 500.0962 655.2197 Td[(3)]TJ -ET -1 0 0 1 93.9178 630.7614 cm + [-23853(3)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -630.7614 cm -BT -/F41 10.9091 Tf 93.9178 630.7614 Td[(3)-925(Co)-31(de)-384(Distribution)]TJ -ET -1 0 0 1 209.9945 630.7614 cm + 0 -24.459 Td [(3)-925(Co)-32(de)-383(Distribution)]TJ 0 g 0 G -1 0 0 1 -209.9945 -630.7614 cm -BT -/F41 10.9091 Tf 500.0962 630.7614 Td[(4)]TJ -ET -1 0 0 1 93.9178 606.3031 cm + [-26593(4)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -606.3031 cm -BT -/F41 10.9091 Tf 93.9178 606.3031 Td[(4)-925(Con)1(\014guring)-383(and)-384(Buildi)-1(ng)-383(ML)1(D2P4)]TJ -ET -1 0 0 1 304.0302 606.3031 cm + 0 -24.458 Td [(4)-925(Con\014guring)-383(and)-384(Building)-383(MLD2P4)]TJ 0 g 0 G -1 0 0 1 -304.0302 -606.3031 cm -BT -/F41 10.9091 Tf 500.0962 606.3031 Td[(5)]TJ -ET -1 0 0 1 110.2815 592.7539 cm + [-17973(5)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -592.7539 cm -BT -/F15 10.9091 Tf 110.2815 592.7539 Td[(4.1)-1022(Pr)1(e)-1(r)1(e)-1(qu)1(isites)]TJ -ET -1 0 0 1 196.615 592.7539 cm +/F15 10.9091 Tf 16.363 -13.549 Td [(4.1)-1022(Prerequisites)]TJ 0 g 0 G -1 0 0 1 -196.615 -592.7539 cm -BT -/F15 10.9091 Tf 206.9466 592.7539 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 500.9144 592.7539 cm + [-947(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -500.9144 -592.7539 cm -BT -/F15 10.9091 Tf 500.9144 592.7539 Td[(5)]TJ -ET -1 0 0 1 506.3689 592.7539 cm + [-1781(5)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -579.2047 cm -BT -/F15 10.9091 Tf 110.2815 579.2047 Td[(4.2)-1022(Op)1(tional)-333(th)1(ird)-332(part)28(y)-333(li)1(brar)1(ie)-1(s)]TJ -ET -1 0 0 1 275.5545 579.2047 cm + 0 -13.549 Td [(4.2)-1022(Optional)-333(third)-334(part)28(y)-333(libraries)]TJ 0 g 0 G -1 0 0 1 -275.5545 -579.2047 cm -BT -/F15 10.9091 Tf 283.3093 579.2047 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 500.9144 579.2047 cm + [-711(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -500.9144 -579.2047 cm -BT -/F15 10.9091 Tf 500.9144 579.2047 Td[(6)]TJ -ET -1 0 0 1 506.3689 579.2047 cm + [-1781(6)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -565.6555 cm -BT -/F15 10.9091 Tf 110.2815 565.6555 Td[(4.3)-1022(Con\014)1(gurat)1(ion)-333(opti)1(ons)]TJ -ET -1 0 0 1 239.0999 565.6555 cm + 0 -13.549 Td [(4.3)-1022(Con\014guration)-333(options)]TJ 0 g 0 G -1 0 0 1 -239.0999 -565.6555 cm -BT -/F15 10.9091 Tf 249.3703 565.6555 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 500.9144 565.6555 cm + [-942(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -500.9144 -565.6555 cm -BT -/F15 10.9091 Tf 500.9144 565.6555 Td[(6)]TJ -ET -1 0 0 1 506.3689 565.6555 cm + [-1781(6)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -552.1063 cm -BT -/F15 10.9091 Tf 110.2815 552.1063 Td[(4.4)-1022(Ex)1(am)-1(p)1(le)-334(an)1(d)-333(te)-1(st)-333(pr)1(ograms)]TJ -ET -1 0 0 1 267.5242 552.1063 cm + 0 -13.55 Td [(4.4)-1022(Example)-334(an)1(d)-334(test)-333(programs)]TJ 0 g 0 G -1 0 0 1 -267.5242 -552.1063 cm -BT -/F15 10.9091 Tf 274.8245 552.1063 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 500.9144 552.1063 cm + [-669(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -500.9144 -552.1063 cm -BT -/F15 10.9091 Tf 500.9144 552.1063 Td[(9)]TJ -ET -1 0 0 1 506.3689 552.1063 cm + [-1780(9)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -527.648 cm -BT -/F41 10.9091 Tf 93.9178 527.648 Td[(5)-925(Multi)-1(-le)-1(v)32(el)-383(Dom)-1(ain)-383(Decom)-1(p)-32(os)1(i)-1(tion)-383(B)-1(ac)32(kgr)1(ound)]TJ -ET -1 0 0 1 372.1752 527.648 cm +/F39 10.9091 Tf -16.363 -24.458 Td [(5)-925(Multi-lev)32(el)-384(Domain)-383(Decomp)-32(osition)-383(Bac)32(kground)]TJ 0 g 0 G -1 0 0 1 -372.1752 -527.648 cm -BT -/F41 10.9091 Tf 493.8236 527.648 Td[(10)]TJ -ET -1 0 0 1 110.2815 514.0988 cm + [-11152(10)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -514.0988 cm -BT -/F15 10.9091 Tf 110.2815 514.0988 Td[(5.1)-1022(Mu)1(lti-lev)28(e)-1(l)-333(S)1(c)27(h)28(w)28(arz)-334(P)1(rec)-1(on)1(diti)1(oners)]TJ -ET -1 0 0 1 306.5847 514.0988 cm +/F15 10.9091 Tf 16.363 -13.549 Td [(5.1)-1022(Multi-lev)28(el)-334(Sc)28(h)28(w)28(arz)-334(Preconditioners)]TJ 0 g 0 G -1 0 0 1 -306.5847 -514.0988 cm -BT -/F15 10.9091 Tf 317.2482 514.0988 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 514.0988 cm + [-977(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -514.0988 cm -BT -/F15 10.9091 Tf 495.4598 514.0988 Td[(11)]TJ -ET -1 0 0 1 506.3689 514.0988 cm + [-1280(11)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -500.5496 cm -BT -/F15 10.9091 Tf 110.2815 500.5496 Td[(5.2)-1022(Smo)-28(oth)1(e)-1(d)-332(Aggre)-1(gat)1(ion)]TJ -ET -1 0 0 1 244.4938 500.5496 cm + 0 -13.549 Td [(5.2)-1022(Smo)-28(othed)-333(Aggregation)]TJ 0 g 0 G -1 0 0 1 -244.4938 -500.5496 cm -BT -/F15 10.9091 Tf 249.3703 500.5496 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 500.5496 cm + [-447(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -500.5496 cm -BT -/F15 10.9091 Tf 495.4598 500.5496 Td[(13)]TJ -ET -1 0 0 1 506.3689 500.5496 cm + [-1281(13)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -476.0913 cm -BT -/F41 10.9091 Tf 93.9178 476.0913 Td[(6)-925(Gett)-1(ing)-383(Started)]TJ -ET -1 0 0 1 197.2733 476.0913 cm +/F39 10.9091 Tf -16.363 -24.459 Td [(6)-925(Getting)-383(Started)]TJ 0 g 0 G -1 0 0 1 -197.2733 -476.0913 cm -BT -/F41 10.9091 Tf 493.8236 476.0913 Td[(16)]TJ -ET -1 0 0 1 110.2815 462.5421 cm + [-27184(16)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -462.5421 cm -BT -/F15 10.9091 Tf 110.2815 462.5421 Td[(6.1)-1022(Ex)1(am)-1(p)1(les)]TJ -ET -1 0 0 1 181.3422 462.5421 cm +/F15 10.9091 Tf 16.363 -13.549 Td [(6.1)-1022(Examples)]TJ 0 g 0 G -1 0 0 1 -181.3422 -462.5421 cm -BT -/F15 10.9091 Tf 189.9771 462.5421 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 495.4598 462.5421 cm + [-792(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -462.5421 cm -BT -/F15 10.9091 Tf 495.4598 462.5421 Td[(18)]TJ -ET -1 0 0 1 506.3689 462.5421 cm + [-1280(18)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -438.0837 cm -BT -/F41 10.9091 Tf 93.9178 438.0837 Td[(7)-925(Us)1(er)-383(In)32(t)-1(er)1(f)-1(ace)]TJ -ET -1 0 0 1 188.4113 438.0837 cm +/F39 10.9091 Tf -16.363 -24.458 Td [(7)-925(User)-383(In)32(terface)]TJ 0 g 0 G -1 0 0 1 -188.4113 -438.0837 cm -BT -/F41 10.9091 Tf 493.8236 438.0837 Td[(21)]TJ -ET -1 0 0 1 110.2815 424.5345 cm + [-27997(21)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -424.5346 cm -BT -/F15 10.9091 Tf 110.2815 424.5346 Td[(7.1)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ +/F15 10.9091 Tf 16.363 -13.549 Td [(7.1)-1022(Subroutine)-333(mld)]TJ ET -1 0 0 1 209.9968 424.5346 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 209.997 424.734 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -209.9968 -424.5346 cm BT -/F15 10.9091 Tf 213.2696 424.5346 Td[(pr)1(e)-1(cin)1(it)]TJ -ET -1 0 0 1 249.6636 424.5346 cm +/F15 10.9091 Tf 213.27 424.535 Td [(precinit)]TJ 0 g 0 G -1 0 0 1 -249.6636 -424.5346 cm -BT -/F15 10.9091 Tf 257.855 424.5346 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 424.5346 cm + [-751(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -424.5346 cm -BT -/F15 10.9091 Tf 495.4598 424.5346 Td[(21)]TJ -ET -1 0 0 1 506.3689 424.5346 cm + [-1281(21)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -410.9854 cm -BT -/F15 10.9091 Tf 110.2815 410.9854 Td[(7.2)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ + -102.989 -13.55 Td [(7.2)-1022(Subroutine)-333(mld)]TJ ET -1 0 0 1 209.9968 410.9854 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 209.997 411.185 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -209.9968 -410.9854 cm BT -/F15 10.9091 Tf 213.2696 410.9854 Td[(pr)1(e)-1(cs)-1(et)]TJ -ET -1 0 0 1 246.6938 410.9854 cm +/F15 10.9091 Tf 213.27 410.985 Td [(precset)]TJ 0 g 0 G -1 0 0 1 -246.6938 -410.9854 cm -BT -/F15 10.9091 Tf 257.855 410.9854 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 410.9854 cm + [-1023(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -410.9854 cm -BT -/F15 10.9091 Tf 495.4598 410.9854 Td[(22)]TJ -ET -1 0 0 1 506.3689 410.9854 cm + [-1281(22)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -397.4362 cm -BT -/F15 10.9091 Tf 110.2815 397.4362 Td[(7.3)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ + -102.989 -13.549 Td [(7.3)-1022(Subroutine)-333(mld)]TJ ET -1 0 0 1 209.9968 397.4362 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 209.997 397.635 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -209.9968 -397.4362 cm BT -/F15 10.9091 Tf 213.2696 397.4362 Td[(pr)1(e)-1(cbl)1(d)]TJ -ET -1 0 0 1 248.4514 397.4362 cm +/F15 10.9091 Tf 213.27 397.436 Td [(precbld)]TJ 0 g 0 G -1 0 0 1 -248.4514 -397.4362 cm -BT -/F15 10.9091 Tf 257.855 397.4362 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 397.4362 cm + [-862(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -397.4362 cm -BT -/F15 10.9091 Tf 495.4598 397.4362 Td[(28)]TJ -ET -1 0 0 1 506.3689 397.4362 cm + [-1281(28)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -383.887 cm -BT -/F15 10.9091 Tf 110.2815 383.887 Td[(7.4)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ + -102.989 -13.549 Td [(7.4)-1022(Subroutine)-333(mld)]TJ ET -1 0 0 1 209.9968 383.887 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 209.997 384.086 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -209.9968 -383.887 cm BT -/F15 10.9091 Tf 213.2696 383.887 Td[(pr)1(e)-1(capl)1(y)]TJ -ET -1 0 0 1 253.603 383.887 cm +/F15 10.9091 Tf 213.27 383.887 Td [(precaply)]TJ 0 g 0 G -1 0 0 1 -253.603 -383.887 cm -BT -/F15 10.9091 Tf 257.855 383.887 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 383.887 cm + [-390(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -383.887 cm -BT -/F15 10.9091 Tf 495.4598 383.887 Td[(29)]TJ -ET -1 0 0 1 506.3689 383.887 cm + [-1281(29)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -370.3378 cm -BT -/F15 10.9091 Tf 110.2815 370.3378 Td[(7.5)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ + -102.989 -13.549 Td [(7.5)-1022(Subroutine)-333(mld)]TJ ET -1 0 0 1 209.9968 370.3378 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 209.997 370.537 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -209.9968 -370.3378 cm BT -/F15 10.9091 Tf 213.2696 370.3378 Td[(pr)1(e)-1(cfr)1(e)-1(e)]TJ -ET -1 0 0 1 250.6029 370.3378 cm +/F15 10.9091 Tf 213.27 370.338 Td [(precfree)]TJ 0 g 0 G -1 0 0 1 -250.6029 -370.3378 cm -BT -/F15 10.9091 Tf 257.855 370.3378 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 495.4598 370.3378 cm + [-665(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -370.3378 cm -BT -/F15 10.9091 Tf 495.4598 370.3378 Td[(29)]TJ -ET -1 0 0 1 506.3689 370.3378 cm + [-1281(29)]TJ 0 g 0 G -1 0 0 1 -396.0874 -13.5492 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -110.2815 -356.7886 cm -BT -/F15 10.9091 Tf 110.2815 356.7886 Td[(7.6)-1022(Su)1(br)1(outin)1(e)-334(mld)]TJ + -102.989 -13.549 Td [(7.6)-1022(Subroutine)-333(mld)]TJ ET -1 0 0 1 209.9968 356.7886 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 209.997 356.988 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -209.9968 -356.7886 cm BT -/F15 10.9091 Tf 213.2696 356.7886 Td[(pr)1(e)-1(cdes)-1(cr)]TJ -ET -1 0 0 1 257.6332 356.7886 cm +/F15 10.9091 Tf 213.27 356.789 Td [(precdescr)]TJ 0 g 0 G -1 0 0 1 -257.6332 -356.7886 cm -BT -/F15 10.9091 Tf 266.3398 356.7886 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 495.4598 356.7886 cm + [-798(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -495.4598 -356.7886 cm -BT -/F15 10.9091 Tf 495.4598 356.7886 Td[(30)]TJ -ET -1 0 0 1 506.3689 356.7886 cm + [-1281(30)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.4583 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -332.3303 cm -BT -/F41 10.9091 Tf 93.9178 332.3303 Td[(8)-925(Er)1(ror)-383(Handling)]TJ -ET -1 0 0 1 194.5461 332.3303 cm +/F39 10.9091 Tf -119.352 -24.459 Td [(8)-925(Error)-383(Handling)]TJ 0 g 0 G -1 0 0 1 -194.5461 -332.3303 cm -BT -/F41 10.9091 Tf 493.8236 332.3303 Td[(31)]TJ -ET -1 0 0 1 93.9178 307.872 cm + [-27434(31)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -307.872 cm -BT -/F41 10.9091 Tf 93.9178 307.872 Td[(A)-631(License)]TJ -ET -1 0 0 1 150.3055 307.872 cm + 0 -24.458 Td [(A)-631(License)]TJ 0 g 0 G -1 0 0 1 -150.3055 -307.872 cm -BT -/F41 10.9091 Tf 493.8236 307.872 Td[(33)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [-31489(33)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -135 0 obj << +145 0 obj << /Type /Page -/Contents 136 0 R -/Resources 134 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 112 0 R -/Annots [ 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 144 0 R 145 0 R 146 0 R 147 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R 159 0 R 160 0 R ] +/Contents 146 0 R +/Resources 144 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 106 0 R +/Annots [ 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R 129 0 R 130 0 R 131 0 R 132 0 R 133 0 R 134 0 R 135 0 R 136 0 R 137 0 R 138 0 R 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R ] >> endobj -139 0 obj << +122 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 678.6818 210.0726 688.25] +/Rect [92.922 678.682 210.073 688.25] /Subtype /Link /A << /S /GoTo /D (section.1) >> >> endobj -140 0 obj << +123 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 654.2234 240.8693 663.7917] +/Rect [92.922 654.223 240.869 663.792] /Subtype /Link /A << /S /GoTo /D (section.2) >> >> endobj -141 0 obj << +124 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 629.7651 210.9907 639.3334] +/Rect [92.922 629.765 210.991 639.333] /Subtype /Link /A << /S /GoTo /D (section.3) >> >> endobj -142 0 obj << +125 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 603.1856 305.0265 614.8751] +/Rect [92.922 603.186 305.026 614.875] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -143 0 obj << +126 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 589.6364 197.6112 601.2047] +/Rect [109.285 589.636 197.611 601.205] /Subtype /Link /A << /S /GoTo /D (subsection.4.1) >> >> endobj -144 0 obj << +127 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 576.0872 276.5508 587.7767] +/Rect [109.285 576.087 276.551 587.777] /Subtype /Link /A << /S /GoTo /D (subsection.4.2) >> >> endobj -145 0 obj << +128 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 562.538 240.0962 574.2275] +/Rect [109.285 562.538 240.096 574.228] /Subtype /Link /A << /S /GoTo /D (subsection.4.3) >> >> endobj -146 0 obj << +129 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 548.9888 268.5204 560.6783] +/Rect [109.285 548.989 268.52 560.678] /Subtype /Link /A << /S /GoTo /D (subsection.4.4) >> >> endobj -147 0 obj << +130 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 524.5305 373.1715 536.22] +/Rect [92.922 524.531 373.171 536.22] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -148 0 obj << +131 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 513.1025 307.581 522.6708] +/Rect [109.285 513.103 307.581 522.671] /Subtype /Link /A << /S /GoTo /D (subsection.5.1) >> >> endobj -149 0 obj << +132 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 497.4321 245.4901 509.1216] +/Rect [109.285 497.432 245.49 509.122] /Subtype /Link /A << /S /GoTo /D (subsection.5.2) >> >> endobj -150 0 obj << +133 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 472.9738 198.2696 484.6633] +/Rect [92.922 472.974 198.27 484.663] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -151 0 obj << +134 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 459.4246 182.3385 471.1141] +/Rect [109.285 459.425 182.338 471.114] /Subtype /Link /A << /S /GoTo /D (subsection.6.1) >> >> endobj -152 0 obj << +135 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 437.0875 189.4076 446.6558] +/Rect [92.922 437.087 189.408 446.656] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -153 0 obj << +136 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 421.4171 250.6598 433.1066] +/Rect [109.285 421.417 250.66 433.107] /Subtype /Link /A << /S /GoTo /D (subsection.7.1) >> >> endobj -154 0 obj << +137 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 407.8679 247.6901 419.5574] +/Rect [109.285 407.868 247.69 419.557] /Subtype /Link /A << /S /GoTo /D (subsection.7.2) >> >> endobj -155 0 obj << +138 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 394.3187 249.4477 406.0082] +/Rect [109.285 394.319 249.448 406.008] /Subtype /Link /A << /S /GoTo /D (subsection.7.3) >> >> endobj -156 0 obj << +139 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 380.7695 254.5992 392.459] +/Rect [109.285 380.77 254.599 392.459] /Subtype /Link /A << /S /GoTo /D (subsection.7.4) >> >> endobj -157 0 obj << +140 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 367.2203 251.5992 378.9098] +/Rect [109.285 367.22 251.599 378.91] /Subtype /Link /A << /S /GoTo /D (subsection.7.5) >> >> endobj -158 0 obj << +141 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [109.2852 353.6711 258.6295 365.3606] +/Rect [109.285 353.671 258.629 365.361] /Subtype /Link /A << /S /GoTo /D (subsection.7.6) >> >> endobj -159 0 obj << +142 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 329.2128 195.5424 340.9023] +/Rect [92.922 329.213 195.542 340.902] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -160 0 obj << +143 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 306.8757 151.3017 316.444] +/Rect [92.922 306.876 151.302 316.444] /Subtype /Link -/A << /S /GoTo /D (section.A) >> +/A << /S /GoTo /D (appendix.A) >> >> endobj -137 0 obj << -/D [135 0 R /XYZ 93.9178 740.0018 null] +147 0 obj << +/D [145 0 R /XYZ 93.918 740.002 null] >> endobj -138 0 obj << -/D [135 0 R /XYZ 93.9178 693.3333 null] +148 0 obj << +/D [145 0 R /XYZ 93.918 693.333 null] >> endobj -134 0 obj << -/Font << /F15 123 0 R /F19 105 0 R /F41 126 0 R >> +144 0 obj << +/Font << /F15 115 0 R /F17 103 0 R /F39 116 0 R >> /ProcSet [ /PDF /Text ] >> endobj -163 0 obj << -/Length 225 +151 0 obj << +/Length 82 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(iv)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(iv)]TJ 0 g 0 G -1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -162 0 obj << +150 0 obj << /Type /Page -/Contents 163 0 R -/Resources 161 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 112 0 R +/Contents 151 0 R +/Resources 149 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 106 0 R >> endobj -164 0 obj << -/D [162 0 R /XYZ 141.7385 740.0018 null] +152 0 obj << +/D [150 0 R /XYZ 141.738 740.002 null] >> endobj -161 0 obj << -/Font << /F15 123 0 R >> +149 0 obj << +/Font << /F15 115 0 R >> /ProcSet [ /PDF /Text ] >> endobj -167 0 obj << -/Length 11573 +162 0 obj << +/Length 8037 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(1)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(1)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Genera)-1(l)-378(O)29(v)-1(e)1(r)88(view)]TJ/F15 10.9091 Tf 396.8452 0 Td[(1)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(General)-378(O)30(ver)88(view)]TJ/F15 10.9091 Tf 406.996 0 Td [(1)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(1)-1125(G)-1(ener)-1(al)-375(Ov)31(ervi)-1(ew)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(The)]TJ/F42 10.9091 Tf 23.4074 0 Td[(Mul)66(ti-Level)-473(Dom)1(a)-1(in)-473(Deco)1(mpo)1(sition)-473(P)88(ara)-1(llel)-473(Preco)1(n)-1(diti)-1(o)1(ners)-473(P)88(a)22(ck-)]TJ -23.4074 -13.5492 Td[(a)22(ge)-278(based)-278(o)1(n)-278(PSBLAS)-278(\050MLD2P4)]TJ/F15 10.9091 Tf 174.5401 0 Td[(\051)-238(p)1(ro)28(vid)1(e)-1(s)]TJ/F20 10.9091 Tf 48.9208 0 Td[(mu)1(lti-l)1(evel)-270(Schw)-1(ar)1(z)-270(pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 168.9902 0 Td[([)]TJ -ET -1 0 0 1 489.3992 666.2349 cm +/F17 14.3462 Tf -406.996 -35.866 Td [(1)-1125(General)-375(Ov)31(erview)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)]TJ/F40 10.9091 Tf 23.407 0 Td [(Mul)67(ti-Level)-473(Domain)-472(Decomposition)-472(P)87(arallel)-472(Preconditioners)-473(P)88(a)22(ck-)]TJ -23.407 -13.549 Td [(a)22(ge)-277(ba)-1(s)1(ed)-278(on)-278(PSBLAS)-278(\050MLD)1(2P4)]TJ/F15 10.9091 Tf 174.54 0 Td [(\051)-238(pro)28(vides)]TJ/F18 10.9091 Tf 48.921 0 Td [(multi-level)-270(Schwarz)-270(pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 168.99 0 Td [([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -489.3992 -666.2349 cm -BT -/F15 10.9091 Tf 489.3992 666.2349 Td[(15)]TJ -ET -1 0 0 1 500.3083 666.2349 cm + [(15)]TJ 0 g 0 G -1 0 0 1 -500.3083 -666.2349 cm -BT -/F15 10.9091 Tf 500.3083 666.2349 Td[(],)]TJ -406.3905 -13.5492 Td[(to)-333(b)-28(e)-333(use)-1(d)-333(i)1(n)-333(the)-334(i)1(te)-1(r)1(ativ)28(e)-334(solut)1(ions)-334(of)-332(s)-1(p)1(ars)-1(e)-333(lin)1(e)-1(ar)-333(sys)-1(t)1(e)-1(ms)-1(:)]TJ/F24 10.9091 Tf 186.9794 -23.1523 Td[(Ax)]TJ/F15 10.9091 Tf 17.4469 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(b;)]TJ -ET -1 0 0 1 492.4295 629.5334 cm + [(],)]TJ -392.451 -13.549 Td [(to)-333(b)-28(e)-333(used)-334(in)-333(the)-333(iterativ)28(e)-334(solutions)-333(of)-333(sparse)-334(linear)-333(systems:)]TJ/F22 10.9091 Tf 186.979 -23.153 Td [(Ax)]TJ/F15 10.9091 Tf 17.447 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(b;)]TJ 0 g 0 G -1 0 0 1 -492.4295 -629.5334 cm -BT -/F15 10.9091 Tf 492.4295 629.5334 Td[(\0501\051)]TJ -ET -1 0 0 1 506.3689 629.5334 cm +/F15 10.9091 Tf 182.571 0 Td [(\0501\051)]TJ 0 g 0 G -1 0 0 1 -506.3689 -629.5334 cm -BT -/F15 10.9091 Tf 93.9178 606.3811 Td[(where)]TJ/F24 10.9091 Tf 31.3179 0 Td[(A)]TJ/F15 10.9091 Tf 11.5906 0 Td[(is)-313(a)-312(s)-1(q)1(uare,)-316(re)-1(al)-312(or)-312(com)-1(p)1(le)-1(x)1(,)-317(spar)1(s)-1(e)-313(matri)1(x)-313(with)-312(a)-312(s)-1(y)1(m)-1(metric)-313(spar)1(s)-1(it)28(y)-312(pat)1(te)-1(r)1(n.)]TJ -42.9085 -13.5492 Td[(Thes)-1(e)-333(prec)-1(on)1(di)1(tioners)-334(h)1(a)28(v)28(e)-334(the)-333(foll)1(o)27(win)1(g)-334(general)-333(f)1(e)-1(atu)1(res)-1(:)]TJ -ET -1 0 0 1 93.9178 571.4462 cm + -398.512 -23.152 Td [(where)]TJ/F22 10.9091 Tf 31.318 0 Td [(A)]TJ/F15 10.9091 Tf 11.59 0 Td [(is)-313(a)-312(square,)-317(real)-312(or)-313(complex,)-316(sparse)-313(matrix)-312(with)-313(a)-312(symmetric)-313(sparsit)28(y)-312(pattern.)]TJ -42.908 -13.549 Td [(These)-333(preconditioners)-334(ha)28(v)28(e)-333(the)-334(follo)28(wing)-333(general)-333(features:)]TJ 0 g 0 G -1 0 0 1 -93.9178 -571.4462 cm -BT -/F27 10.9091 Tf 110.2815 571.4462 Td[(\017)]TJ -ET -1 0 0 1 115.736 571.4462 cm +/F25 10.9091 Tf 16.364 -21.386 Td [(\017)]TJ 0 g 0 G -1 0 0 1 -115.736 -571.4462 cm -BT -/F15 10.9091 Tf 121.1906 571.4462 Td[(b)-27(oth)]TJ/F20 10.9091 Tf 24.7943 0 Td[(additive)-276(a)-1(nd)-276(hybri)1(d)-277(mu)1(ltil)1(evel)]TJ/F15 10.9091 Tf 141.7891 0 Td[(v)56(arian)29(ts)-246(ar)1(e)-246(impl)1(e)-1(me)-1(n)29(te)-1(d)1(,)-263(i.)1(e)-1(.)-245(v)56(ar)1(ian)28(ts)-245(that)-245(ar)1(e)]TJ -166.5834 -13.5492 Td[(add)1(itiv)28(e)-226(among)-225(the)-226(lev)28(e)-1(l)1(s)-227(an)1(d)-225(inside)-226(eac)27(h)-225(lev)28(e)-1(l,)-247(an)1(d)-225(v)55(ar)1(ian)28(ts)-226(th)1(at)-226(are)-226(m)28(ulti)1(pli)1(c)-1(ativ)28(e)]TJ 0 -13.5492 Td[(among)-334(the)-334(lev)28(e)-1(ls)-334(and)-334(ad)1(di)1(tiv)28(e)-335(in)1(s)-1(i)1(de)-335(eac)27(h)-333(le)-1(v)28(el;)-334(the)-334(basic)-335(Ad)1(diti)1(v)28(e)-335(S)1(c)27(h)28(w)28(arz)-335(\050AS)1(\051)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-334(are)-334(ob)1(tain)1(e)-1(d)-333(b)29(y)-334(consid)1(e)-1(r)1(ing)-333(onl)1(y)-334(on)1(e)-334(lev)28(e)-1(l)1(;)]TJ -ET -1 0 0 1 93.9178 508.7349 cm +/F15 10.9091 Tf 10.909 0 Td [(b)-28(oth)]TJ/F18 10.9091 Tf 24.794 0 Td [(additive)-276(a)-1(nd)-276(hybrid)-276(multilevel)]TJ/F15 10.9091 Tf 141.789 0 Td [(v)56(arian)27(ts)-245(are)-245(implemen)28(ted,)-263(i.e.)-245(v)56(arian)28(ts)-245(that)-245(are)]TJ -166.583 -13.549 Td [(additiv)28(e)-226(among)-226(th)1(e)-226(lev)28(els)-226(and)-226(inside)-226(eac)28(h)-226(lev)28(el,)-247(and)-226(v)56(arian)28(ts)-226(that)-226(are)-225(m)27(ultip)1(licativ)27(e)]TJ 0 -13.549 Td [(among)-334(the)-334(lev)27(els)-334(and)-334(additiv)28(e)-334(inside)-334(eac)27(h)-334(lev)28(el;)-335(the)-334(basic)-334(Additiv)28(e)-334(Sc)27(h)28(w)28(arz)-334(\050AS\051)]TJ 0 -13.549 Td [(preconditioners)-333(are)-334(ob)1(tained)-334(b)28(y)-333(considering)-334(on)1(ly)-334(one)-333(lev)28(el;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -508.7349 cm -BT -/F27 10.9091 Tf 110.2815 508.7349 Td[(\017)]TJ -ET -1 0 0 1 115.736 508.7349 cm +/F25 10.9091 Tf -10.909 -22.064 Td [(\017)]TJ 0 g 0 G -1 0 0 1 -115.736 -508.7349 cm -BT -/F15 10.9091 Tf 121.1906 508.7349 Td[(a)]TJ/F20 10.9091 Tf 10.3888 0 Td[(pur)52(ely)-467(al)1(gebr)51(aic)]TJ/F15 10.9091 Tf 80.6232 0 Td[(app)1(roac)28(h)-452(is)-453(u)1(s)-1(ed)-452(to)-452(ge)-1(n)1(e)-1(r)1(ate)-453(a)-452(s)-1(equence)-453(of)-452(coarse)-1(-lev)28(e)-1(l)-452(cor-)]TJ -91.012 -13.5492 Td[(rec)-1(t)1(ions)-415(to)-415(a)-415(b)1(as)-1(ic)-415(AS)-414(pr)1(e)-1(cond)1(ition)1(e)-1(r,)-435(wit)1(hout)-414(e)-1(xp)1(licitly)-414(using)-414(an)28(y)-415(in)1(for)1(m)-1(ati)1(on)]TJ 0 -13.5492 Td[(on)-373(the)-374(ge)-1(ometry)-374(of)-373(the)-374(ori)1(ginal)-373(prob)1(lem)-375(\050e.g.)-373(the)-374(disc)-1(r)1(e)-1(ti)1(z)-1(ati)1(on)-374(of)-373(a)-374(PDE)1(\051.)-374(The)]TJ/F20 10.9091 Tf 0 -13.5492 Td[(smo)51(othe)51(d)-313(aggr)51(e)52(ga)-1(ti)1(o)-1(n)]TJ/F15 10.9091 Tf 103.9531 0 Td[(tec)27(hn)1(iqu)1(e)-285(is)-285(ap)1(plied)-284(as)-285(algebrai)1(c)-285(c)-1(oar)1(s)-1(enin)1(g)-285(strategy)-284([)]TJ -ET -1 0 0 1 477.8105 468.0873 cm +/F15 10.9091 Tf 10.909 0 Td [(a)]TJ/F18 10.9091 Tf 10.388 0 Td [(pur)51(ely)-467(algebr)51(aic)]TJ/F15 10.9091 Tf 80.624 0 Td [(approac)28(h)-452(is)-453(used)-452(to)-452(generate)-453(a)-452(sequence)-452(of)-453(coarse-lev)28(el)-452(cor-)]TJ -91.012 -13.549 Td [(rections)-415(to)-415(a)-415(basic)-415(AS)-414(preconditioner,)-435(without)-415(explicitly)-415(using)-415(an)28(y)-415(information)]TJ 0 -13.549 Td [(on)-374(the)-374(geometry)-374(of)-374(the)-373(original)-374(problem)-374(\050e.g.)-374(the)-374(discretization)-374(of)-374(a)-374(P)1(DE\051.)-374(The)]TJ/F18 10.9091 Tf 0 -13.55 Td [(smo)51(othe)51(d)-313(aggr)52(e)51(gation)]TJ/F15 10.9091 Tf 103.953 0 Td [(tec)28(hnique)-285(is)-284(applied)-285(as)-284(algebraic)-285(coarsening)-284(strategy)-285([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -477.8105 -468.0873 cm -BT -/F15 10.9091 Tf 477.8105 468.0873 Td[(1)]TJ -ET -1 0 0 1 483.265 468.0873 cm + [(1)]TJ 0 g 0 G -1 0 0 1 -483.265 -468.0873 cm -BT -/F15 10.9091 Tf 483.265 468.0873 Td[(,)]TJ -ET -1 0 0 1 489.3992 468.0873 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -489.3992 -468.0873 cm -BT -/F15 10.9091 Tf 489.3992 468.0873 Td[(19)]TJ -ET -1 0 0 1 500.3083 468.0873 cm + [-284(19)]TJ 0 g 0 G -1 0 0 1 -500.3083 -468.0873 cm -BT -/F15 10.9091 Tf 500.3083 468.0873 Td[(].)]TJ -389.454 -21.3857 Td[(The)-287(p)1(ac)27(k)56(age)-288(i)1(s)-287(w)-1(r)1(itten)-287(i)1(n)]TJ/F20 10.9091 Tf 122.3962 0 Td[(F)77(ortr)51(an)-315(95)]TJ/F15 10.9091 Tf 50.4226 0 Td[(,)-296(f)1(ollo)28(wing)-286(an)]TJ/F20 10.9091 Tf 66.4546 0 Td[(obje)51(ct-or)1(ient)-1(e)52(d)-315(ap)-1(pr)52(o)51(ach)]TJ/F15 10.9091 Tf 118.6351 0 Td[(th)1(rough)]TJ -374.845 -13.5492 Td[(th)1(e)-331(e)-1(xp)1(loitat)1(ion)-330(of)-330(featur)1(e)-1(s)-331(suc)28(h)-330(as)-331(abstract)-331(d)1(ata)-331(t)28(yp)-27(e)-331(creation,)-330(fun)1(c)-1(t)1(ional)-330(o)28(v)28(e)-1(r)1(loadi)1(ng)]TJ 0 -13.5492 Td[(and)-359(dy)1(namic)-361(mem)-1(or)1(y)-360(m)-1(an)1(age)-1(men)28(t.)-524(The)-360(paral)1(le)-1(l)-359(im)-1(p)1(lem)-1(en)28(tati)1(on)-360(is)-360(base)-1(d)-359(on)-360(a)-360(S)1(ingle)]TJ 0 -13.5492 Td[(Pr)1(ogram)-231(Mu)1(ltip)1(le)-231(Data)-230(\050SP)1(MD\051)-230(parad)1(igm)-231(f)1(or)-231(d)1(is)-1(t)1(rib)1(uted-m)-1(emory)-230(arc)27(h)1(itec)-1(tu)1(res)-1(.)-410(S)1(ingle)]TJ 0 -13.5492 Td[(and)-376(d)1(oubl)1(e)-378(p)1(rec)-1(ision)-376(impleme)-1(n)28(t)1(ations)-377(of)-376(MLD2P)1(4)-377(are)-377(a)28(v)55(ai)1(lable)-377(f)1(or)-377(b)-27(oth)-376(the)-377(real)-377(an)1(d)]TJ 0 -13.5492 Td[(th)1(e)-334(c)-1(ompl)1(e)-1(x)-333(cas)-1(e,)-333(that)-333(can)-333(b)-28(e)-333(use)-1(d)-333(th)1(rou)1(gh)-333(a)-334(sin)1(gle)-334(in)28(t)1(e)-1(rf)1(ac)-1(e.)]TJ 16.9365 -13.5492 Td[(MLD2P)1(4)-230(h)1(as)-230(b)-27(e)-1(en)-229(des)-1(i)1(gned)-229(to)-230(imp)1(le)-1(men)28(t)-230(scalable)-229(and)-229(eas)-1(y-to-use)-230(m)27(u)1(ltil)1(e)-1(v)28(el)-230(p)1(rec)-1(on)1(-)]TJ -16.9365 -13.5492 Td[(di)1(tioners)-348(in)-348(th)1(e)-349(c)-1(on)29(te)-1(x)1(t)-349(of)-347(the)]TJ/F20 10.9091 Tf 147.4316 0 Td[(PS)-1(B)1(L)-1(AS)-372(\050Par)51(al)-50(lel)-371(Sp)51(arse)-371(BLA)-1(S\051)-371(c)51(omputationa)-1(l)-371(f)1(r)51(ame-)]TJ -147.4316 -13.5492 Td[(wo)-1(r)1(k)]TJ/F15 10.9091 Tf 27.2865 0 Td[([)]TJ -ET -1 0 0 1 124.2346 338.308 cm + [(].)]TJ -114.29 -21.385 Td [(The)-287(pac)28(k)56(age)-287(is)-287(written)-287(in)]TJ/F18 10.9091 Tf 122.397 0 Td [(F)77(ortr)51(an)-315(95)]TJ/F15 10.9091 Tf 50.422 0 Td [(,)-296(follo)28(wing)-287(an)]TJ/F18 10.9091 Tf 66.455 0 Td [(obje)51(ct-oriente)51(d)-315(appr)52(o)51(ach)]TJ/F15 10.9091 Tf 118.635 0 Td [(through)]TJ -374.845 -13.55 Td [(the)-330(exploitation)-331(of)-330(features)-331(suc)28(h)-330(as)-331(abstract)-330(data)-331(t)28(yp)-28(e)-330(creation,)-331(functional)-331(o)28(v)28(erloading)]TJ 0 -13.549 Td [(and)-360(dynamic)-360(memory)-360(managemen)28(t.)-525(The)-360(parallel)-360(implemen)28(tation)-360(is)-360(based)-360(on)-360(a)-360(Single)]TJ 0 -13.549 Td [(Program)-231(Mu)1(ltiple)-231(Data)-231(\050SPMD\051)-230(paradigm)-231(for)-230(distributed-memory)-231(arc)28(hitectures.)-410(Single)]TJ 0 -13.549 Td [(and)-377(double)-376(precision)-377(implemen)28(tations)-377(of)-377(MLD2P4)-377(are)-377(a)28(v)56(ailable)-377(for)-377(b)-28(oth)-376(the)-377(real)-377(and)]TJ 0 -13.549 Td [(the)-333(complex)-334(case,)-333(that)-333(can)-334(b)-27(e)-334(used)-333(through)-333(a)-334(single)-333(in)28(terface.)]TJ 16.936 -13.549 Td [(MLD2P4)-229(has)-230(b)-28(een)-229(designed)-229(to)-230(implemen)28(t)-230(scalable)-229(and)-229(easy-)-1(t)1(o-)-1(u)1(s)-1(e)-229(m)28(ultilev)28(el)-230(precon-)]TJ -16.936 -13.55 Td [(ditioners)-348(in)-348(the)-349(con)28(text)-348(of)-348(the)]TJ/F18 10.9091 Tf 147.431 0 Td [(PSBLAS)-372(\050Par)51(al)-51(lel)-371(Sp)51(arse)-371(BLAS\051)-372(c)51(omputational)-371(fr)51(ame-)]TJ -147.431 -13.549 Td [(work)]TJ/F15 10.9091 Tf 27.286 0 Td [([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -124.2346 -338.308 cm -BT -/F15 10.9091 Tf 124.2346 338.308 Td[(12)]TJ -ET -1 0 0 1 135.1437 338.308 cm + [(12)]TJ 0 g 0 G -1 0 0 1 -135.1437 -338.308 cm -BT -/F15 10.9091 Tf 135.1437 338.308 Td[(].)-453(PS)1(B)-1(LAS)-336(i)1(s)-337(a)-337(l)1(ibr)1(ary)-336(origin)1(ally)-336(d)1(e)-1(v)28(elop)-27(e)-1(d)-336(to)-336(add)1(res)-1(s)-337(th)1(e)-337(par)1(allel)-336(im)-1(p)1(lem)-1(en-)]TJ -41.2259 -13.5492 Td[(tation)-441(of)-442(i)1(te)-1(r)1(ativ)28(e)-442(s)-1(olv)28(ers)-442(for)-441(s)-1(p)1(arse)-443(l)1(inear)-442(syste)-1(m,)-469(b)28(y)-441(pro)28(vi)1(din)1(g)-442(basic)-442(linear)-442(al)1(ge)-1(b)1(ra)]TJ 0 -13.5492 Td[(op)-27(e)-1(r)1(ators)-443(an)1(d)-442(dat)1(a)-443(manageme)-1(n)28(t)-442(f)1(ac)-1(il)1(ities)-443(f)1(or)-442(distri)1(but)1(e)-1(d)-442(spar)1(s)-1(e)-443(matr)1(ic)-1(es)-1(;)-496(it)-442(also)-442(in-)]TJ 0 -13.5492 Td[(clud)1(e)-1(s)-337(par)1(allel)-337(Kr)1(ylo)28(v)-337(solv)28(e)-1(r)1(s)-1(,)-337(bu)1(ilt)-337(on)-336(the)-337(top)-336(of)-337(th)1(e)-338(b)1(as)-1(i)1(c)-338(P)1(SBLAS)-337(k)28(ern)1(e)-1(ls.)-455(The)-337(pr)1(e)-1(-)]TJ 0 -13.5492 Td[(condi)1(tioners)-380(a)28(v)56(ailab)1(le)-380(in)-379(MLD)1(2P4)-380(can)-379(b)-27(e)-380(use)-1(d)-379(with)-379(th)1(e)-1(se)-380(Kry)1(lo)28(v)-380(solv)28(ers)-1(.)-582(T)-1(h)1(e)-380(c)27(h)1(oic)-1(e)]TJ 0 -13.5492 Td[(of)-361(PS)1(B)-1(LAS)-361(h)1(as)-363(b)-27(ee)-1(n)-361(mainl)1(y)-362(motiv)56(ate)-1(d)-361(b)28(y)-361(th)1(e)-363(n)1(e)-1(ed)-361(of)-362(h)1(a)28(vin)1(g)-362(a)-362(p)-27(ortab)1(le)-362(and)-361(e\016)-1(cien)28(t)]TJ 0 -13.5492 Td[(soft)28(w)27(ar)1(e)-313(in)1(frastru)1(c)-1(t)1(ure)-312(im)-1(p)1(lem)-1(en)28(tin)1(g)-312(\134de)-313(f)1(ac)-1(to")-312(stand)1(ard)-312(p)1(arallel)-312(s)-1(p)1(arse)-313(lin)1(e)-1(ar)-312(al)1(ge)-1(b)1(ra)]TJ 0 -13.5492 Td[(k)28(ernels,)-304(to)-297(p)1(ursue)-297(goal)1(s)-298(suc)28(h)-297(as)-297(p)-27(erfor)1(m)-1(an)1(c)-1(e,)-304(p)-27(ortab)1(ilit)28(y)84(,)-304(mo)-28(du)1(larit)28(y)-296(e)-1(d)-296(extensibil)1(it)28(y)-297(i)1(n)]TJ 0 -13.5492 Td[(th)1(e)-273(dev)28(e)-1(lop)1(me)-1(n)28(t)-272(of)-272(th)1(e)-273(precondi)1(tioner)-272(pac)28(k)55(age.)-424(On)-272(th)1(e)-273(other)-272(han)1(d,)-284(the)-272(im)-1(p)1(lem)-1(en)28(tati)1(on)]TJ 0 -13.5492 Td[(of)-378(MLD2P)1(4)-379(has)-379(led)-379(to)-378(s)-1(ome)-379(revis)-1(i)1(ons)-379(and)-378(exte)-1(n)29(tions)-379(of)-378(the)-379(P)1(SBLAS)-379(k)28(ern)1(e)-1(ls,)-390(leadi)1(ng)]TJ 0 -13.5492 Td[(to)-439(th)1(e)-440(r)1(e)-1(ce)-1(n)29(t)-439(PS)1(B)-1(LAS)-438(2.0)-438(v)28(e)-1(rsion)-438([)]TJ -ET -1 0 0 1 268.9762 202.8161 cm + [(].)-454(PSBLAS)-336(is)-336(a)-337(library)-336(originally)-336(dev)27(elop)-27(ed)-337(to)-336(address)-337(th)1(e)-337(parallel)-336(implemen-)]TJ -27.286 -13.549 Td [(tation)-442(of)-442(iterativ)28(e)-442(solv)28(ers)-442(for)-442(sparse)-442(linear)-442(system,)-469(b)28(y)-442(pro)28(viding)-442(basic)-442(linear)-442(algebra)]TJ 0 -13.549 Td [(op)-28(erators)-442(and)-442(data)-442(managemen)27(t)-442(facilities)-442(for)-442(distributed)-442(sparse)-443(matrices;)-496(it)-443(also)-442(in-)]TJ 0 -13.549 Td [(cludes)-337(parallel)-337(Krylo)28(v)-337(solv)28(ers,)-338(built)-337(on)-336(the)-337(top)-337(of)-337(the)-337(basic)-337(PSBLAS)-337(k)28(ernels.)-455(The)-337(pre-)]TJ 0 -13.55 Td [(conditioners)-379(a)27(v)56(ailable)-380(in)-379(MLD2P4)-380(can)-379(b)-28(e)-379(used)-380(with)-379(these)-380(Krylo)28(v)-380(solv)28(ers.)-583(The)-380(c)28(hoice)]TJ 0 -13.549 Td [(of)-362(PSBLAS)-361(has)-362(b)-28(een)-361(mainly)-362(motiv)56(ated)-362(b)28(y)-362(the)-362(need)-361(of)-362(ha)28(ving)-362(a)-361(p)-28(ortable)-362(and)-361(e\016cien)27(t)]TJ 0 -13.549 Td [(soft)28(w)28(are)-313(infrastructure)-312(implemen)28(ting)-312(\134de)-313(facto")-312(standard)-312(parallel)-312(sparse)-313(linear)-312(algebra)]TJ 0 -13.549 Td [(k)28(ernels,)-304(to)-297(pursue)-297(goals)-296(suc)27(h)-296(as)-297(p)-28(erformance,)-304(p)-27(ortabilit)27(y)84(,)-304(mo)-28(dularit)28(y)-297(ed)-296(e)-1(x)1(te)-1(n)1(s)-1(ib)1(ilit)27(y)-296(in)]TJ 0 -13.549 Td [(the)-272(dev)27(elopmen)28(t)-272(of)-273(the)-272(preconditioner)-272(pac)27(k)56(age.)-424(On)-273(the)-272(other)-272(hand,)-285(the)-272(implemen)27(tation)]TJ 0 -13.55 Td [(of)-379(MLD2P4)-378(has)-379(led)-379(to)-379(some)-379(revisions)-379(and)-378(exten)27(tion)1(s)-379(of)-379(the)-379(PSBLAS)-379(k)28(ernels,)-390(leading)]TJ 0 -13.549 Td [(to)-439(the)-439(recen)28(t)-439(PSBLAS)-439(2.0)-438(v)27(ersion)-438([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -268.9762 -202.8161 cm -BT -/F15 10.9091 Tf 268.9762 202.8161 Td[(11)]TJ -ET -1 0 0 1 279.8853 202.8161 cm + [(11)]TJ 0 g 0 G -1 0 0 1 -279.8853 -202.8161 cm -BT -/F15 10.9091 Tf 279.8853 202.8161 Td[(].)-761(Th)1(e)-440(i)1(n)28(te)-1(r)1(-)-1(p)1(ro)-28(ces)-1(s)-439(c)-1(om)28(un)1(ic)-1(at)1(ion)-439(r)1(e)-1(qu)1(ired)-438(b)28(y)]TJ -185.9675 -13.5492 Td[(MLD2P)1(4)-355(is)-355(encapsul)1(ate)-1(d)-354(in)29(to)-355(th)1(e)-355(PSBLAS)-354(rou)1(tines,)-360(e)-1(x)1(c)-1(ept)-354(few)-355(c)-1(ases)-356(wh)1(e)-1(r)1(e)-356(M)1(PI)-354([)]TJ -ET -1 0 0 1 492.4295 189.2669 cm + [(].)-761(The)-439(in)28(te)-1(r)1(-)-1(p)1(ro)-28(cess)-439(com)27(un)1(ic)-1(at)1(ion)-439(required)-439(b)28(y)]TJ 0 -13.549 Td [(MLD2P4)-355(is)-354(encapsulated)-355(in)28(to)-355(th)1(e)-355(PSBLAS)-355(routines,)-360(except)-354(few)-355(cases)-355(where)-354(MPI)-355([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -492.4295 -189.2669 cm -BT -/F15 10.9091 Tf 492.4295 189.2669 Td[(16)]TJ -ET -1 0 0 1 503.3386 189.2669 cm + [(16)]TJ 0 g 0 G -1 0 0 1 -503.3386 -189.2669 cm -BT -/F15 10.9091 Tf 503.3386 189.2669 Td[(])]TJ -409.4208 -13.5492 Td[(is)-458(e)-1(x)1(pli)1(c)-1(itl)1(y)-458(called.)-818(Therefor)1(e)-1(,)-489(M)1(LD2P4)-458(can)-457(b)-28(e)-458(ru)1(n)-458(on)-457(an)28(y)-458(p)1(arall)1(e)-1(l)-457(m)-1(ac)28(hin)1(e)-459(wh)1(e)-1(re)]TJ 0 -13.5492 Td[(PS)1(BLAS)-333(and)-333(M)1(PI)-333(im)-1(p)1(lem)-1(en)28(tati)1(ons)-334(ar)1(e)-334(a)28(v)55(ai)1(lable.)]TJ 16.9365 -13.5492 Td[(MLD2P)1(4)-342(h)1(as)-342(a)-342(la)28(y)28(e)-1(r)1(e)-1(d)-341(an)1(d)-342(mo)-28(d)1(ular)-341(soft)28(w)27(ar)1(e)-342(arc)27(h)1(itec)-1(tu)1(re)-342(where)-342(th)1(re)-1(e)-342(main)-341(la)28(y)28(ers)]TJ -16.9365 -13.5492 Td[(can)-458(b)-27(e)-459(id)1(e)-1(n)28(t)1(i\014ed.)-818(The)-459(l)1(o)27(w)28(er)-458(la)28(y)28(e)-1(r)-457(c)-1(on)1(s)-1(ists)-459(of)-457(the)-458(PS)1(B)-1(LAS)-457(k)28(e)-1(r)1(nels,)-490(t)1(he)-458(m)-1(id)1(dl)1(e)-459(one)]TJ 0 -13.5492 Td[(impl)1(e)-1(me)-1(n)29(ts)-458(the)-458(constru)1(c)-1(t)1(ion)-457(and)-457(ap)1(pli)1(c)-1(ati)1(on)-457(phases)-458(of)-457(the)-458(p)1(rec)-1(on)1(dit)1(ioners,)-489(an)1(d)-457(the)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [(])]TJ 0 -13.549 Td [(is)-458(explicitly)-458(called.)-818(Therefore,)-489(MLD2P4)-457(c)-1(an)-457(b)-28(e)-458(run)-458(on)-458(an)28(y)-458(parall)1(e)-1(l)-457(mac)27(hine)-457(w)-1(h)1(e)-1(r)1(e)]TJ 0 -13.549 Td [(PSBLAS)-333(and)-333(MPI)-334(implemen)28(tations)-333(are)-334(a)28(v)56(ailable.)]TJ 16.936 -13.55 Td [(MLD2P4)-342(has)-341(a)-342(la)28(y)28(ered)-342(and)-342(mo)-27(dular)-342(soft)28(w)28(are)-342(arc)28(hitecture)-342(where)-342(three)-341(main)-342(la)28(y)28(ers)]TJ -16.936 -13.549 Td [(can)-458(b)-28(e)-458(iden)28(ti\014ed.)-819(The)-458(lo)28(w)28(er)-458(la)27(y)28(er)-458(consists)-458(of)-458(the)-458(PSBLAS)-458(k)28(ernels,)-490(the)-458(middle)-458(one)]TJ 0 -13.549 Td [(implemen)28(ts)-458(the)-457(construction)-457(and)-458(application)-457(phases)-458(of)-457(the)-457(preconditioners,)-489(and)-457(the)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -166 0 obj << +161 0 obj << /Type /Page -/Contents 167 0 R -/Resources 165 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 185 0 R -/Annots [ 168 0 R 172 0 R 180 0 R 181 0 R 182 0 R 183 0 R 184 0 R ] +/Contents 162 0 R +/Resources 160 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 167 0 R +/Annots [ 159 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R ] >> endobj -168 0 obj << +159 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.1) >> >> endobj -172 0 obj << +153 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.4029 665.2387 501.3046 674.2615] +/Rect [488.403 665.239 501.305 674.261] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -180 0 obj << +154 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [476.8142 467.0911 484.2613 476.1139] +/Rect [476.814 467.091 484.261 476.114] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -181 0 obj << +155 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.4029 467.0911 501.3046 476.1139] +/Rect [488.403 467.091 501.305 476.114] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -182 0 obj << +156 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [123.2383 337.3118 136.14 346.3346] +/Rect [123.238 337.312 136.14 346.335] /Subtype /Link /A << /S /GoTo /D (cite.psblas_00) >> >> endobj -183 0 obj << +157 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [267.98 201.8198 280.8816 210.8426] +/Rect [267.98 201.82 280.882 210.843] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -184 0 obj << +158 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [491.4332 188.2706 504.3349 197.2934] +/Rect [491.433 188.271 504.335 197.293] /Subtype /Link /A << /S /GoTo /D (cite.MPI1) >> >> endobj 10 0 obj << -/D [166 0 R /XYZ 93.9178 715.0952 null] +/D [161 0 R /XYZ 93.918 715.095 null] >> endobj -173 0 obj << -/D [166 0 R /XYZ 280.8972 643.0826 null] +164 0 obj << +/D [161 0 R /XYZ 280.897 643.083 null] >> endobj -165 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F20 171 0 R /F24 176 0 R /F27 179 0 R >> +160 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F18 163 0 R /F22 165 0 R /F25 166 0 R >> /ProcSet [ /PDF /Text ] >> endobj -194 0 obj << -/Length 6806 +184 0 obj << +/Length 4159 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(2)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(2)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F15 10.9091 Tf 141.7385 704.1363 Td[(up)1(p)-27(e)-1(r)-310(on)1(e)-311(p)1(ro)28(vid)1(e)-1(s)-310(a)-310(un)1(ifor)1(m)-311(an)1(d)-310(eas)-1(y)1(-)-1(to-u)1(s)-1(e)-310(in)28(terf)1(ac)-1(e)-310(to)-310(all)-310(th)1(e)-311(p)1(rec)-1(on)1(diti)1(oners)-1(.)-436(This)]TJ 0 -13.5492 Td[(arc)28(hitecture)-446(allo)28(ws)-447(f)1(or)-446(di)1(\013)-1(eren)28(t)-446(lev)28(e)-1(ls)-446(of)-446(u)1(s)-1(e)-446(of)-446(th)1(e)-447(pac)28(k)55(age:)-670(f)1(e)-1(w)-446(bl)1(ac)27(k-b)-28(o)28(x)-446(r)1(outin)1(e)-1(s)]TJ 0 -13.5492 Td[(at)-384(th)1(e)-385(u)1(pp)-27(e)-1(r)-383(la)28(y)28(e)-1(r)-383(allo)28(w)-384(non-exp)-27(e)-1(rt)-383(use)-1(rs)-384(to)-384(eas)-1(il)1(y)-384(bu)1(ild)-383(an)28(y)-384(p)1(re)-1(cond)1(ition)1(e)-1(r)-383(a)28(v)55(ai)1(lable)]TJ 0 -13.5492 Td[(in)-364(MLD2P)1(4)-365(and)-364(to)-365(app)1(ly)-365(i)1(t)-365(withi)1(n)-365(a)-365(P)1(SBLAS)-364(Kryl)1(o)27(v)-364(s)-1(olv)28(er.)-539(O)1(n)-365(th)1(e)-366(ot)1(her)-365(h)1(and,)-372(the)]TJ 0 -13.5492 Td[(rou)1(tin)1(e)-1(s)-253(of)-253(the)-253(midd)1(le)-254(an)1(d)-253(lo)28(w)28(e)-1(r)-253(l)1(a)27(y)28(er)-253(can)-253(b)-27(e)-254(u)1(s)-1(ed)-253(an)1(d)-253(exte)-1(n)1(ded)-253(b)28(y)-252(e)-1(xp)-27(ert)-253(use)-1(r)1(s)-254(to)-253(b)1(uil)1(d)]TJ 0 -13.5492 Td[(new)-367(v)28(ersions)-367(of)-366(m)27(u)1(lti-lev)28(e)-1(l)-366(Sc)28(h)28(w)28(arz)-367(pr)1(e)-1(cond)1(ition)1(e)-1(rs.)-544(W)83(e)-367(p)1(ro)28(vid)1(e)-367(here)-367(a)-367(d)1(e)-1(sc)-1(r)1(ipt)1(ion)-366(of)]TJ 0 -13.5492 Td[(th)1(e)-334(up)1(p)-28(er-la)28(y)28(e)-1(r)-333(r)1(outi)1(nes)-1(,)-333(bu)1(t)-333(not)-333(of)-333(th)1(e)-334(m)-1(edi)1(um-)-1(l)1(a)27(y)28(er)-333(ones.)]TJ 16.9365 -13.5492 Td[(This)-270(gui)1(de)-270(is)-271(or)1(ganize)-1(d)-269(as)-271(f)1(ollo)28(ws)-1(.)-423(The)-270(not)1(ational)-270(con)28(v)28(en)28(tion)1(s)-271(u)1(s)-1(ed)-270(in)-269(the)-270(gui)1(de)-270(and)]TJ -16.9365 -13.5492 Td[(in)-362(th)1(e)-364(n)1(aming)-362(of)-363(th)1(e)-363(MLD2P)1(4)-363(rou)1(tin)1(e)-1(s)-363(are)-363(r)1(e)-1(p)-27(orted)-362(in)-362(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 448.9237 595.7428 cm +/F15 10.9091 Tf -203.265 -35.866 Td [(upp)-28(er)-310(one)-310(pro)28(vides)-310(a)-310(uniform)-310(and)-310(easy-to-use)-310(in)28(terface)-310(to)-310(all)-310(the)-310(preconditioners.)-437(This)]TJ 0 -13.549 Td [(arc)28(hitecture)-446(allo)27(ws)-446(for)-446(di\013eren)28(t)-446(lev)28(els)-447(of)-446(use)-446(of)-446(the)-446(pac)28(k)55(age:)-670(few)-446(blac)28(k-b)-28(o)28(x)-446(routines)]TJ 0 -13.549 Td [(at)-384(the)-384(upp)-28(er)-384(la)28(y)28(er)-384(allo)28(w)-384(non-exp)-28(ert)-384(users)-384(to)-384(easily)-384(build)-384(an)28(y)-384(preconditioner)-384(a)28(v)55(ail)1(able)]TJ 0 -13.549 Td [(in)-365(MLD2P4)-365(and)-364(to)-365(apply)-365(it)-365(within)-365(a)-365(P)1(SBLAS)-365(Krylo)28(v)-365(solv)28(e)-1(r.)-539(On)-364(the)-365(other)-365(hand,)-373(the)]TJ 0 -13.549 Td [(routines)-253(of)-253(the)-253(middle)-253(and)-253(lo)27(w)28(er)-253(la)28(y)28(er)-253(can)-253(b)-28(e)-253(used)-253(and)-253(e)-1(xt)1(e)-1(nd)1(e)-1(d)-253(b)28(y)-253(exp)-28(ert)-253(users)-253(to)-253(build)]TJ 0 -13.55 Td [(new)-367(v)28(ersions)-367(of)-366(m)28(ulti-lev)27(el)-366(Sc)28(h)27(w)28(arz)-367(pr)1(e)-1(cond)1(itioners.)-545(W)84(e)-367(pro)28(vide)-367(here)-367(a)-366(description)-367(of)]TJ 0 -13.549 Td [(the)-333(upp)-28(er-la)28(y)28(e)-1(r)-333(routines,)-333(but)-333(not)-334(of)-333(the)-333(medium-la)28(y)27(er)-333(ones.)]TJ 16.937 -13.549 Td [(This)-270(guide)-270(is)-270(organized)-270(as)-270(follo)28(ws.)-424(The)-270(notational)-270(con)28(v)28(en)28(tions)-270(used)-270(in)-270(the)-270(guide)-270(and)]TJ -16.937 -13.549 Td [(in)-363(the)-362(naming)-363(of)-362(the)-363(MLD2P4)-363(routines)-362(are)-363(rep)-28(orted)-362(in)-363(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -448.9237 -595.7428 cm -BT -/F15 10.9091 Tf 448.9237 595.7428 Td[(2)]TJ -ET -1 0 0 1 454.3782 595.7428 cm + [-362(2)]TJ 0 g 0 G -1 0 0 1 -454.3782 -595.7428 cm -BT -/F15 10.9091 Tf 454.3782 595.7428 Td[(.)-532(Inf)1(ormation)-362(on)-362(the)]TJ -312.6397 -13.5492 Td[(di)1(s)-1(tr)1(ibu)1(tion)-272(of)-273(th)1(e)-274(sour)1(c)-1(e)-273(co)-28(de)-273(and)-272(th)1(e)-274(r)1(e)-1(lated)-272(lice)-1(n)1(s)-1(e)-273(is)-273(giv)28(e)-1(n)-272(in)-272(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 483.801 582.1936 cm + [(.)-533(Information)-362(on)-363(the)]TJ 0 -13.549 Td [(distribution)-273(of)-273(t)1(he)-273(source)-273(co)-28(de)-273(and)-273(the)-273(related)-273(l)1(ic)-1(ense)-272(is)-273(giv)27(en)-272(in)-273(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -483.801 -582.1936 cm -BT -/F15 10.9091 Tf 483.801 582.1936 Td[(3)]TJ -ET -1 0 0 1 489.2555 582.1936 cm + [-273(3)]TJ 0 g 0 G -1 0 0 1 -489.2555 -582.1936 cm -BT -/F15 10.9091 Tf 489.2555 582.1936 Td[(,)-285(whi)1(le)-273(details)]TJ -347.517 -13.5492 Td[(on)-371(th)1(e)-372(con\014)1(gur)1(ation)-371(an)1(d)-371(in)1(s)-1(tal)1(lation)-370(of)-371(pac)28(k)55(age)-371(are)-371(giv)28(e)-1(n)-370(in)-371(S)1(e)-1(ction)]TJ -ET -1 0 0 1 475.1787 568.6444 cm + [(,)-285(while)-273(details)]TJ 0 -13.55 Td [(on)-371(the)-371(con\014guration)-371(and)-371(installation)-371(of)-371(pac)28(k)55(age)-371(are)-371(giv)28(en)-371(in)-371(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -475.1787 -568.6444 cm -BT -/F15 10.9091 Tf 475.1787 568.6444 Td[(4)]TJ -ET -1 0 0 1 480.6333 568.6444 cm + [-371(4)]TJ 0 g 0 G -1 0 0 1 -480.6333 -568.6444 cm -BT -/F15 10.9091 Tf 480.6333 568.6444 Td[(.)-557(A)-372(d)1(e)-1(scrip)1(tion)]TJ -338.8948 -13.5492 Td[(of)-416(m)28(ult)1(i-)-1(l)1(e)-1(v)28(el)-416(Sc)28(h)28(w)28(arz)-417(p)1(rec)-1(on)1(diti)1(oners)-417(b)1(as)-1(ed)-416(on)-415(s)-1(mo)-28(oth)1(e)-1(d)-415(aggregation)-416(is)-416(pr)1(o)28(vided)-416(i)1(n)]TJ 0 -13.5492 Td[(Section)]TJ -ET -1 0 0 1 178.8646 541.546 cm + [(.)-558(A)-371(description)]TJ 0 -13.549 Td [(of)-416(m)28(ulti-lev)28(e)-1(l)-416(Sc)28(h)28(w)28(arz)-416(preconditioners)-416(based)-416(on)-416(smo)-28(othed)-416(aggregation)-416(is)-416(pro)27(vi)1(ded)-417(in)]TJ 0 -13.549 Td [(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -178.8646 -541.546 cm -BT -/F15 10.9091 Tf 178.8646 541.546 Td[(5)]TJ -ET -1 0 0 1 184.3191 541.546 cm + [-237(5)]TJ 0 g 0 G -1 0 0 1 -184.3191 -541.546 cm -BT -/F15 10.9091 Tf 184.3191 541.546 Td[(,)-256(to)-236(help)-236(th)1(e)-237(use)-1(rs)-237(i)1(n)-236(c)27(ho)-27(os)-1(in)1(g)-237(among)-236(the)-237(d)1(i\013e)-1(r)1(e)-1(n)28(t)-236(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-237(im)-1(p)1(lem)-1(en)28(ted)]TJ -42.5806 -13.5492 Td[(in)-317(MLD2P)1(4.)-439(The)-318(b)1(as)-1(ics)-318(for)-317(bu)1(ild)1(ing)-317(and)-317(ap)1(plyi)1(ng)-318(t)1(he)-318(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-318(w)-1(i)1(th)-318(t)1(he)-318(Kr)1(ylo)28(v)]TJ 0 -13.5492 Td[(solv)28(e)-1(r)1(s)-323(imp)1(le)-1(men)28(te)-1(d)-321(in)-322(P)1(SBLAS)-322(ar)1(e)-323(r)1(e)-1(p)-27(orted)-322(i)1(n)-322(Sec)-1(t)1(ion)]TJ -ET -1 0 0 1 412.3575 514.4476 cm + [(,)-255(to)-237(help)-236(the)-237(users)-237(in)-236(c)28(ho)-28(osing)-237(among)-236(the)-237(di\013eren)28(t)-236(preconditioners)-237(implemen)28(ted)]TJ 0 -13.549 Td [(in)-318(MLD2P4.)-439(The)-317(basics)-318(for)-318(bu)1(ilding)-318(and)-317(applying)-318(the)-317(prec)-1(on)1(ditioners)-318(with)-318(the)-317(Krylo)28(v)]TJ 0 -13.549 Td [(solv)28(ers)-322(implemen)27(ted)-322(in)-322(PS)1(B)-1(LAS)-321(are)-323(r)1(e)-1(p)-27(orted)-322(in)-322(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -412.3575 -514.4476 cm -BT -/F15 10.9091 Tf 412.3575 514.4476 Td[(6)]TJ -ET -1 0 0 1 417.8121 514.4476 cm + [-322(6)]TJ 0 g 0 G -1 0 0 1 -417.8121 -514.4476 cm -BT -/F15 10.9091 Tf 417.8121 514.4476 Td[(,)-324(where)-322(the)-322(F)83(or)1(tran)-322(95)-322(co)-28(d)1(e)-1(s)]TJ -276.0736 -13.5492 Td[(of)-273(a)-273(few)-274(sample)-274(p)1(rogr)1(am)-1(s)-274(ar)1(e)-274(also)-274(sho)28(wn.)-424(A)-273(reference)-274(gui)1(de)-274(f)1(or)-273(the)-273(up)1(p)-28(er-la)28(y)28(e)-1(r)-273(r)1(outin)1(e)-1(s)]TJ 0 -13.5492 Td[(of)-379(MLD2P)1(4,)-391(that)-379(are)-380(th)1(e)-380(use)-1(r)-379(in)28(terf)1(ac)-1(e,)-391(is)-380(p)1(ro)28(vid)1(e)-1(d)-379(in)-379(Section)]TJ -ET -1 0 0 1 447.9381 487.3492 cm + [(,)-324(where)-323(th)1(e)-323(F)84(ortran)-322(95)-322(co)-28(des)]TJ 0 -13.55 Td [(of)-273(a)-274(few)-273(sample)-273(programs)-274(are)-273(also)-273(sho)28(w)-1(n)1(.)-425(A)-273(reference)-274(gu)1(ide)-274(for)-273(the)-273(upp)-28(er-la)28(y)28(er)-274(routines)]TJ 0 -13.549 Td [(of)-380(MLD2P4,)-391(that)-379(are)-380(the)-379(user)-380(in)28(terface,)-391(is)-380(pro)28(vided)-380(in)-379(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -447.9381 -487.3492 cm -BT -/F15 10.9091 Tf 447.9381 487.3492 Td[(7)]TJ -ET -1 0 0 1 453.3927 487.3492 cm + [-380(7)]TJ 0 g 0 G -1 0 0 1 -453.3927 -487.3492 cm -BT -/F15 10.9091 Tf 453.3927 487.3492 Td[(.)-583(The)-380(error)-379(h)1(andl)1(ing)]TJ -311.6542 -13.5492 Td[(me)-1(c)28(hani)1(s)-1(m)-348(u)1(s)-1(ed)-347(b)28(y)-347(the)-348(p)1(ac)27(k)56(age)-348(is)-348(br)1(ie)-1(\015)1(y)-347(des)-1(crib)-27(e)-1(d)-347(i)1(n)-348(S)1(e)-1(ction)]TJ -ET -1 0 0 1 442.6857 473.8 cm + [(.)-583(The)-380(error)-379(handling)]TJ 0 -13.549 Td [(mec)28(hanism)-348(used)-347(b)27(y)-347(the)-348(pac)28(k)56(age)-348(is)-348(brie\015y)-347(describ)-28(ed)-347(in)-348(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -442.6857 -473.8 cm -BT -/F15 10.9091 Tf 442.6857 473.8 Td[(8)]TJ -ET -1 0 0 1 448.1403 473.8 cm + [-347(8)]TJ 0 g 0 G -1 0 0 1 -448.1403 -473.8 cm -BT -/F15 10.9091 Tf 448.1403 473.8 Td[(.)-487(The)-348(cop)28(yr)1(igh)28(t)-347(te)-1(r)1(m)-1(s)]TJ -306.4018 -13.5492 Td[(conce)-1(rn)1(in)1(g)-333(the)-333(distrib)1(uti)1(on)-333(an)1(d)-333(mo)-28(di\014)1(c)-1(at)1(ion)-333(of)-332(MLD2P4)-333(ar)1(e)-334(r)1(e)-1(p)-27(orted)-333(in)-332(App)-27(e)-1(n)1(di)1(x)]TJ -ET -1 0 0 1 542.9775 460.2508 cm + [(.)-488(The)-347(cop)28(yrigh)27(t)-347(terms)]TJ 0 -13.549 Td [(concerning)-333(the)-333(distribution)-333(and)-333(mo)-28(di\014cation)-333(of)-333(MLD2P)1(4)-334(are)-333(rep)-27(orted)-333(in)-333(App)-28(endix)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -542.9775 -460.2508 cm -BT -/F15 10.9091 Tf 542.9775 460.2508 Td[(A)]TJ -ET -1 0 0 1 551.1593 460.2508 cm + [-333(A)]TJ 0 g 0 G -1 0 0 1 -551.1593 -460.2508 cm -BT -/F15 10.9091 Tf 551.1593 460.2508 Td[(.)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [(.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -193 0 obj << +183 0 obj << /Type /Page -/Contents 194 0 R -/Resources 192 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 185 0 R -/Annots [ 195 0 R 196 0 R 197 0 R 198 0 R 199 0 R 200 0 R 201 0 R 202 0 R ] +/Contents 184 0 R +/Resources 182 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 167 0 R +/Annots [ 174 0 R 175 0 R 176 0 R 177 0 R 178 0 R 179 0 R 180 0 R 181 0 R ] >> endobj -195 0 obj << +174 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [447.9274 592.6253 455.3745 604.3148] +/Rect [447.927 592.625 455.374 604.315] /Subtype /Link /A << /S /GoTo /D (section.2) >> >> endobj -196 0 obj << +175 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [482.8047 579.0761 490.2518 590.7656] +/Rect [482.805 579.076 490.252 590.766] /Subtype /Link /A << /S /GoTo /D (section.3) >> >> endobj -197 0 obj << +176 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [474.1825 565.5269 481.6295 577.2164] +/Rect [474.182 565.527 481.63 577.216] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -198 0 obj << +177 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [177.8683 538.4285 185.3154 550.118] +/Rect [177.868 538.429 185.315 550.118] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -199 0 obj << +178 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [411.3613 511.3301 418.8083 523.0196] +/Rect [411.361 511.33 418.808 523.02] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -200 0 obj << +179 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [446.9419 484.2317 454.3889 495.9212] +/Rect [446.942 484.232 454.389 495.921] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -201 0 obj << +180 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [441.6895 470.6825 449.1365 482.372] +/Rect [441.689 470.683 449.137 482.372] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -202 0 obj << +181 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [541.9812 457.1333 552.1556 468.8228] +/Rect [541.981 457.133 552.156 468.823] /Subtype /Link -/A << /S /GoTo /D (section.A) >> +/A << /S /GoTo /D (appendix.A) >> >> endobj -192 0 obj << -/Font << /F15 123 0 R /F42 129 0 R >> +182 0 obj << +/Font << /F15 115 0 R /F40 117 0 R >> /ProcSet [ /PDF /Text ] >> endobj -205 0 obj << -/Length 1446 +188 0 obj << +/Length 958 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(2)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(2)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(No)1(t)66(a)66(tio)1(n)-1(al)-378(Conv)-1(e)1(n)-1(tio)1(n)-1(s)]TJ/F15 10.9091 Tf 396.8452 0 Td[(3)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Not)67(a)67(tional)-378(Conventions)]TJ/F15 10.9091 Tf 406.996 0 Td [(3)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(2)-1125(No)-1(tat)-1(io)-1(na)1(l)-376(Co)-1(n)31(v)32(en)31(t)-1(io)-1(ns)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(-)-334(caratteri)-333(ti)1(p)-28(ogr)1(a\014ci)-334(u)1(s)-1(at)1(i)-334(n)1(e)-1(l)1(la)-333(guid)1(a)-334(\050v)28(edi)-333(gu)1(ida)-333(ML)-333(rece)-1(n)28(te)-333(e)-334(gui)1(da)-333(Az)-1(tec)-1(\051)]TJ 0 -13.5492 Td[(-)-376(con)28(v)28(enzioni)-374(s)-1(u)1(i)-375(nomi)-375(di)-375(rou)1(tin)1(e)-376(\050an)1(c)27(he)-375(di\013erenza)-376(n)1(e)-1(i)-375(n)1(omi)-375(tra)-375(high)1(-le)-1(v)28(el)-375(e)-376(mediu)1(m)-1(-)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)1(?)-1(\051,)-333(stru)1(ttur)1(e)-334(dat)1(i,)-333(m)-1(o)-27(dul)1(i,)-333(c)-1(ostan)28(ti)1(,)-334(etc.)-445(\050)1(v)28(e)-1(d)1(i)-334(gu)1(id)1(a)-334(p)1(s)-1(b)1(las)-1(\051)]TJ 0 -13.5492 Td[(-)-334(v)28(ersione)-333(reale)-334(e)-334(com)-1(p)1(les)-1(sa,)-333(s)-1(in)1(gola)-333(e)-334(dop)1(pi)1(a)-334(p)1(rec)-1(ision)1(e)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F17 14.3462 Tf -406.996 -35.866 Td [(2)-1125(Notational)-375(Con)31(v)31(en)32(tions)]TJ/F15 10.9091 Tf 0 -24.352 Td [(-)-333(caratteri)-334(tip)-27(ogra\014ci)-334(usati)-333(nella)-333(guida)-333(\050v)27(edi)-333(guida)-333(ML)-334(r)1(e)-1(cen)28(te)-333(e)-334(gu)1(ida)-334(Aztec\051)]TJ 0 -13.549 Td [(-)-375(con)28(v)27(enzioni)-375(sui)-375(nomi)-375(di)-375(routine)-375(\050anc)27(h)1(e)-376(di\013erenza)-375(nei)-375(nomi)-375(tra)-375(high-lev)27(el)-375(e)-375(medium-)]TJ 0 -13.549 Td [(lev)28(el?\051,)-334(strutt)1(ure)-334(dati,)-333(mo)-28(duli,)-333(costan)28(ti,)-334(etc.)-444(\050v)28(edi)-334(guid)1(a)-334(psblas\051)]TJ 0 -13.549 Td [(-)-333(v)27(ersione)-333(reale)-333(e)-334(complessa,)-333(singola)-333(e)-334(doppia)-333(precisione)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -204 0 obj << +187 0 obj << /Type /Page -/Contents 205 0 R -/Resources 203 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 185 0 R -/Annots [ 207 0 R ] +/Contents 188 0 R +/Resources 186 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 167 0 R +/Annots [ 185 0 R ] >> endobj -207 0 obj << +185 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.2) >> >> endobj -206 0 obj << -/D [204 0 R /XYZ 93.9178 740.0018 null] +189 0 obj << +/D [187 0 R /XYZ 93.918 740.002 null] >> endobj 14 0 obj << -/D [204 0 R /XYZ 93.9178 715.0952 null] +/D [187 0 R /XYZ 93.918 715.095 null] >> endobj -203 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R >> +186 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R >> /ProcSet [ /PDF /Text ] >> endobj -210 0 obj << -/Length 2122 +193 0 obj << +/Length 1403 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(4)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(4)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F19 14.3462 Tf 141.7385 704.1363 Td[(3)-1125(C)-1(o)-32(de)-375(Di)-1(str)-1(ibut)-1(io)-1(n)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(MLD2P)1(4)-333(is)-334(a)28(v)56(ailabl)1(e)-334(fr)1(om)-334(our)-333(p)1(ro)-55(jec)-1(t)-333(w)28(e)-1(b)-333(site)]TJ -ET -1 0 0 1 158.1022 657.2685 cm +/F17 14.3462 Tf -203.265 -35.866 Td [(3)-1125(Co)-31(de)-375(Distribution)]TJ/F15 10.9091 Tf 0 -24.352 Td [(MLD2P4)-333(is)-334(a)28(v)56(ailable)-334(fr)1(om)-334(our)-333(pro)-56(ject)-333(w)28(eb)-334(site)]TJ 0 g 0 G -1 0 0 1 21.8182 0 cm 0 g 0 G -1 0 0 1 -179.9204 -657.2685 cm -BT -/F48 10.9091 Tf 185.3749 657.2685 Td[(http://www.mld2p4.it)]TJ/F15 10.9091 Tf -43.6364 -22.5155 Td[(where)-334(y)28(ou)-333(wil)1(l)-333(als)-1(o)-333(\014n)1(d)-333(con)28(tac)-1(t)-333(p)-27(oin)28(ts)-333(for)-333(f)1(urth)1(e)-1(r)-333(i)1(nf)1(ormation)-333(and)-332(bug)-333(rep)-27(orts.)]TJ 16.9365 -13.5492 Td[(The)-318(s)-1(of)1(t)28(w)27(are)-318(is)-319(a)28(v)56(ailab)1(le)-318(und)1(e)-1(r)-317(a)-319(mo)-28(d)1(i\014ed)-318(BSD)-318(l)1(ic)-1(ense,)-321(as)-319(sp)-28(ec)-1(i)1(\014ed)-318(in)-318(ap)1(p)-27(e)-1(n)1(dix)]TJ -ET -1 0 0 1 542.9775 621.2038 cm +/F46 10.9091 Tf 43.637 -22.515 Td [(http://www.mld2p4.it)]TJ/F15 10.9091 Tf -43.637 -22.516 Td [(where)-333(y)27(ou)-333(will)-333(also)-334(\014n)1(d)-334(con)28(tact)-333(p)-28(oin)28(ts)-334(for)-333(further)-333(information)-333(and)-333(bug)-334(rep)-27(orts.)]TJ 16.937 -13.549 Td [(The)-318(soft)28(w)27(are)-318(is)-318(a)28(v)55(ailab)1(le)-319(under)-318(a)-318(mo)-28(di\014ed)-318(BSD)-318(license,)-321(as)-318(sp)-28(eci\014ed)-318(in)-318(app)-28(endix)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -542.9775 -621.2038 cm -BT -/F15 10.9091 Tf 542.9775 621.2038 Td[(A)]TJ -ET -1 0 0 1 551.1593 621.2038 cm + [-318(A)]TJ 0 g 0 G -1 0 0 1 -551.1593 -621.2038 cm -BT -/F15 10.9091 Tf 551.1593 621.2038 Td[(;)]TJ -409.4208 -13.5492 Td[(pl)1(e)-1(ase)-449(n)1(ote)-449(t)1(hat)-448(som)-1(e)-448(of)-448(th)1(e)-449(op)1(tion)1(al)-448(thi)1(rd)-448(p)1(art)28(y)-448(l)1(ibr)1(aries)-449(ma)28(y)-448(b)-27(e)-449(li)1(c)-1(ense)-1(d)-447(un)1(der)-448(a)]TJ 0 -13.5492 Td[(di)1(\013)-1(eren)28(t)-366(an)1(d)-366(more)-366(s)-1(tr)1(ingen)28(t)-366(l)1(ic)-1(ense,)-374(m)-1(ost)-366(n)1(otably)-365(the)-366(GP)1(L,)-366(and)-365(thi)1(s)-367(shou)1(ld)-365(b)-28(e)-366(tak)28(en)]TJ 0 -13.5492 Td[(in)28(t)1(o)-334(acc)-1(ou)1(n)28(t)-333(when)-333(treating)-333(d)1(e)-1(ri)1(v)28(e)-1(d)-333(w)28(orks.)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [(;)]TJ -16.937 -13.549 Td [(please)-448(note)-448(that)-448(some)-448(of)-448(the)-448(optional)-448(third)-448(part)28(y)-448(libraries)-448(ma)28(y)-448(b)-28(e)-448(licensed)-448(under)-448(a)]TJ 0 -13.55 Td [(di\013eren)28(t)-366(and)-366(more)-366(stringen)28(t)-366(license,)-374(most)-366(notably)-366(the)-366(GPL,)-366(and)-365(this)-366(should)-366(b)-28(e)-366(tak)28(en)]TJ 0 -13.549 Td [(in)28(to)-334(accoun)28(t)-333(when)-333(treating)-334(deriv)28(ed)-333(w)28(orks.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -209 0 obj << +192 0 obj << /Type /Page -/Contents 210 0 R -/Resources 208 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 185 0 R -/Annots [ 215 0 R ] +/Contents 193 0 R +/Resources 191 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 167 0 R +/Annots [ 190 0 R ] >> endobj -215 0 obj << +190 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [541.9812 618.0863 552.1556 629.7758] +/Rect [541.981 618.086 552.156 629.776] /Subtype /Link -/A << /S /GoTo /D (section.A) >> +/A << /S /GoTo /D (appendix.A) >> >> endobj -211 0 obj << -/D [209 0 R /XYZ 141.7385 740.0018 null] +194 0 obj << +/D [192 0 R /XYZ 141.738 740.002 null] >> endobj 18 0 obj << -/D [209 0 R /XYZ 141.7385 715.0952 null] +/D [192 0 R /XYZ 141.738 715.095 null] >> endobj -208 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F19 105 0 R /F48 214 0 R >> +191 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F17 103 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -218 0 obj << -/Length 8551 +199 0 obj << +/Length 6515 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(4)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(4)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Configuri)-1(ng)-378(an)-1(d)-378(Build)-1(ing)-378(ML)-1(D2)1(P4)]TJ/F15 10.9091 Tf 396.8452 0 Td[(5)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Configuring)-378(and)-377(Bu)-1(ilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.996 0 Td [(5)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(4)-1125(C)-1(on\014g)-1(uri)-1(ng)-375(and)-375(Bui)-1(ldi)-1(ng)-375(MLD2)-1(P)1(4)]TJ/F15 10.9091 Tf 0 -27.0987 Td[(T)83(o)-324(bu)1(ild)-324(M)1(LD2P4)-324(it)-324(is)-324(nec)-1(es)-1(sary)-324(to)-324(se)-1(t)-324(u)1(p)-324(a)-324(Mak)28(e)-1(\014)1(le)-325(with)-323(app)1(ropr)1(iate)-325(v)56(alu)1(e)-1(s)-324(for)-324(y)28(ou)1(r)]TJ 0 -13.5492 Td[(sys)-1(tem;)-363(th)1(is)-354(i)1(s)-354(d)1(one)-354(b)29(y)-353(me)-1(an)1(s)-354(of)-353(t)1(he)]TJ/F48 10.9091 Tf 179.0991 0 Td[(configure)]TJ/F15 10.9091 Tf 55.3961 0 Td[(sc)-1(ri)1(pt.)-503(The)-353(distri)1(but)1(ion)-353(also)-353(in)1(c)-1(lu)1(des)]TJ -234.4952 -13.5492 Td[(th)1(e)-413(auto)-27(c)-1(on)1(f)-412(and)-411(automak)28(e)-413(sources)-413(e)-1(mp)1(lo)28(y)28(e)-1(d)-412(to)-412(generate)-412(the)-413(scrip)1(t,)-432(bu)1(t)-412(thi)1(s)-413(s)-1(h)1(oul)1(d)]TJ 0 -13.5492 Td[(not)-333(n)1(ormally)-333(b)-27(e)-334(nee)-1(d)1(e)-1(d)-332(to)-334(b)1(uil)1(d)-333(the)-333(s)-1(of)1(t)27(w)28(are.)]TJ 16.9365 -14.9628 Td[(MLD2P)1(4)-333(is)-334(impl)1(e)-1(me)-1(n)29(te)-1(d)-333(al)1(m)-1(ost)-333(e)-1(n)28(ti)1(rely)-333(in)-333(F)84(ortran)-333(95,)-333(with)-332(s)-1(ome)-334(in)28(t)1(e)-1(rf)1(ac)-1(es)-334(to)-333(ex-)]TJ -16.9365 -13.5492 Td[(ternal)-252(li)1(brar)1(ie)-1(s)-253(i)1(n)-252(C)-1(;)-252(w)28(e)-253(re)-1(q)1(uir)1(e)-253(the)-253(F)84(ortr)1(an)-253(compil)1(e)-1(r)-252(to)-253(sup)1(p)-27(ort)-253(t)1(he)-253(F)84(ortran)-252(95)-252(s)-1(tan)1(dar)1(d)]TJ 0 -13.5492 Td[(pl)1(us)-408(the)-408(e)-1(xtension)-407(T)-1(R15581,)-426(w)-1(h)1(ic)27(h)-407(e)-1(n)1(han)1(c)-1(es)-409(th)1(e)-409(u)1(s)-1(ab)1(ilit)28(y)-408(of)]TJ/F48 10.9091 Tf 300.3641 0 Td[(ALLOCATABLE)]TJ/F15 10.9091 Tf 67.4506 0 Td[(v)56(ariab)1(les)-1(.)]TJ -367.8147 -13.5492 Td[(Most)-342(mo)-28(dern)-342(F)84(ortr)1(an)-342(com)-1(p)1(ilers)-342(s)-1(u)1(pp)-27(ort)-342(th)1(is)-343(l)1(anguage)-342(lev)28(e)-1(l)1(.)-471(In)-342(p)1(articul)1(ar,)-344(thi)1(s)-343(is)-342(s)-1(u)1(p-)]TJ 0 -13.5492 Td[(p)-27(orted)-297(b)28(y)-296(the)-297(GNU)-296(F)83(or)1(tran)-296(c)-1(ompil)1(e)-1(r)-296(as)-298(of)-296(v)28(ersion)-297(4.)1(2.0;)-309(h)1(o)27(w)28(e)-1(v)28(er)-297(w)28(e)-297(rec)-1(omme)-1(n)1(d)-297(to)-297(u)1(s)-1(e)]TJ 0 -13.5492 Td[(th)1(e)-296(lates)-1(t)-295(a)28(v)55(ai)1(labl)1(e)-296(rele)-1(ase)-296(\0504.3.)1(1)-296(at)-295(th)1(e)-296(time)-296(of)-295(thi)1(s)-296(writi)1(ng\051.)-432(Th)1(e)-296(s)-1(of)1(t)28(w)27(ar)1(e)-296(de\014n)1(e)-1(s)-296(d)1(ata)]TJ 0 -13.5492 Td[(t)28(yp)-27(e)-1(s)-333(and)-333(in)29(te)-1(r)1(face)-1(s)-334(f)1(or)-333(real)-333(and)-333(com)-1(p)1(lex)-334(d)1(ata,)-333(in)-333(b)-27(oth)-333(singl)1(e)-334(and)-333(d)1(oub)1(le)-334(p)1(re)-1(cision.)]TJ/F19 11.9552 Tf 0 -37.2909 Td[(4.)-1(1)-1125(Pre)-1(re)-1(q)1(ui)-1(sit)-1(es)]TJ/F15 10.9091 Tf 0 -23.3411 Td[(The)-334(f)1(ollo)28(win)1(g)-334(b)1(as)-1(e)-334(l)1(ibr)1(aries)-334(are)-333(nee)-1(d)1(e)-1(d)1(:)]TJ -ET -1 0 0 1 88.4633 451.33 cm +/F17 14.3462 Tf -406.996 -35.866 Td [(4)-1125(Con\014guring)-375(and)-375(Building)-375(MLD2P4)]TJ/F15 10.9091 Tf 0 -27.098 Td [(T)83(o)-324(build)-324(MLD2P4)-324(it)-324(is)-325(necessary)-324(to)-324(set)-324(up)-325(a)-324(Mak)28(e\014le)-324(with)-324(appropriate)-325(v)56(alues)-324(for)-324(y)27(our)]TJ 0 -13.55 Td [(system;)-363(this)-353(is)-353(done)-353(b)28(y)-353(means)-353(of)-353(the)]TJ/F46 10.9091 Tf 179.099 0 Td [(configure)]TJ/F15 10.9091 Tf 55.396 0 Td [(script.)-503(T)-1(h)1(e)-354(d)1(is)-1(tr)1(ibution)-353(also)-353(includes)]TJ -234.495 -13.549 Td [(the)-412(auto)-28(conf)-412(and)-412(automak)28(e)-413(sources)-412(emplo)28(y)28(ed)-413(to)-412(generate)-412(the)-412(script,)-432(but)-412(this)-413(shou)1(ld)]TJ 0 -13.549 Td [(not)-333(normally)-333(b)-28(e)-334(needed)-333(to)-333(build)-333(the)-334(soft)28(w)28(are.)]TJ 16.936 -14.963 Td [(MLD2P4)-333(is)-334(implemen)28(ted)-333(almost)-334(en)28(tirely)-333(in)-333(F)83(ortran)-333(95,)-333(with)-334(some)-333(in)28(terfaces)-334(to)-333(ex-)]TJ -16.936 -13.549 Td [(ternal)-252(libraries)-253(in)-252(C;)-253(w)28(e)-253(require)-252(the)-253(F)83(or)1(tran)-253(compiler)-253(to)-252(supp)-28(ort)-252(the)-253(F)84(ortran)-253(95)-252(standard)]TJ 0 -13.549 Td [(plus)-408(the)-408(extension)-408(TR15581,)-427(whic)28(h)-408(enhances)-408(the)-409(usabili)1(t)27(y)-408(of)]TJ/F46 10.9091 Tf 300.364 0 Td [(ALLOCATABLE)]TJ/F15 10.9091 Tf 67.451 0 Td [(v)56(ariables.)]TJ -367.815 -13.549 Td [(Most)-342(mo)-28(dern)-342(F)83(ort)1(ran)-342(c)-1(ompil)1(e)-1(rs)-342(supp)-27(ort)-342(this)-342(language)-342(lev)27(el.)-470(In)-342(particular,)-344(this)-343(is)-342(sup-)]TJ 0 -13.55 Td [(p)-28(orted)-297(b)28(y)-296(the)-297(GNU)-297(F)83(ortran)-296(c)-1(ompi)1(le)-1(r)-296(as)-297(of)-297(v)28(ersion)-297(4.2.0;)-309(ho)28(w)28(ev)27(er)-296(w)27(e)-297(recommend)-296(to)-297(use)]TJ 0 -13.549 Td [(the)-295(latest)-296(a)28(v)56(ailable)-296(release)-295(\0504.3.1)-296(at)-295(the)-295(time)-296(of)-295(this)-296(writ)1(ing\051.)-432(The)-296(soft)28(w)28(are)-295(de\014nes)-296(data)]TJ 0 -13.549 Td [(t)28(yp)-28(es)-333(and)-334(in)28(terfaces)-333(for)-333(real)-334(and)-333(complex)-333(data,)-334(in)-333(b)-28(oth)-333(single)-333(and)-333(double)-334(precision.)]TJ/F17 11.9552 Tf 0 -37.291 Td [(4.1)-1125(Prerequisites)]TJ/F15 10.9091 Tf 0 -23.341 Td [(The)-333(follo)28(wing)-334(base)-333(libraries)-333(are)-334(needed:)]TJ 0 g 0 G -1 0 0 1 -88.4633 -451.33 cm -BT -/F41 10.9091 Tf 93.9178 451.33 Td[(BLAS)]TJ -ET -1 0 0 1 126.8418 451.33 cm +/F39 10.9091 Tf 0 -28.17 Td [(BLAS)]TJ 0 g 0 G -1 0 0 1 -126.8418 -451.33 cm -BT -/F15 10.9091 Tf 132.2964 451.33 Td[(The)-341(Bas)-1(ic)-341(Lin)1(e)-1(ar)-340(Algebr)1(a)-341(s)-1(u)1(bp)1(rograms.)-467(Man)29(y)-341(v)28(end)1(ors)-341(pr)1(o)27(v)1(ide)-341(opt)1(im)-1(i)1(z)-1(ed)-341(v)28(er-)]TJ -11.1058 -13.5492 Td[(sions;)-534(if)-466(no)-467(v)28(end)1(or)-467(v)28(e)-1(r)1(s)-1(ion)-466(is)-467(a)27(v)56(ail)1(able)-467(for)-467(a)-467(gi)1(v)28(e)-1(n)-466(platf)1(orm,)-500(the)-467(A)83(TLAS)-467(soft-)]TJ 0 -13.5492 Td[(w)28(are)]TJ/F48 10.9091 Tf 27.2523 0 Td[(http://www.netlib.org/atlas)]TJ/F15 10.9091 Tf 159.7355 0 Td[(ma)27(y)-467(b)-27(e)-468(e)-1(mpl)1(o)27(y)28(ed.)-847(Th)1(e)-468(refere)-1(n)1(c)-1(e)-468(BLAS)]TJ -186.9878 -13.5492 Td[(fr)1(om)-319(Netlib)]TJ/F48 10.9091 Tf 58.4945 0 Td[(http://www.netlib.org/blas)]TJ/F15 10.9091 Tf 152.382 0 Td[(are)-319(mean)28(t)-319(t)1(o)-319(d)1(e)-1(\014n)1(e)-319(th)1(e)-319(s)-1(tan)1(dard)-318(b)-27(e-)]TJ -210.8765 -13.5492 Td[(ha)28(vi)1(our)-298(of)-299(t)1(he)-299(BLAS)-299(i)1(n)28(te)-1(r)1(face)-1(,)-305(s)-1(o)-298(they)-299(n)1(ot)-299(op)1(timiz)-1(ed)-298(for)-298(an)28(y)-298(parti)1(c)-1(u)1(lar)-298(plaf)1(torm,)]TJ 0 -13.5492 Td[(and)-389(s)-1(h)1(ould)-390(on)1(ly)-390(b)-27(e)-391(u)1(s)-1(ed)-390(as)-391(a)-390(last)-391(r)1(e)-1(sort.)-615(Note)-390(that)-390(BLAS)-390(com)-1(p)1(utati)1(on)-390(for)1(m)-391(a)]TJ 0 -13.5492 Td[(relativ)28(ely)-404(sm)-1(al)1(l)-405(p)1(art)-404(of)-404(th)1(e)-405(MLD2P)1(4/PS)1(B)-1(LAS)-404(comput)1(ations;)-440(th)1(e)-1(y)-404(ar)1(e)-405(ho)28(w)28(e)-1(v)28(er)]TJ 0 -13.5492 Td[(critical)-406(w)-1(h)1(e)-1(n)-406(u)1(s)-1(in)1(g)-407(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-407(base)-1(d)-406(on)-406(the)-407(UM)1(FP)84(A)27(CK)-406(or)-406(Sup)-27(erLU)-407(t)1(hir)1(d)]TJ 0 -13.5492 Td[(par)1(t)28(y)-333(libr)1(aries)-1(.)]TJ -ET -1 0 0 1 88.4633 314.7664 cm +/F15 10.9091 Tf 38.378 0 Td [(The)-341(Basic)-341(Linear)-340(Algebra)-341(subprograms.)-467(Man)28(y)-341(v)28(endors)-340(pro)27(vide)-340(optimized)-341(v)28(er-)]TJ -11.105 -13.549 Td [(sions;)-534(if)-467(no)-467(v)28(endor)-467(v)28(ersion)-467(is)-467(a)27(v)56(ailable)-467(for)-467(a)-467(giv)28(en)-467(platform,)-501(the)-467(A)84(TLAS)-467(soft-)]TJ 0 -13.549 Td [(w)28(are)]TJ/F46 10.9091 Tf 27.252 0 Td [(http://www.netlib.org/atlas)]TJ/F15 10.9091 Tf 159.735 0 Td [(ma)28(y)-468(b)-28(e)-467(emplo)28(y)27(ed.)-847(The)-467(reference)-468(BLAS)]TJ -186.987 -13.55 Td [(from)-318(Netlib)]TJ/F46 10.9091 Tf 58.494 0 Td [(http://www.netlib.org/blas)]TJ/F15 10.9091 Tf 152.382 0 Td [(are)-319(mean)28(t)-318(to)-319(de\014ne)-318(the)-319(standard)-318(b)-28(e-)]TJ -210.876 -13.549 Td [(ha)28(viour)-299(of)-298(the)-299(BLAS)-299(in)28(terface,)-306(so)-298(they)-299(not)-299(optimized)-298(for)-299(an)28(y)-299(particular)-298(plaftorm,)]TJ 0 -13.549 Td [(and)-390(should)-390(only)-390(b)-28(e)-390(us)-1(ed)-390(as)-390(a)-390(last)-391(resort.)-615(Note)-390(that)-390(BLAS)-390(c)-1(ompu)1(tation)-391(form)-390(a)]TJ 0 -13.549 Td [(relativ)28(ely)-404(s)-1(mall)-404(part)-404(of)-404(the)-405(MLD2P4/PSBLAS)-404(computations;)-440(they)-404(are)-404(ho)27(w)28(ev)28(er)]TJ 0 -13.549 Td [(critical)-407(when)-406(using)-407(preconditioners)-406(based)-407(on)-407(the)-406(UMFP)83(A)28(CK)-407(or)-406(Sup)-28(erLU)-406(third)]TJ 0 -13.55 Td [(part)28(y)-333(libraries.)]TJ 0 g 0 G -1 0 0 1 -88.4633 -314.7664 cm -BT -/F41 10.9091 Tf 93.9178 314.7664 Td[(MPI)]TJ -ET -1 0 0 1 119.1601 314.7664 cm +/F39 10.9091 Tf -27.273 -28.17 Td [(MPI)]TJ 0 g 0 G -1 0 0 1 -119.1601 -314.7664 cm -BT -/F15 10.9091 Tf 124.6147 314.7664 Td[(A)-373(v)28(e)-1(r)1(s)-1(ion)-372(of)-373(MPI)-373(is)-373(a)27(v)56(ail)1(able)-374(on)-372(m)-1(ost)-373(high)-373(p)-27(erfor)1(m)-1(an)1(c)-1(e)-373(c)-1(ompu)1(ting)-373(sys)-1(t)1(e)-1(m;)-393(w)27(e)]TJ -3.4241 -13.5492 Td[(onl)1(y)-333(re)-1(q)1(uir)1(e)-334(v)28(e)-1(r)1(s)-1(i)1(on)-333(1.1.)]TJ -ET -1 0 0 1 88.4633 273.0473 cm +/F15 10.9091 Tf 30.697 0 Td [(A)-373(v)28(ers)-1(i)1(on)-374(of)-373(MPI)-373(is)-374(a)28(v)56(ailable)-373(on)-374(most)-373(high)-373(p)-28(erformance)-373(computing)-374(system;)-393(w)28(e)]TJ -3.424 -13.549 Td [(only)-333(require)-333(v)27(ersion)-333(1.1.)]TJ 0 g 0 G -1 0 0 1 -88.4633 -273.0473 cm -BT -/F41 10.9091 Tf 93.9178 273.0473 Td[(BLA)32(CS)]TJ -ET -1 0 0 1 135.5539 273.0473 cm +/F39 10.9091 Tf -27.273 -28.17 Td [(BLA)32(CS)]TJ 0 g 0 G -1 0 0 1 -135.5539 -273.0473 cm -BT -/F15 10.9091 Tf 141.0085 273.0473 Td[(The)-274(Basic)-274(Lin)1(e)-1(ar)-273(Algebr)1(a)-274(Comm)27(u)1(nication)-273(S)1(ubr)1(outi)1(nes)-274(are)-274(a)28(v)56(ailab)1(le)-274(in)-273(sour)1(c)-1(e)]TJ -19.8179 -13.5492 Td[(for)1(m)-380(f)1(rom)]TJ/F48 10.9091 Tf 52.5736 0 Td[(http://www.netlib.org/blacs)]TJ/F15 10.9091 Tf 154.6347 0 Td[(;)-402(some)-380(v)28(endor)1(s)-380(in)1(c)-1(l)1(ud)1(e)-380(th)1(e)-1(m)-379(in)-379(t)1(heir)]TJ -207.2083 -13.5492 Td[(par)1(allel)-333(c)-1(ompu)1(tin)1(g)-334(sup)1(p)-28(or)1(t)-334(l)1(ibr)1(aries)-1(.)]TJ -10.3363 -28.17 Td[(The)-222(MLD2P4)-222(soft)28(w)28(are)-223(r)1(e)-1(qu)1(ires)-223(P)1(SBLAS)-222(v)28(ersion)-222(2.3)-222(\050at)-222(leas)-1(t)1(\051,)-245(a)28(v)56(ailab)1(le)-223(f)1(rom)]TJ/F48 10.9091 Tf 361.8477 0 Td[(http://www.ce.uniroma2.it/psblas)]TJ/F15 10.9091 Tf 183.2708 0 Td[(;)]TJ -562.055 -13.5492 Td[(in)1(dee)-1(d)1(,)-300(all)-292(th)1(e)-292(prerequi)1(s)-1(it)1(e)-1(s)-292(liste)-1(d)-291(so)-292(far)1(e)-293(ar)1(e)-293(also)-292(p)1(rere)-1(q)1(uisites)-293(of)-291(PS)1(BLAS.)-292(P)1(leas)-1(e)-292(note)]TJ 0 -13.5492 Td[(th)1(at)-361(t)1(o)-361(b)1(ui)1(ld)-360(th)1(e)-361(MLD2P)1(4)-360(lib)1(rary)-360(i)1(t)-360(is)-361(n)1(e)-1(ce)-1(ss)-1(ar)1(y)-360(to)-360(ge)-1(t)-360(acc)-1(es)-1(s)-360(to)-360(the)-360(s)-1(ou)1(rce)-361(PS)1(BLAS)]TJ 0 -13.5492 Td[(di)1(rec)-1(tor)1(y)-381(u)1(s)-1(ed)-380(to)-380(bu)1(ild)-380(th)1(e)-381(v)28(e)-1(r)1(s)-1(i)1(on)-380(und)1(e)-1(r)-380(u)1(s)-1(e;)-404(af)1(te)-1(r)-380(th)1(e)-381(b)1(uild)-380(p)1(ro)-28(ces)-1(s)-381(complete)-1(s,)-392(on)1(ly)]TJ 0 -13.5492 Td[(th)1(e)-334(c)-1(ompi)1(le)-1(d)-332(form)-333(of)-333(the)-333(libr)1(ary)-333(is)-334(n)1(e)-1(ces)-1(sary)-333(to)-333(bu)1(ild)-333(u)1(s)-1(er)-333(app)1(lications.)]TJ 16.9365 -14.9628 Td[(Pl)1(e)-1(ase)-463(n)1(ote)-463(th)1(at)-462(all)-462(t)1(he)-463(l)1(ibr)1(aries)-463(l)1(is)-1(ted)-462(so)-462(far)1(e)-463(\050BLAS,)-461(MPI,)-461(B)-1(LA)28(CS,)-462(P)1(SBLAS\051)]TJ -16.9365 -13.5492 Td[(m)27(u)1(s)-1(t)-417(h)1(a)27(v)28(e)-417(F)83(ort)1(ran)-417(in)28(t)1(e)-1(rf)1(ac)-1(es)-418(com)-1(p)1(atib)1(le)-418(with)-417(th)1(e)-418(MLD2P)1(4;)-459(usuall)1(y)-418(t)1(his)-418(means)-418(th)1(at)]TJ 0 -13.5492 Td[(th)1(e)-1(y)-333(shoul)1(d)-333(all)-333(b)-27(e)-334(bu)1(ilt)-333(with)-333(th)1(e)-334(s)-1(ame)-334(compiler.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F15 10.9091 Tf 47.091 0 Td [(The)-273(Basic)-274(Linear)-273(Algebra)-274(Comm)28(unication)-273(Subroutines)-273(are)-274(a)28(v)55(ailab)1(le)-274(in)-273(source)]TJ -19.818 -13.549 Td [(form)-379(from)]TJ/F46 10.9091 Tf 52.573 0 Td [(http://www.netlib.org/blacs)]TJ/F15 10.9091 Tf 154.635 0 Td [(;)-402(some)-379(v)28(endors)-379(include)-379(them)-379(in)-379(their)]TJ -207.208 -13.549 Td [(parallel)-333(computing)-333(s)-1(u)1(pp)-28(ort)-333(libraries.)]TJ -10.337 -28.17 Td [(The)-222(MLD2P4)-222(soft)27(w)28(are)-222(requires)-222(PSBLAS)-222(v)27(ersion)-222(2.3)-222(\050at)-222(least\051,)-245(a)28(v)56(ailable)-222(from)]TJ/F46 10.9091 Tf 361.848 0 Td [(http://www.ce.uniroma2.it/psblas)]TJ/F15 10.9091 Tf 183.271 0 Td [(;)]TJ -562.055 -13.549 Td [(indeed,)-328(all)-326(the)-327(prerequisites)-327(l)1(is)-1(ted)-326(so)-327(far)-326(are)-327(also)-326(prerequisites)-327(of)-327(P)1(SBLAS.)-327(Please)-327(note)]TJ 0 -13.549 Td [(that)-360(to)-360(build)-360(the)-360(MLD2P4)-360(library)-360(it)-361(is)-360(necessary)-360(to)-360(get)-360(acce)-1(ss)-360(to)-360(the)-360(source)-360(PSBLAS)]TJ 0 -13.55 Td [(directory)-380(used)-381(to)-380(build)-380(the)-381(v)28(ersion)-380(under)-380(use;)-404(after)-381(the)-380(build)-380(pro)-28(cess)-381(completes,)-392(only)]TJ 0 -13.549 Td [(the)-333(compiled)-334(form)-333(of)-333(the)-334(lib)1(rary)-334(is)-333(necessary)-334(to)-333(build)-333(user)-333(applications.)]TJ 16.936 -14.963 Td [(Please)-462(note)-462(that)-462(all)-462(the)-462(libraries)-462(listed)-462(so)-462(fare)-462(\050BLAS,)-462(MPI,)-462(BLA)28(CS,)-462(PSBLAS\051)]TJ -16.936 -13.549 Td [(m)28(ust)-418(ha)28(v)28(e)-417(F)83(ortran)-417(in)28(terfaces)-418(compatible)-417(with)-418(th)1(e)-418(MLD2P4;)-459(usually)-417(this)-418(means)-417(that)]TJ 0 -13.549 Td [(they)-333(should)-334(al)1(l)-334(b)-28(e)-333(built)-333(with)-333(the)-334(same)-333(compiler.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -217 0 obj << +198 0 obj << /Type /Page -/Contents 218 0 R -/Resources 216 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 185 0 R -/Annots [ 220 0 R ] +/Contents 199 0 R +/Resources 197 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 167 0 R +/Annots [ 196 0 R ] >> endobj -220 0 obj << +196 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -219 0 obj << -/D [217 0 R /XYZ 93.9178 740.0018 null] +200 0 obj << +/D [198 0 R /XYZ 93.918 740.002 null] >> endobj 22 0 obj << -/D [217 0 R /XYZ 93.9178 715.0952 null] +/D [198 0 R /XYZ 93.918 715.095 null] >> endobj 26 0 obj << -/D [217 0 R /XYZ 93.9178 516.0812 null] +/D [198 0 R /XYZ 93.918 516.081 null] >> endobj -216 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F48 214 0 R /F41 126 0 R >> +197 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F46 195 0 R /F39 116 0 R >> /ProcSet [ /PDF /Text ] >> endobj -223 0 obj << -/Length 6767 +203 0 obj << +/Length 5253 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(6)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(6)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F19 11.9552 Tf 141.7385 704.1363 Td[(4.)-1(2)-1125(Opt)-1(io)-1(nal)-375(t)-1(hir)-1(d)-375(part)31(y)-375(l)-1(ibr)-1(a)1(r)-1(ie)-1(s)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(W)84(e)-427(pro)28(vi)1(de)-427(in)28(t)1(e)-1(rf)1(ac)-1(es)-427(to)-426(the)-427(f)1(ollo)28(wing)-426(thi)1(rd-par)1(t)28(y)-427(soft)28(w)28(are)-427(li)1(brar)1(ie)-1(s;)-473(not)1(e)-427(that)-426(thes)-1(e)]TJ 0 -13.5492 Td[(are)-370(op)1(tional)1(,)-379(bu)1(t)-370(if)-369(y)28(ou)-370(enab)1(le)-370(them)-370(s)-1(ome)-370(defau)1(lts)-370(for)-369(m)27(u)1(ltilev)28(el)-370(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-371(ma)28(y)]TJ 0 -13.5492 Td[(c)27(h)1(ange)-334(t)1(o)-334(r)1(e)-1(\015)1(e)-1(ct)-334(t)1(heir)-333(pr)1(e)-1(se)-1(n)1(c)-1(e.)]TJ -ET -1 0 0 1 136.2839 632.1523 cm +/F17 11.9552 Tf -203.265 -35.866 Td [(4.2)-1125(Optional)-375(third)-375(part)31(y)-375(libraries)]TJ/F15 10.9091 Tf 0 -20.594 Td [(W)83(e)-426(pro)28(vide)-427(in)28(terfaces)-427(to)-426(the)-427(follo)28(wing)-426(third-part)28(y)-427(soft)28(w)28(are)-427(libraries;)-473(note)-427(th)1(at)-427(these)]TJ 0 -13.549 Td [(are)-370(optional,)-379(but)-369(if)-370(y)28(ou)-370(enable)-370(them)-370(some)-370(defaults)-369(for)-370(m)28(ultilev)28(e)-1(l)-369(preconditioners)-370(ma)28(y)]TJ 0 -13.55 Td [(c)28(hange)-334(to)-333(re\015ect)-333(their)-334(pr)1(e)-1(sence.)]TJ 0 g 0 G -1 0 0 1 -136.2839 -632.1523 cm -BT -/F41 10.9091 Tf 141.7385 632.1523 Td[(UM)1(FP)96(A)31(C)1(K)]TJ -ET -1 0 0 1 206.7532 632.1523 cm +/F39 10.9091 Tf 0 -24.291 Td [(UMFP)96(A)32(CK)]TJ 0 g 0 G -1 0 0 1 -206.7532 -632.1523 cm -BT -/F15 10.9091 Tf 212.2078 632.1523 Td[(A)-333(s)-1(p)1(arse)-334(dir)1(e)-1(ct)-333(factorization)-333(p)1(ac)27(k)56(age)-334(a)28(v)56(ailab)1(le)-334(fr)1(om)]TJ/F48 10.9091 Tf -43.1965 -13.5492 Td[(http://www.cise.ufl.edu/research/sparse/umfpack/)]TJ/F15 10.9091 Tf 274.9061 0 Td[(;)-359(pro)28(vi)1(des)-352(serial)-350(factor-)]TJ -274.9061 -13.5492 Td[(ization)-328(and)-328(solu)1(tion)-328(for)-328(d)1(oub)1(le)-329(pr)1(e)-1(cis)-1(i)1(on)-328(real)-329(an)1(d)-328(c)-1(ompl)1(e)-1(x)-328(dou)1(ble)-329(p)1(rec)-1(ision)-328(d)1(ata.)]TJ 0 -13.5492 Td[(W)84(e)-334(ha)28(v)28(e)-334(tes)-1(t)1(e)-1(d)-333(v)28(ersions)-333(4.4)-334(an)1(d)-333(5.1;)]TJ -ET -1 0 0 1 136.2839 569.3936 cm +/F15 10.9091 Tf 70.47 0 Td [(A)-333(sparse)-334(direct)-333(factorization)-333(pac)28(k)55(age)-333(a)27(v)56(ailable)-333(from)]TJ/F46 10.9091 Tf -43.197 -13.549 Td [(http://www.cise.ufl.edu/research/sparse/umfpack/)]TJ/F15 10.9091 Tf 274.906 0 Td [(;)-360(p)1(ro)27(vides)-350(se)-1(r)1(ial)-351(factor-)]TJ -274.906 -13.549 Td [(ization)-328(and)-329(solution)-328(for)-329(double)-328(precision)-329(real)-328(and)-329(complex)-328(double)-328(precision)-329(data.)]TJ 0 -13.549 Td [(W)83(e)-333(ha)28(v)28(e)-334(tested)-333(v)28(ersions)-334(4.4)-333(and)-333(5.1;)]TJ 0 g 0 G -1 0 0 1 -136.2839 -569.3936 cm -BT -/F41 10.9091 Tf 141.7385 569.3936 Td[(Sup)-32(er)1(LU)]TJ -ET -1 0 0 1 191.1094 569.3936 cm +/F39 10.9091 Tf -27.273 -22.111 Td [(Sup)-32(erLU)]TJ 0 g 0 G -1 0 0 1 -191.1094 -569.3936 cm -BT -/F15 10.9091 Tf 196.5639 569.3936 Td[(A)-333(s)-1(p)1(arse)-334(dir)1(e)-1(ct)-333(factorization)-333(p)1(ac)27(k)56(age)-334(a)28(v)56(ailab)1(le)-334(fr)1(om)]TJ/F48 10.9091 Tf -27.5526 -13.5492 Td[(http://crd.lbl.gov/~xiaoye/SuperLU/)]TJ/F15 10.9091 Tf 200.4523 0 Td[(;)-543(p)1(ro)28(vid)1(e)-1(s)-474(serial)-473(f)1(ac)-1(tor)1(iz)-1(ati)1(on)-473(and)-472(s)-1(o-)]TJ -200.4523 -13.5492 Td[(lu)1(tion)-450(for)-450(s)-1(in)1(gle)-451(and)-450(dou)1(bl)1(e)-452(p)1(rec)-1(ision)-450(real)-451(an)1(d)-451(complex)-451(d)1(ata.)-797(W)84(e)-451(ha)28(v)28(e)-451(te)-1(sted)]TJ 0 -13.5492 Td[(v)28(ers)-1(i)1(ons)-334(3.)1(0)-334(an)1(d)-333(3.1.)]TJ -ET -1 0 0 1 136.2839 506.6349 cm +/F15 10.9091 Tf 54.826 0 Td [(A)-333(sparse)-334(direct)-333(factorization)-333(pac)28(k)55(age)-333(a)27(v)56(ailable)-333(from)]TJ/F46 10.9091 Tf -27.553 -13.55 Td [(http://crd.lbl.gov/~xiaoye/SuperLU/)]TJ/F15 10.9091 Tf 200.453 0 Td [(;)-543(pro)28(vides)-473(se)-1(r)1(ial)-474(factorization)-473(and)-473(so-)]TJ -200.453 -13.549 Td [(lution)-451(for)-450(single)-451(and)-451(double)-450(precision)-451(real)-451(and)-451(complex)-450(data.)-797(W)83(e)-451(ha)28(v)28(e)-451(tested)]TJ 0 -13.549 Td [(v)28(ersions)-334(3.0)-333(and)-333(3.1.)]TJ 0 g 0 G -1 0 0 1 -136.2839 -506.6349 cm -BT -/F41 10.9091 Tf 141.7385 506.6349 Td[(Sup)-32(er)1(LU)]TJ +/F39 10.9091 Tf -27.273 -22.111 Td [(Sup)-32(erLU)]TJ ET -1 0 0 1 191.8621 506.6349 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.7636 0.1992 l -S +1 0 0 1 191.862 506.834 cm +[]0 d 0 J 0.398 w 0 0 m 3.764 0 l S Q -1 0 0 1 -191.8621 -506.6349 cm BT -/F41 10.9091 Tf 195.6257 506.6349 Td[(Dist)]TJ -ET -1 0 0 1 218.5589 506.6349 cm +/F39 10.9091 Tf 195.626 506.635 Td [(Dist)]TJ 0 g 0 G -1 0 0 1 -218.5589 -506.6349 cm -BT -/F15 10.9091 Tf 224.0134 506.6349 Td[(A)-370(sparse)-370(dir)1(e)-1(ct)-370(factori)1(z)-1(ation)-369(pac)28(k)55(age)-370(a)28(v)56(ailabl)1(e)-371(f)1(rom)-370(the)-370(sam)-1(e)-370(s)-1(i)1(te)-371(as)]TJ -55.0021 -13.5492 Td[(Su)1(p)-27(e)-1(rLU;)-284(pro)28(vi)1(des)-286(p)1(arall)1(e)-1(l)-285(f)1(ac)-1(tor)1(ization)-285(an)1(d)-285(solut)1(ion)-285(f)1(or)-285(real)-285(an)1(d)-285(com)-1(p)1(lex)-285(dou)1(ble)]TJ 0 -13.5492 Td[(pr)1(e)-1(cision)-333(dat)1(a.)-445(W)84(e)-334(h)1(a)27(v)28(e)-333(te)-1(ste)-1(d)-332(v)28(e)-1(rsion)-333(2.)1(1.)]TJ/F19 11.9552 Tf -27.2728 -29.0221 Td[(4.)-1(3)-1125(C)-1(on\014g)-1(urat)-1(io)-1(n)-375(opt)-1(io)-1(ns)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(T)83(o)-302(bu)1(ild)-302(M)1(LD2P4)-302(th)1(e)-303(\014r)1(s)-1(t)-302(ste)-1(p)-301(is)-303(to)-302(use)-303(th)1(e)]TJ/F48 10.9091 Tf 214.0019 0 Td[(configure)]TJ/F15 10.9091 Tf 54.8421 0 Td[(sc)-1(ri)1(pt)-302(in)-302(t)1(he)-303(main)-302(d)1(irec)-1(t)1(ory)-302(to)]TJ -268.844 -13.5492 Td[(generate)-334(th)1(e)-334(nece)-1(ss)-1(ar)1(y)-334(mak)28(e\014le\050s\051.)]TJ 16.9365 -13.5492 Td[(As)-334(a)-333(minimal)-333(exam)-1(p)1(le)-334(consid)1(e)-1(r)-333(th)1(e)-334(fol)1(lo)28(w)-1(i)1(ng:)]TJ -ET -1 0 0 1 136.2839 381.3169 cm +/F15 10.9091 Tf 28.387 0 Td [(A)-370(sparse)-370(direct)-370(factorization)-370(pac)28(k)56(age)-370(a)27(v)56(ailable)-370(from)-370(the)-370(same)-370(site)-370(as)]TJ -55.002 -13.549 Td [(Sup)-28(erLU;)-285(pro)28(vides)-285(parallel)-285(factorization)-284(and)-285(solution)-285(for)-285(real)-285(and)-285(complex)-285(double)]TJ 0 -13.549 Td [(precision)-333(data.)-445(W)84(e)-334(ha)28(v)28(e)-333(te)-1(sted)-333(v)28(ersion)-333(2.1.)]TJ/F17 11.9552 Tf -27.273 -29.023 Td [(4.3)-1125(Con\014guration)-375(options)]TJ/F15 10.9091 Tf 0 -20.594 Td [(T)83(o)-302(build)-302(MLD2P4)-302(the)-302(\014rst)-303(step)-302(is)-302(to)-302(use)-303(the)]TJ/F46 10.9091 Tf 214.002 0 Td [(configure)]TJ/F15 10.9091 Tf 54.842 0 Td [(script)-302(in)-302(the)-303(main)-302(directory)-302(to)]TJ -268.844 -13.549 Td [(generate)-333(the)-334(necessary)-333(mak)28(e\014le\050s)-1(\051)1(.)]TJ 16.937 -13.55 Td [(As)-333(a)-334(minimal)-333(example)-333(consider)-334(the)-333(follo)28(wing:)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -136.2839 -381.3169 cm -BT -/F48 10.9091 Tf 141.7385 381.3169 Td[(./configure)-525(--with-psblas=/home/user/PSBLAS/psblas-2.3)]TJ/F15 10.9091 Tf 0 -21.5044 Td[(This)-317(as)-1(sumes)-318(th)1(at)-317(the)-317(v)56(ariou)1(s)-318(MP)1(I)-317(c)-1(ompi)1(le)-1(r)1(s)-318(an)1(d)-317(supp)-27(ort)-317(l)1(ibr)1(aries)-318(ar)1(e)-318(a)28(v)56(ailab)1(le)-318(in)-316(the)]TJ 0 -13.5492 Td[(stand)1(ard)-415(d)1(irectories)-416(on)-414(th)1(e)-416(syste)-1(m.)-689(Note)-415(th)1(at)-415(the)-415(PS)1(BLAS)-415(b)1(uil)1(d)-415(d)1(irec)-1(tor)1(y)-415(m)27(u)1(s)-1(t)-414(b)-28(e)]TJ 0 -13.5492 Td[(sp)-28(ec)-1(i)1(\014ed)-308(with)-307(an)]TJ/F20 10.9091 Tf 83.1682 0 Td[(absolu)1(t)-1(e)]TJ/F15 10.9091 Tf 41.2739 0 Td[(pat)1(h.)-436(The)-308(f)1(ull)-307(s)-1(et)-308(of)-308(op)1(tion)1(s)-309(ma)28(y)-308(b)-27(e)-309(l)1(o)-28(ok)28(e)-1(d)-307(at)-308(b)28(y)-307(is)-1(sui)1(ng)-308(th)1(e)]TJ -124.4421 -13.5492 Td[(com)-1(mand)]TJ/F48 10.9091 Tf 49.697 0 Td[(./configure)-525(--help)]TJ/F15 10.9091 Tf 103.0898 0 Td[(,)-333(whic)28(h)-333(pr)1(o)-28(du)1(c)-1(es)-1(:)]TJ -ET -1 0 0 1 136.2839 297.6604 cm +/F46 10.9091 Tf -16.937 -21.504 Td [(./configure)-525(--with-psblas=/home/user/PSBLAS/psblas-2.3)]TJ/F15 10.9091 Tf 0 -21.504 Td [(This)-317(assumes)-317(that)-317(the)-317(v)55(arious)-317(MPI)-317(compilers)-317(and)-317(supp)-28(ort)-317(librari)1(e)-1(s)-317(are)-317(a)28(v)56(ailable)-317(in)-317(the)]TJ 0 -13.55 Td [(standard)-415(directories)-415(on)-414(the)-415(system.)-689(Note)-415(that)-415(the)-415(PSBLAS)-415(build)-414(directory)-415(m)28(ust)-415(b)-28(e)]TJ 0 -13.549 Td [(sp)-28(eci\014ed)-308(with)-308(an)]TJ/F18 10.9091 Tf 83.169 0 Td [(absolute)]TJ/F15 10.9091 Tf 41.274 0 Td [(path.)-436(The)-308(full)-308(set)-308(of)-307(options)-308(ma)28(y)-308(b)-28(e)-308(lo)-28(ok)28(ed)-308(at)-308(b)28(y)-308(issuing)-308(the)]TJ -124.443 -13.549 Td [(command)]TJ/F46 10.9091 Tf 49.697 0 Td [(./configure)-525(--help)]TJ/F15 10.9091 Tf 103.09 0 Td [(,)-333(whic)27(h)-333(pro)-28(du)1(c)-1(es:)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -136.2839 -297.6604 cm -BT -/F48 10.9091 Tf 141.7385 297.6604 Td[(`configure')-525(configures)-525(MLD2P4)-525(1.0)-525(to)-525(adapt)-525(to)-525(many)-525(kinds)-525(of)-525(systems.)]TJ 0 -27.0984 Td[(Usage:)-525(./configure)-525([OPTION]...)-525([VAR=VALUE]...)]TJ 0 -27.0984 Td[(To)-525(assign)-525(environment)-525(variables)-525(\050e.g.,)-525(CC,)-525(CFLAGS...\051,)-525(specify)-525(them)-525(as)]TJ 0 -13.5492 Td[(VAR=VALUE.)-1050(See)-525(below)-525(for)-525(descriptions)-525(of)-525(some)-525(of)-525(the)-525(useful)-525(variables.)]TJ 0 -27.0984 Td[(Defaults)-525(for)-525(the)-525(options)-525(are)-525(specified)-525(in)-525(brackets.)]TJ 0 -27.0984 Td[(Configuration:)]TJ 11.4544 -13.5492 Td[(-h,)-525(--help)-7350(display)-525(this)-525(help)-525(and)-525(exit)]TJ 22.9089 -13.5492 Td[(--help=short)-4200(display)-525(options)-525(specific)-525(to)-525(this)-525(package)]TJ 0 -13.5492 Td[(--help=recursive)-2100(display)-525(the)-525(short)-525(help)-525(of)-525(all)-525(the)-525(included)-525(packages)]TJ -22.9089 -13.5492 Td[(-V,)-525(--version)-5775(display)-525(version)-525(information)-525(and)-525(exit)]TJ -ET -1 0 0 1 141.7385 91.633 cm +/F46 10.9091 Tf -152.787 -21.505 Td [(`configure')-525(configures)-525(MLD2P4)-525(1.0)-525(to)-525(adapt)-525(to)-525(many)-525(kinds)-525(of)-525(systems.)]TJ 0 -27.098 Td [(Usage:)-525(./configure)-525([OPTION]...)-525([VAR=VALUE]...)]TJ 0 -27.098 Td [(To)-525(assign)-525(environment)-525(variables)-525(\050e.g.,)-525(CC,)-525(CFLAGS...\051,)-525(specify)-525(them)-525(as)]TJ 0 -13.549 Td [(VAR=VALUE.)-1050(See)-525(below)-525(for)-525(descriptions)-525(of)-525(some)-525(of)-525(the)-525(useful)-525(variables.)]TJ 0 -27.099 Td [(Defaults)-525(for)-525(the)-525(options)-525(are)-525(specified)-525(in)-525(brackets.)]TJ 0 -27.098 Td [(Configuration:)]TJ 11.455 -13.549 Td [(-h,)-525(--help)-7350(display)-525(this)-525(help)-525(and)-525(exit)]TJ 22.909 -13.55 Td [(--help=short)-4200(display)-525(options)-525(specific)-525(to)-525(this)-525(package)]TJ 0 -13.549 Td [(--help=recursive)-2100(display)-525(the)-525(short)-525(help)-525(of)-525(all)-525(the)-525(included)-525(packages)]TJ -22.909 -13.549 Td [(-V,)-525(--version)-5775(display)-525(version)-525(information)-525(and)-525(exit)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -222 0 obj << +202 0 obj << /Type /Page -/Contents 223 0 R -/Resources 221 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 185 0 R +/Contents 203 0 R +/Resources 201 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 167 0 R >> endobj -224 0 obj << -/D [222 0 R /XYZ 141.7385 740.0018 null] +204 0 obj << +/D [202 0 R /XYZ 141.738 740.002 null] >> endobj 30 0 obj << -/D [222 0 R /XYZ 141.7385 715.0952 null] +/D [202 0 R /XYZ 141.738 715.095 null] >> endobj 34 0 obj << -/D [222 0 R /XYZ 141.7385 462.3409 null] +/D [202 0 R /XYZ 141.738 462.341 null] >> endobj -221 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F19 105 0 R /F41 126 0 R /F48 214 0 R /F20 171 0 R >> +201 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F17 103 0 R /F39 116 0 R /F46 195 0 R /F18 163 0 R >> /ProcSet [ /PDF /Text ] >> endobj -227 0 obj << -/Length 4135 +208 0 obj << +/Length 3836 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(4)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(4)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Configuri)-1(ng)-378(an)-1(d)-378(Build)-1(ing)-378(ML)-1(D2)1(P4)]TJ/F15 10.9091 Tf 396.8452 0 Td[(7)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Configuring)-378(and)-377(Bu)-1(ilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.996 0 Td [(7)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F48 10.9091 Tf 105.3722 704.1363 Td[(-q,)-525(--quiet,)-525(--silent)-1575(do)-525(not)-525(print)-525(`checking...')-525(messages)]TJ 22.9089 -13.5492 Td[(--cache-file=FILE)-1575(cache)-525(test)-525(results)-525(in)-525(FILE)-525([disabled])]TJ -22.9089 -13.5492 Td[(-C,)-525(--config-cache)-3150(alias)-525(for)-525(`--cache-file=config.cache')]TJ 0 -13.5492 Td[(-n,)-525(--no-create)-4725(do)-525(not)-525(create)-525(output)-525(files)]TJ 22.9089 -13.5492 Td[(--srcdir=DIR)-4200(find)-525(the)-525(sources)-525(in)-525(DIR)-525([configure)-525(dir)-525(or)-525(`..'])]TJ -34.3633 -27.0984 Td[(Installation)-525(directories:)]TJ 11.4544 -13.5492 Td[(--prefix=PREFIX)-4725(install)-525(architecture-independent)-525(files)-525(in)-525(PREFIX)]TJ 0 -13.5492 Td[([/usr/local])]TJ 0 -13.5492 Td[(--exec-prefix=EPREFIX)-1575(install)-525(architecture-dependent)-525(files)-525(in)-525(EPREFIX)]TJ 0 -13.5492 Td[([PREFIX])]TJ -11.4544 -27.0984 Td[(By)-525(default,)-525(`make)-525(install')-525(will)-525(install)-525(all)-525(the)-525(files)-525(in)]TJ 0 -13.5492 Td[(`/usr/local/bin',)-525(`/usr/local/lib')-525(etc.)-1050(You)-525(can)-525(specify)]TJ 0 -13.5492 Td[(an)-525(installation)-525(prefix)-525(other)-525(than)-525(`/usr/local')-525(using)-525(`--prefix',)]TJ 0 -13.5492 Td[(for)-525(instance)-525(`--prefix=$HOME'.)]TJ 0 -27.0984 Td[(For)-525(better)-525(control,)-525(use)-525(the)-525(options)-525(below.)]TJ 0 -27.0984 Td[(Fine)-525(tuning)-525(of)-525(the)-525(installation)-525(directories:)]TJ 11.4544 -13.5492 Td[(--bindir=DIR)-5775(user)-525(executables)-525([EPREFIX/bin])]TJ 0 -13.5492 Td[(--sbindir=DIR)-5250(system)-525(admin)-525(executables)-525([EPREFIX/sbin])]TJ 0 -13.5492 Td[(--libexecdir=DIR)-3675(program)-525(executables)-525([EPREFIX/libexec])]TJ 0 -13.5492 Td[(--sysconfdir=DIR)-3675(read-only)-525(single-machine)-525(data)-525([PREFIX/etc])]TJ 0 -13.5492 Td[(--sharedstatedir=DIR)-1575(modifiable)-525(architecture-independent)-525(data)-525([PREFIX/com])]TJ 0 -13.5492 Td[(--localstatedir=DIR)-2100(modifiable)-525(single-machine)-525(data)-525([PREFIX/var])]TJ 0 -13.5492 Td[(--libdir=DIR)-5775(object)-525(code)-525(libraries)-525([EPREFIX/lib])]TJ 0 -13.5492 Td[(--includedir=DIR)-3675(C)-525(header)-525(files)-525([PREFIX/include])]TJ 0 -13.5492 Td[(--oldincludedir=DIR)-2100(C)-525(header)-525(files)-525(for)-525(non-gcc)-525([/usr/include])]TJ 0 -13.5492 Td[(--datarootdir=DIR)-3150(read-only)-525(arch.-independent)-525(data)-525(root)-525([PREFIX/share])]TJ 0 -13.5492 Td[(--datadir=DIR)-5250(read-only)-525(architecture-independent)-525(data)-525([DATAROOTDIR])]TJ 0 -13.5492 Td[(--infodir=DIR)-5250(info)-525(documentation)-525([DATAROOTDIR/info])]TJ 0 -13.5492 Td[(--localedir=DIR)-4200(locale-dependent)-525(data)-525([DATAROOTDIR/locale])]TJ 0 -13.5492 Td[(--mandir=DIR)-5775(man)-525(documentation)-525([DATAROOTDIR/man])]TJ 0 -13.5492 Td[(--docdir=DIR)-5775(documentation)-525(root)-525([DATAROOTDIR/doc/mld2p4])]TJ 0 -13.5492 Td[(--htmldir=DIR)-5250(html)-525(documentation)-525([DOCDIR])]TJ 0 -13.5492 Td[(--dvidir=DIR)-5775(dvi)-525(documentation)-525([DOCDIR])]TJ 0 -13.5492 Td[(--pdfdir=DIR)-5775(pdf)-525(documentation)-525([DOCDIR])]TJ 0 -13.5492 Td[(--psdir=DIR)-6300(ps)-525(documentation)-525([DOCDIR])]TJ -11.4544 -27.0984 Td[(Optional)-525(Packages:)]TJ 11.4544 -13.5492 Td[(--with-PACKAGE[=ARG])-2100(use)-525(PACKAGE)-525([ARG=yes])]TJ 0 -13.5492 Td[(--without-PACKAGE)-3675(do)-525(not)-525(use)-525(PACKAGE)-525(\050same)-525(as)-525(--with-PACKAGE=no\051)]TJ 0 -13.5492 Td[(--with-psblas)-5775(The)-525(source)-525(directory)-525(for)-525(PSBLAS,)-525(for)-525(example,)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F46 10.9091 Tf -395.542 -35.866 Td [(-q,)-525(--quiet,)-525(--silent)-1575(do)-525(not)-525(print)-525(`checking...')-525(messages)]TJ 22.909 -13.549 Td [(--cache-file=FILE)-1575(cache)-525(test)-525(results)-525(in)-525(FILE)-525([disabled])]TJ -22.909 -13.549 Td [(-C,)-525(--config-cache)-3150(alias)-525(for)-525(`--cache-file=config.cache')]TJ 0 -13.549 Td [(-n,)-525(--no-create)-4725(do)-525(not)-525(create)-525(output)-525(files)]TJ 22.909 -13.549 Td [(--srcdir=DIR)-4200(find)-525(the)-525(sources)-525(in)-525(DIR)-525([configure)-525(dir)-525(or)-525(`..'])]TJ -34.363 -27.099 Td [(Installation)-525(directories:)]TJ 11.454 -13.549 Td [(--prefix=PREFIX)-4725(install)-525(architecture-independent)-525(files)-525(in)-525(PREFIX)]TJ 0 -13.549 Td [([/usr/local])]TJ 0 -13.549 Td [(--exec-prefix=EPREFIX)-1575(install)-525(architecture-dependent)-525(files)-525(in)-525(EPREFIX)]TJ 0 -13.55 Td [([PREFIX])]TJ -11.454 -27.098 Td [(By)-525(default,)-525(`make)-525(install')-525(will)-525(install)-525(all)-525(the)-525(files)-525(in)]TJ 0 -13.549 Td [(`/usr/local/bin',)-525(`/usr/local/lib')-525(etc.)-1050(You)-525(can)-525(specify)]TJ 0 -13.549 Td [(an)-525(installation)-525(prefix)-525(other)-525(than)-525(`/usr/local')-525(using)-525(`--prefix',)]TJ 0 -13.55 Td [(for)-525(instance)-525(`--prefix=$HOME'.)]TJ 0 -27.098 Td [(For)-525(better)-525(control,)-525(use)-525(the)-525(options)-525(below.)]TJ 0 -27.098 Td [(Fine)-525(tuning)-525(of)-525(the)-525(installation)-525(directories:)]TJ 11.454 -13.55 Td [(--bindir=DIR)-5775(user)-525(executables)-525([EPREFIX/bin])]TJ 0 -13.549 Td [(--sbindir=DIR)-5250(system)-525(admin)-525(executables)-525([EPREFIX/sbin])]TJ 0 -13.549 Td [(--libexecdir=DIR)-3675(program)-525(executables)-525([EPREFIX/libexec])]TJ 0 -13.549 Td [(--sysconfdir=DIR)-3675(read-only)-525(single-machine)-525(data)-525([PREFIX/etc])]TJ 0 -13.549 Td [(--sharedstatedir=DIR)-1575(modifiable)-525(architecture-independent)-525(data)-525([PREFIX/com])]TJ 0 -13.549 Td [(--localstatedir=DIR)-2100(modifiable)-525(single-machine)-525(data)-525([PREFIX/var])]TJ 0 -13.55 Td [(--libdir=DIR)-5775(object)-525(code)-525(libraries)-525([EPREFIX/lib])]TJ 0 -13.549 Td [(--includedir=DIR)-3675(C)-525(header)-525(files)-525([PREFIX/include])]TJ 0 -13.549 Td [(--oldincludedir=DIR)-2100(C)-525(header)-525(files)-525(for)-525(non-gcc)-525([/usr/include])]TJ 0 -13.549 Td [(--datarootdir=DIR)-3150(read-only)-525(arch.-independent)-525(data)-525(root)-525([PREFIX/share])]TJ 0 -13.549 Td [(--datadir=DIR)-5250(read-only)-525(architecture-independent)-525(data)-525([DATAROOTDIR])]TJ 0 -13.55 Td [(--infodir=DIR)-5250(info)-525(documentation)-525([DATAROOTDIR/info])]TJ 0 -13.549 Td [(--localedir=DIR)-4200(locale-dependent)-525(data)-525([DATAROOTDIR/locale])]TJ 0 -13.549 Td [(--mandir=DIR)-5775(man)-525(documentation)-525([DATAROOTDIR/man])]TJ 0 -13.549 Td [(--docdir=DIR)-5775(documentation)-525(root)-525([DATAROOTDIR/doc/mld2p4])]TJ 0 -13.549 Td [(--htmldir=DIR)-5250(html)-525(documentation)-525([DOCDIR])]TJ 0 -13.55 Td [(--dvidir=DIR)-5775(dvi)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--pdfdir=DIR)-5775(pdf)-525(documentation)-525([DOCDIR])]TJ 0 -13.549 Td [(--psdir=DIR)-6300(ps)-525(documentation)-525([DOCDIR])]TJ -11.454 -27.098 Td [(Optional)-525(Packages:)]TJ 11.454 -13.55 Td [(--with-PACKAGE[=ARG])-2100(use)-525(PACKAGE)-525([ARG=yes])]TJ 0 -13.549 Td [(--without-PACKAGE)-3675(do)-525(not)-525(use)-525(PACKAGE)-525(\050same)-525(as)-525(--with-PACKAGE=no\051)]TJ 0 -13.549 Td [(--with-psblas)-5775(The)-525(source)-525(directory)-525(for)-525(PSBLAS,)-525(for)-525(example,)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -226 0 obj << +207 0 obj << /Type /Page -/Contents 227 0 R -/Resources 225 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 230 0 R -/Annots [ 229 0 R ] +/Contents 208 0 R +/Resources 206 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 210 0 R +/Annots [ 205 0 R ] >> endobj -229 0 obj << +205 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -228 0 obj << -/D [226 0 R /XYZ 93.9178 740.0018 null] +209 0 obj << +/D [207 0 R /XYZ 93.918 740.002 null] >> endobj -225 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F48 214 0 R >> +206 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -233 0 obj << -/Length 4070 +213 0 obj << +/Length 3826 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(8)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(8)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F48 10.9091 Tf 290.646 704.1363 Td[(--with-psblas=/opt/packages/psblas-2.2)]TJ -137.4531 -13.5492 Td[(--with-libs)-6825(List)-525(additional)-525(libraries)-525(here.)-525(For)-525(example,)]TJ 137.4531 -13.5492 Td[(--with-libs=-lsuperlu)-525(or)]TJ 0 -13.5492 Td[(--with-libs=/path/libsuperlu.a)]TJ -137.4531 -13.5492 Td[(--with-clibs)-6300(additional)-525(CLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.4531 -13.5492 Td[(to)-525(CLIBS)]TJ -137.4531 -13.5492 Td[(--with-flibs)-6300(additional)-525(FLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.4531 -13.5492 Td[(to)-525(FLIBS)]TJ -137.4531 -13.5492 Td[(--with-library-path)-2625(additional)-525(LIBRARYPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.4531 -13.5492 Td[(prepend)-525(to)-525(LIBRARYPATH)]TJ -137.4531 -13.5492 Td[(--with-include-path)-2625(additional)-525(INCLUDEPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.4531 -13.5492 Td[(prepend)-525(to)-525(INCLUDEPATH)]TJ -137.4531 -13.5492 Td[(--with-module-path)-3150(additional)-525(MODULE_PATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.4531 -13.5492 Td[(prepend)-525(to)-525(MODULE_PATH)]TJ -137.4531 -13.5492 Td[(--with-umfpack=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(UMFPACK)-525(library.)]TJ 137.4531 -13.5492 Td[(Default:)-525("-lumfpack)-525(-lamd")]TJ -137.4531 -13.5492 Td[(--with-umfpackdir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library)-525(and)]TJ 137.4531 -13.5492 Td[(includes.)]TJ -137.4531 -13.5492 Td[(--with-superlu=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(SUPERLU)-525(library.)]TJ 137.4531 -13.5492 Td[(Default:)-525("-lslu")]TJ -137.4531 -13.5492 Td[(--with-superludir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library)-525(and)]TJ 137.4531 -13.5492 Td[(includes.)]TJ -137.4531 -13.5492 Td[(--with-superludist=LIBNAME)]TJ 137.4531 -13.5492 Td[(Specify)-525(the)-525(libname)-525(for)-525(SUPERLUDIST)-525(library.)]TJ 0 -13.5492 Td[(Requires)-525(you)-525(also)-525(specify)-525(SuperLU.)-525(Default:)-525("-lslud")]TJ -137.4531 -13.5492 Td[(--with-superludistdir=DIR)]TJ 137.4531 -13.5492 Td[(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library)-525(and)]TJ 0 -13.5492 Td[(includes.)]TJ -148.9075 -27.0984 Td[(Some)-525(influential)-525(environment)-525(variables:)]TJ 11.4544 -13.5492 Td[(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.5492 Td[(FCFLAGS)-2625(Fortran)-525(compiler)-525(flags)]TJ 0 -13.5492 Td[(LDFLAGS)-2625(linker)-525(flags,)-525(e.g.)-525(-L)-525(if)-525(you)-525(have)-525(libraries)-525(in)-525(a)]TJ 68.7265 -13.5492 Td[(nonstandard)-525(directory)-525()]TJ -68.7265 -13.5492 Td[(LIBS)-4200(libraries)-525(to)-525(pass)-525(to)-525(the)-525(linker,)-525(e.g.)-525(-l)]TJ 0 -13.5492 Td[(CC)-5250(C)-525(compiler)-525(command)]TJ 0 -13.5492 Td[(CFLAGS)-3150(C)-525(compiler)-525(flags)]TJ 0 -13.5492 Td[(CPPFLAGS)-2100(C/C++/Objective)-525(C)-525(preprocessor)-525(flags,)-525(e.g.)-525(-I)-525(if)]TJ 68.7265 -13.5492 Td[(you)-525(have)-525(headers)-525(in)-525(a)-525(nonstandard)-525(directory)-525()]TJ -68.7265 -13.5492 Td[(CPP)-4725(C)-525(preprocessor)]TJ 0 -13.5492 Td[(MPICC)-3675(MPI)-525(C)-525(compiler)-525(command)]TJ -11.4544 -27.0984 Td[(Use)-525(these)-525(variables)-525(to)-525(override)-525(the)-525(choices)-525(made)-525(by)-525(`configure')-525(or)-525(to)-525(help)]TJ 0 -13.5492 Td[(it)-525(to)-525(find)-525(libraries)-525(and)-525(programs)-525(with)-525(nonstandard)-525(names/locations.)]TJ -ET -1 0 0 1 141.7385 91.633 cm +/F46 10.9091 Tf -54.357 -35.866 Td [(--with-psblas=/opt/packages/psblas-2.2)]TJ -137.453 -13.549 Td [(--with-libs)-6825(List)-525(additional)-525(libraries)-525(here.)-525(For)-525(example,)]TJ 137.453 -13.549 Td [(--with-libs=-lsuperlu)-525(or)]TJ 0 -13.549 Td [(--with-libs=/path/libsuperlu.a)]TJ -137.453 -13.549 Td [(--with-clibs)-6300(additional)-525(CLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.55 Td [(to)-525(CLIBS)]TJ -137.453 -13.549 Td [(--with-flibs)-6300(additional)-525(FLIBS)-525(flags)-525(to)-525(be)-525(added:)-525(will)-525(prepend)]TJ 137.453 -13.549 Td [(to)-525(FLIBS)]TJ -137.453 -13.549 Td [(--with-library-path)-2625(additional)-525(LIBRARYPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525(LIBRARYPATH)]TJ -137.453 -13.55 Td [(--with-include-path)-2625(additional)-525(INCLUDEPATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525(INCLUDEPATH)]TJ -137.453 -13.549 Td [(--with-module-path)-3150(additional)-525(MODULE_PATH)-525(flags)-525(to)-525(be)-525(added:)-525(will)]TJ 137.453 -13.549 Td [(prepend)-525(to)-525(MODULE_PATH)]TJ -137.453 -13.549 Td [(--with-umfpack=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(UMFPACK)-525(library.)]TJ 137.453 -13.55 Td [(Default:)-525("-lumfpack)-525(-lamd")]TJ -137.453 -13.549 Td [(--with-umfpackdir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(UMFPACK)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superlu=LIBNAME)-1050(Specify)-525(the)-525(library)-525(name)-525(for)-525(SUPERLU)-525(library.)]TJ 137.453 -13.549 Td [(Default:)-525("-lslu")]TJ -137.453 -13.55 Td [(--with-superludir=DIR)-1575(Specify)-525(the)-525(directory)-525(for)-525(SUPERLU)-525(library)-525(and)]TJ 137.453 -13.549 Td [(includes.)]TJ -137.453 -13.549 Td [(--with-superludist=LIBNAME)]TJ 137.453 -13.549 Td [(Specify)-525(the)-525(libname)-525(for)-525(SUPERLUDIST)-525(library.)]TJ 0 -13.549 Td [(Requires)-525(you)-525(also)-525(specify)-525(SuperLU.)-525(Default:)-525("-lslud")]TJ -137.453 -13.549 Td [(--with-superludistdir=DIR)]TJ 137.453 -13.55 Td [(Specify)-525(the)-525(directory)-525(for)-525(SUPERLUDIST)-525(library)-525(and)]TJ 0 -13.549 Td [(includes.)]TJ -148.907 -27.098 Td [(Some)-525(influential)-525(environment)-525(variables:)]TJ 11.454 -13.549 Td [(FC)-5250(Fortran)-525(compiler)-525(command)]TJ 0 -13.55 Td [(FCFLAGS)-2625(Fortran)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(LDFLAGS)-2625(linker)-525(flags,)-525(e.g.)-525(-L)-525(if)-525(you)-525(have)-525(libraries)-525(in)-525(a)]TJ 68.726 -13.549 Td [(nonstandard)-525(directory)-525()]TJ -68.726 -13.549 Td [(LIBS)-4200(libraries)-525(to)-525(pass)-525(to)-525(the)-525(linker,)-525(e.g.)-525(-l)]TJ 0 -13.549 Td [(CC)-5250(C)-525(compiler)-525(command)]TJ 0 -13.55 Td [(CFLAGS)-3150(C)-525(compiler)-525(flags)]TJ 0 -13.549 Td [(CPPFLAGS)-2100(C/C++/Objective)-525(C)-525(preprocessor)-525(flags,)-525(e.g.)-525(-I)-525(if)]TJ 68.726 -13.549 Td [(you)-525(have)-525(headers)-525(in)-525(a)-525(nonstandard)-525(directory)-525()]TJ -68.726 -13.549 Td [(CPP)-4725(C)-525(preprocessor)]TJ 0 -13.549 Td [(MPICC)-3675(MPI)-525(C)-525(compiler)-525(command)]TJ -11.454 -27.099 Td [(Use)-525(these)-525(variables)-525(to)-525(override)-525(the)-525(choices)-525(made)-525(by)-525(`configure')-525(or)-525(to)-525(help)]TJ 0 -13.549 Td [(it)-525(to)-525(find)-525(libraries)-525(and)-525(programs)-525(with)-525(nonstandard)-525(names/locations.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -232 0 obj << +212 0 obj << /Type /Page -/Contents 233 0 R -/Resources 231 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 230 0 R +/Contents 213 0 R +/Resources 211 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 210 0 R >> endobj -234 0 obj << -/D [232 0 R /XYZ 141.7385 740.0018 null] +214 0 obj << +/D [212 0 R /XYZ 141.738 740.002 null] >> endobj -231 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F48 214 0 R >> +211 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -237 0 obj << -/Length 5551 +218 0 obj << +/Length 4174 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(4)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(4)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Configuri)-1(ng)-378(an)-1(d)-378(Build)-1(ing)-378(ML)-1(D2)1(P4)]TJ/F15 10.9091 Tf 396.8452 0 Td[(9)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Configuring)-378(and)-377(Bu)-1(ilding)-377(MLD2P4)]TJ/F15 10.9091 Tf 406.996 0 Td [(9)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F48 10.9091 Tf 93.9178 690.5871 Td[(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 0 -22.5155 Td[(Th)28(us,)-352(a)-348(sample)-348(bu)1(ild)-348(wit)1(h)-348(lib)1(rari)1(e)-1(s)-348(in)-348(in)1(s)-1(t)1(allation)-347(dir)1(e)-1(ctories)-349(sp)-27(e)-1(ci\014cs)-348(to)-348(the)-348(GNU)-348(4.3)]TJ 0 -13.5492 Td[(com)-1(p)1(iler)-333(s)-1(u)1(ite)-334(migh)28(t)-333(b)-27(e)-334(as)-334(f)1(ollo)28(ws)-1(,)-333(sp)-28(ec)-1(i)1(fyi)1(ng)-333(only)-333(th)1(e)-334(UMF)1(P)83(A)28(CK)-333(e)-1(x)1(te)-1(r)1(nal)-333(pac)28(k)55(age:)]TJ -ET -1 0 0 1 88.4633 632.0068 cm +/F46 10.9091 Tf -406.996 -49.415 Td [(Report)-525(bugs)-525(to)-525(.)]TJ/F15 10.9091 Tf 0 -22.515 Td [(Th)28(us,)-352(a)-348(sample)-348(build)-348(with)-348(libraries)-348(in)-348(installation)-348(directories)-348(sp)-28(eci\014cs)-348(to)-348(the)-348(GNU)-348(4.3)]TJ 0 -13.55 Td [(compiler)-333(suite)-334(migh)28(t)-333(b)-28(e)-333(as)-334(follo)28(ws,)-333(sp)-28(ecifying)-333(only)-333(the)-334(UMFP)84(A)27(CK)-333(external)-333(pac)28(k)55(age:)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -88.4633 -632.0068 cm -BT -/F48 10.9091 Tf 99.645 632.0068 Td[(./configure)-525(--with-psblas=/home/user/psblas-2.3/)-525(\134)]TJ 0 -13.5492 Td[(--with-libs="-L/usr/local/BLAS/gnu43)-525(-L/usr/local/BLACS/gnu43")-525(\134)]TJ 0 -13.5492 Td[(--with-blacs=-lmpiblacs)-1050(--with-umfpackdir=/usr/local/UMFPACK/gnu43)]TJ/F15 10.9091 Tf -5.7272 -22.5156 Td[(On)1(c)-1(e)-529(the)-530(con\014)1(gur)1(e)-530(sc)-1(ri)1(pt)-529(has)-529(c)-1(ompl)1(e)-1(ted)-529(exe)-1(cut)1(ion,)-578(it)-529(wil)1(l)-529(ha)28(v)28(e)-530(generated)-529(the)-529(\014le)]TJ/F48 10.9091 Tf 0 -13.5492 Td[(Make.inc)]TJ/F15 10.9091 Tf 49.454 0 Td[(whic)28(h)-333(will)-333(th)1(e)-1(n)-333(b)-27(e)-334(u)1(s)-1(ed)-333(b)28(y)-333(all)-333(Mak)28(e\014l)1(e)-1(s)-334(i)1(n)-333(the)-334(d)1(irectory)-333(tree)-1(.)]TJ -32.5175 -13.5492 Td[(T)83(o)-333(bu)1(ild)-333(th)1(e)-334(lib)1(rar)1(y)-334(t)1(he)-334(u)1(s)-1(er)-333(will)-333(no)28(w)-333(e)-1(n)28(ter)]TJ -ET -1 0 0 1 88.4633 532.7789 cm +/F46 10.9091 Tf 5.727 -22.515 Td [(./configure)-525(--with-psblas=/home/user/psblas-2.3/)-525(\134)]TJ 0 -13.549 Td [(--with-libs="-L/usr/local/BLAS/gnu43)-525(-L/usr/local/BLACS/gnu43")-525(\134)]TJ 0 -13.55 Td [(--with-blacs=-lmpiblacs)-1050(--with-umfpackdir=/usr/local/UMFPACK/gnu43)]TJ/F15 10.9091 Tf -5.727 -22.515 Td [(Once)-529(the)-529(con\014gure)-530(script)-529(has)-529(completed)-529(execution,)-578(it)-530(will)-529(ha)28(v)28(e)-529(ge)-1(n)1(e)-1(rat)1(e)-1(d)-529(the)-529(\014le)]TJ/F46 10.9091 Tf 0 -13.549 Td [(Make.inc)]TJ/F15 10.9091 Tf 49.454 0 Td [(whic)28(h)-333(w)-1(i)1(ll)-334(then)-333(b)-28(e)-333(used)-334(b)28(y)-333(all)-333(Mak)28(e)-1(\014)1(les)-334(in)-333(the)-333(directory)-334(tree.)]TJ -32.518 -13.55 Td [(T)83(o)-333(build)-333(the)-334(li)1(brary)-334(the)-333(user)-333(will)-334(no)28(w)-333(en)28(ter)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -88.4633 -532.7789 cm -BT -/F48 10.9091 Tf 93.9178 532.7789 Td[(make)]TJ/F15 10.9091 Tf 0 -22.5156 Td[(fol)1(lo)28(w)27(ed)-333(\050opt)1(ionall)1(y\051)-333(b)28(y)]TJ -ET -1 0 0 1 88.4633 487.7477 cm +/F46 10.9091 Tf -16.936 -22.515 Td [(make)]TJ/F15 10.9091 Tf 0 -22.516 Td [(follo)28(w)28(ed)-334(\050optionally\051)-333(b)28(y)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -88.4633 -487.7477 cm -BT -/F48 10.9091 Tf 93.9178 487.7477 Td[(make)-525(install)]TJ/F19 11.9552 Tf 0 -29.2128 Td[(4.)-1(4)-1125(E)-1(xampl)-1(e)-375(and)-375(te)-1(s)1(t)-376(pro)-1(gr)-1(ams)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(The)-419(pac)28(k)55(age)-419(con)28(tain)1(s)-420(th)1(e)]TJ/F48 10.9091 Tf 128.3386 0 Td[(examples)]TJ/F15 10.9091 Tf 50.3871 0 Td[(and)]TJ/F48 10.9091 Tf 22.1452 0 Td[(tests)]TJ/F15 10.9091 Tf 33.2055 0 Td[(di)1(rec)-1(tor)1(ie)-1(s;)-462(b)-27(oth)-418(of)-419(th)1(e)-1(m)-419(ar)1(e)-420(f)1(ur)1(ther)]TJ -234.0764 -13.5492 Td[(di)1(vid)1(e)-1(d)-333(in)29(to)]TJ/F48 10.9091 Tf 60.6061 0 Td[(fileread)]TJ/F15 10.9091 Tf 49.4541 0 Td[(and)]TJ/F48 10.9091 Tf 21.2121 0 Td[(pargen)]TJ/F15 10.9091 Tf 37.9996 0 Td[(sub)-27(dir)1(e)-1(ctories.)-445(Th)1(e)-1(ir)-333(p)1(ur)1(p)-28(ose)-334(is)-334(as)-333(foll)1(o)27(ws:)]TJ -ET -1 0 0 1 88.4633 401.8755 cm +/F46 10.9091 Tf 0 -22.515 Td [(make)-525(install)]TJ/F17 11.9552 Tf 0 -29.213 Td [(4.4)-1125(Example)-375(and)-375(test)-375(programs)]TJ/F15 10.9091 Tf 0 -20.595 Td [(The)-419(pac)28(k)55(age)-418(con)27(tains)-418(the)]TJ/F46 10.9091 Tf 128.338 0 Td [(examples)]TJ/F15 10.9091 Tf 50.387 0 Td [(and)]TJ/F46 10.9091 Tf 22.146 0 Td [(tests)]TJ/F15 10.9091 Tf 33.205 0 Td [(directories;)-462(b)-27(oth)-419(of)-419(them)-419(are)-419(further)]TJ -234.076 -13.549 Td [(divided)-333(in)28(to)]TJ/F46 10.9091 Tf 60.606 0 Td [(fileread)]TJ/F15 10.9091 Tf 49.454 0 Td [(and)]TJ/F46 10.9091 Tf 21.212 0 Td [(pargen)]TJ/F15 10.9091 Tf 38 0 Td [(sub)-28(directories.)-444(Their)-333(purp)-28(ose)-333(is)-334(as)-333(follo)28(ws:)]TJ 0 g 0 G -1 0 0 1 -88.4633 -401.8755 cm -BT -/F48 10.9091 Tf 93.9178 401.8755 Td[(examples)]TJ -ET -1 0 0 1 139.7355 401.8755 cm +/F46 10.9091 Tf -169.272 -22.515 Td [(examples)]TJ 0 g 0 G -1 0 0 1 -139.7355 -401.8755 cm -BT -/F15 10.9091 Tf 145.19 401.8755 Td[(con)28(tain)1(s)-246(a)-244(s)-1(et)-245(of)-244(simple)-245(example)-245(p)1(rograms)-245(with)-244(a)-245(p)1(re)-1(d)1(e)-1(\014)1(ned)-244(c)27(hoi)1(c)-1(e)-245(of)-244(pr)1(e)-1(con-)]TJ -23.9994 -13.5492 Td[(di)1(tioners,)-294(se)-1(l)1(e)-1(ctable)-284(vi)1(a)-284(in)28(tege)-1(r)-283(v)55(al)1(ues)-1(.)-428(Th)1(e)-1(se)-285(ar)1(e)-285(in)29(te)-1(n)1(ded)-284(to)-284(get)-284(an)-283(ac)-1(qu)1(ain)28(tan)1(c)-1(e)]TJ 0 -13.5492 Td[(with)-333(th)1(e)-334(m)27(u)1(ltil)1(e)-1(v)28(el)-333(precondi)1(tioners.)]TJ -ET -1 0 0 1 88.4633 352.2616 cm +/F15 10.9091 Tf 51.272 0 Td [(con)28(tains)-245(a)-245(set)-244(of)-245(simple)-245(example)-244(programs)-245(with)-244(a)-245(prede\014ned)-245(c)28(hoice)-245(of)-244(precon-)]TJ -23.999 -13.55 Td [(ditioners,)-294(selectable)-284(via)-284(in)28(teger)-284(v)56(alues.)-428(These)-284(are)-284(in)28(te)-1(n)1(ded)-284(to)-284(get)-284(an)-284(acquain)28(tance)]TJ 0 -13.549 Td [(with)-333(the)-334(m)28(ultilev)28(el)-333(preconditioners.)]TJ 0 g 0 G -1 0 0 1 -88.4633 -352.2616 cm -BT -/F48 10.9091 Tf 93.9178 352.2616 Td[(test)]TJ -ET -1 0 0 1 116.8267 352.2616 cm +/F46 10.9091 Tf -27.273 -22.515 Td [(test)]TJ 0 g 0 G -1 0 0 1 -116.8267 -352.2616 cm -BT -/F15 10.9091 Tf 122.2812 352.2616 Td[(con)28(tain)1(s)-420(a)-420(se)-1(t)-419(of)-419(more)-420(sophi)1(s)-1(ti)1(c)-1(ated)-419(e)-1(xamp)1(le)-1(s)-420(t)1(hat)-419(w)-1(i)1(ll)-419(allo)28(w)-420(th)1(e)-420(use)-1(r)1(,)-441(via)-419(the)]TJ -1.0906 -13.5492 Td[(in)1(pu)1(t)-287(\014)1(le)-1(s)-286(in)-286(the)]TJ/F48 10.9091 Tf 80.4383 0 Td[(runs)]TJ/F15 10.9091 Tf 26.0336 0 Td[(sub)-27(dir)1(e)-1(ctories,)-296(to)-286(e)-1(xp)-27(erime)-1(n)29(t)-287(with)-286(t)1(he)-287(f)1(ull)-286(ran)1(ge)-287(of)-286(pr)1(e)-1(con-)]TJ -106.4719 -13.5492 Td[(di)1(tioners)-333(im)-1(p)1(lem)-1(en)28(ted)-333(in)-333(th)1(e)-334(lib)1(rar)1(y)83(.)]TJ -27.2728 -22.5156 Td[(The)]TJ/F48 10.9091 Tf 21.8096 0 Td[(fileread)]TJ/F15 10.9091 Tf 48.8395 0 Td[(di)1(rec)-1(tor)1(ie)-1(s)-277(c)-1(on)29(tain)-277(sample)-277(pr)1(ograms)-278(th)1(at)-277(read)-277(spar)1(s)-1(e)-277(m)-1(atr)1(ice)-1(s)-277(from)-277(\014)1(le)-1(s,)]TJ -70.6491 -13.5492 Td[(acc)-1(ord)1(in)1(g)-354(to)-354(t)1(he)-354(Matr)1(ix)-353(Mark)28(et)-354(storage)-354(f)1(ormat;)-364(th)1(e)]TJ/F48 10.9091 Tf 252.3943 0 Td[(pargen)]TJ/F15 10.9091 Tf 38.2207 0 Td[(in)1(s)-1(tead)-353(ge)-1(n)1(e)-1(r)1(ate)-354(m)-1(atr)1(ice)-1(s)]TJ -290.615 -13.5492 Td[(in)-333(f)1(ull)-333(p)1(arall)1(e)-1(l)-333(mo)-28(de)-333(from)-333(the)-334(d)1(isc)-1(r)1(e)-1(tization)-333(of)-332(a)-334(sam)-1(p)1(le)-334(P)1(DE.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F15 10.9091 Tf 28.363 0 Td [(con)28(tains)-420(a)-419(set)-420(of)-419(more)-420(sophisticated)-419(examples)-420(that)-419(will)-420(al)1(lo)27(w)-419(the)-420(user,)-441(via)-419(the)]TJ -1.09 -13.55 Td [(input)-286(\014les)-287(in)-286(the)]TJ/F46 10.9091 Tf 80.438 0 Td [(runs)]TJ/F15 10.9091 Tf 26.034 0 Td [(sub)-28(directories,)-296(t)1(o)-287(exp)-28(erimen)28(t)-286(with)-287(the)-286(full)-286(range)-287(of)-286(precon-)]TJ -106.472 -13.549 Td [(ditioners)-333(implemen)28(te)-1(d)-333(in)-333(the)-333(library)83(.)]TJ -27.273 -22.515 Td [(The)]TJ/F46 10.9091 Tf 21.809 0 Td [(fileread)]TJ/F15 10.9091 Tf 48.84 0 Td [(directories)-277(con)28(tain)-277(sample)-277(programs)-277(that)-277(read)-277(sparse)-277(matrices)-277(from)-277(\014les,)]TJ -70.649 -13.55 Td [(according)-354(to)-353(the)-354(Matrix)-353(Mark)28(et)-354(storage)-354(format;)-363(the)]TJ/F46 10.9091 Tf 252.394 0 Td [(pargen)]TJ/F15 10.9091 Tf 38.221 0 Td [(instead)-354(generate)-353(matrices)]TJ -290.615 -13.549 Td [(in)-333(full)-333(parallel)-334(mo)-28(d)1(e)-334(from)-333(the)-333(discretiz)-1(ati)1(on)-334(of)-333(a)-333(sample)-334(PDE.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -236 0 obj << +217 0 obj << /Type /Page -/Contents 237 0 R -/Resources 235 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 230 0 R -/Annots [ 239 0 R ] +/Contents 218 0 R +/Resources 216 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 210 0 R +/Annots [ 215 0 R ] >> endobj -239 0 obj << +215 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -238 0 obj << -/D [236 0 R /XYZ 93.9178 740.0018 null] +219 0 obj << +/D [217 0 R /XYZ 93.918 740.002 null] >> endobj 38 0 obj << -/D [236 0 R /XYZ 93.9178 472.4826 null] +/D [217 0 R /XYZ 93.918 472.483 null] >> endobj -235 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F48 214 0 R /F19 105 0 R >> +216 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F46 195 0 R /F17 103 0 R >> /ProcSet [ /PDF /Text ] >> endobj -242 0 obj << -/Length 11484 +228 0 obj << +/Length 8119 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(10)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(10)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F19 14.3462 Tf 141.7385 704.1363 Td[(5)-1125(M)-1(ult)-1(i-l)-1(ev)32(e)-1(l)-375(D)-1(om)-1(a)1(i)-1(n)-375(Deco)-1(mp)-32(osit)-1(io)-1(n)-375(Bac)32(kg)-1(ro)-1(und)]TJ/F20 10.9091 Tf 0 -25.25 Td[(Domain)-282(De)51(c)51(om)1(p)51(o)-1(s)1(ition)]TJ/F15 10.9091 Tf 113.1711 0 Td[(\050DD\051)-250(prec)-1(on)1(di)1(tioners,)-267(c)-1(ou)1(pled)-251(with)-250(Kry)1(lo)28(v)-251(iterativ)28(e)-251(solv)28(e)-1(r)1(s)-1(,)-267(are)]TJ -113.1711 -13.5492 Td[(widely)-315(u)1(s)-1(ed)-315(in)-315(th)1(e)-316(p)1(arallel)-315(s)-1(ol)1(ution)-315(of)-314(large)-316(an)1(d)-315(sparse)-316(li)1(near)-315(s)-1(ystem)-1(s.)-438(T)-1(h)1(e)-1(se)-316(p)1(rec)-1(on)1(di-)]TJ 0 -13.5492 Td[(tion)1(e)-1(r)1(s)-286(ar)1(e)-286(b)1(as)-1(ed)-284(on)-285(th)1(e)-286(d)1(ivid)1(e)-285(and)-284(c)-1(on)1(quer)-285(tec)27(h)1(niq)1(ue:)-420(the)-285(matrix)-284(to)-285(b)-27(e)-286(p)1(rec)-1(on)1(diti)1(oned)]TJ 0 -13.5492 Td[(is)-423(d)1(ivid)1(e)-1(d)-422(in)28(t)1(o)-423(s)-1(u)1(bmatri)1(c)-1(es)-1(,)-444(a)-423(\134lo)-28(cal")-422(linear)-422(s)-1(ystem)-423(in)28(v)28(olv)1(ing)-422(e)-1(ac)27(h)-422(sub)1(m)-1(atr)1(ix)-422(is)-423(\050ap-)]TJ 0 -13.5492 Td[(pr)1(o)28(ximate)-1(l)1(y\051)-356(s)-1(ol)1(v)28(e)-1(d)1(,)-362(an)1(d)-356(th)1(e)-357(l)1(o)-28(c)-1(al)-355(s)-1(olu)1(tion)1(s)-357(ar)1(e)-357(u)1(s)-1(ed)-356(to)-356(b)1(ui)1(ld)-356(a)-356(p)1(rec)-1(on)1(diti)1(oner)-356(for)-355(the)]TJ 0 -13.5492 Td[(whole)-407(or)1(iginal)-406(m)-1(at)1(rix.)-664(T)-1(h)1(is)-407(pr)1(o)-28(c)-1(ess)-408(of)1(te)-1(n)-406(corres)-1(p)-27(ond)1(s)-407(to)-407(di)1(vid)1(ing)-407(a)-406(ph)28(ysical)-407(d)1(om)-1(ai)1(n)]TJ 0 -13.5492 Td[(ass)-1(o)-28(ciated)-299(to)-299(th)1(e)-300(ori)1(ginal)-298(m)-1(atr)1(ix)-299(in)28(t)1(o)-300(sub)-27(d)1(om)-1(ain)1(s)-1(,)-305(e)-1(.g.)-432(in)-299(a)-299(P)1(DE)-299(d)1(is)-1(cretization,)-305(to)-299(\050ap-)]TJ 0 -13.5492 Td[(pr)1(o)28(ximate)-1(l)1(y\051)-276(s)-1(olv)1(ing)-276(the)-276(s)-1(u)1(bpr)1(oblems)-277(c)-1(or)1(res)-1(p)-27(ond)1(ing)-276(to)-276(the)-276(s)-1(u)1(b)-28(d)1(om)-1(ai)1(ns)-277(an)1(d)-276(to)-276(bui)1(ldi)1(ng)]TJ 0 -13.5492 Td[(an)-333(ap)1(pro)28(xi)1(m)-1(ate)-333(s)-1(olu)1(tion)-333(of)-333(th)1(e)-334(ori)1(ginal)-333(p)1(robl)1(e)-1(m)-333(from)-333(the)-334(l)1(o)-28(c)-1(al)-333(solu)1(tions)-333([)]TJ -ET -1 0 0 1 493.254 570.4927 cm +/F17 14.3462 Tf -203.265 -35.866 Td [(5)-1125(Multi-lev)31(el)-375(Domain)-375(Decomp)-31(osition)-375(Bac)31(kground)]TJ/F18 10.9091 Tf 0 -25.25 Td [(Domain)-282(De)51(c)51(omp)51(osition)]TJ/F15 10.9091 Tf 113.172 0 Td [(\050DD\051)-251(preconditioners,)-267(coupled)-251(with)-251(Krylo)28(v)-251(iterativ)28(e)-251(solv)28(ers,)-268(are)]TJ -113.172 -13.549 Td [(widely)-315(used)-316(in)-315(the)-315(parallel)-315(solution)-315(of)-316(large)-315(and)-315(sparse)-316(li)1(near)-316(systems.)-438(These)-316(precondi-)]TJ 0 -13.549 Td [(tioners)-285(are)-285(based)-285(on)-284(the)-285(divide)-285(and)-285(conquer)-285(tec)28(hnique:)-420(the)-285(matrix)-285(to)-285(b)-27(e)-285(preconditioned)]TJ 0 -13.549 Td [(is)-423(divided)-422(in)28(to)-423(submatrices,)-445(a)-423(\134lo)-27(cal")-423(linear)-423(system)-422(in)27(v)28(olving)-422(eac)27(h)-422(submatrix)-423(is)-422(\050ap-)]TJ 0 -13.549 Td [(pro)28(ximately\051)-356(solv)28(ed,)-362(and)-356(the)-356(lo)-27(c)-1(al)-355(solutions)-356(are)-356(used)-356(to)-356(build)-356(a)-356(preconditioner)-356(for)-356(the)]TJ 0 -13.55 Td [(whole)-407(original)-407(matri)1(x.)-665(This)-407(pro)-28(cess)-407(often)-407(corresp)-27(onds)-407(to)-407(dividing)-407(a)-406(ph)27(y)1(s)-1(ical)-406(domain)]TJ 0 -13.549 Td [(asso)-28(ciated)-299(to)-299(the)-299(original)-299(matrix)-299(in)28(to)-299(sub)-28(domains,)-306(e.g.)-433(in)-299(a)-299(PDE)-299(discretization,)-306(to)-299(\050ap-)]TJ 0 -13.549 Td [(pro)28(ximately\051)-277(solvi)1(ng)-277(the)-276(subproblems)-276(corres)-1(p)-27(onding)-276(to)-277(the)-276(sub)-28(domains)-276(and)-276(to)-277(building)]TJ 0 -13.549 Td [(an)-333(appro)28(ximate)-334(solution)-333(of)-333(the)-334(original)-333(problem)-333(from)-333(the)-334(lo)-27(c)-1(al)-333(solutions)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -493.254 -570.4927 cm -BT -/F15 10.9091 Tf 493.254 570.4927 Td[(6)]TJ -ET -1 0 0 1 498.7086 570.4927 cm + [(6)]TJ 0 g 0 G -1 0 0 1 -498.7086 -570.4927 cm -BT -/F15 10.9091 Tf 498.7086 570.4927 Td[(,)]TJ -ET -1 0 0 1 505.3752 570.4927 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -505.3752 -570.4927 cm -BT -/F15 10.9091 Tf 505.3752 570.4927 Td[(7)]TJ -ET -1 0 0 1 510.8298 570.4927 cm + [-333(7)]TJ 0 g 0 G -1 0 0 1 -510.8298 -570.4927 cm -BT -/F15 10.9091 Tf 510.8298 570.4927 Td[(,)]TJ -ET -1 0 0 1 517.4965 570.4927 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -517.4965 -570.4927 cm -BT -/F15 10.9091 Tf 517.4965 570.4927 Td[(15)]TJ -ET -1 0 0 1 528.4056 570.4927 cm + [-334(15)]TJ 0 g 0 G -1 0 0 1 -528.4056 -570.4927 cm -BT -/F15 10.9091 Tf 528.4056 570.4927 Td[(].)]TJ/F20 10.9091 Tf -369.7306 -14.0112 Td[(A)51(dditive)-468(Schw)-1(arz)]TJ/F15 10.9091 Tf 89.0586 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-454(are)-453(DD)-453(prec)-1(on)1(di)1(tioners)-453(using)-453(o)28(v)28(e)-1(r)1(lapp)1(ing)-453(sub)1(-)]TJ -105.9951 -13.5492 Td[(matrice)-1(s,)-403(i.)1(e)-1(.)-389(with)-388(s)-1(ome)-389(c)-1(omm)-1(on)-388(ro)28(ws)-1(,)-403(t)1(o)-389(c)-1(ou)1(ple)-389(the)-389(lo)-28(cal)-389(in)1(formation)-388(relate)-1(d)-388(to)-389(the)]TJ 0 -13.5492 Td[(submatr)1(ic)-1(es)-362(\050s)-1(ee)-1(,)-369(e.g.,)-368([)]TJ -ET -1 0 0 1 253.9509 529.3831 cm + [(].)]TJ/F18 10.9091 Tf 16.937 -14.011 Td [(A)51(dditive)-468(Schwarz)]TJ/F15 10.9091 Tf 89.059 0 Td [(preconditioners)-453(are)-453(DD)-454(pr)1(e)-1(cond)1(itioners)-454(using)-453(o)28(v)28(erlapping)-453(s)-1(u)1(b-)]TJ -105.996 -13.55 Td [(matrices,)-403(i.e.)-389(with)-389(some)-389(comm)-1(on)-389(r)1(o)27(ws,)-403(to)-389(couple)-389(the)-389(lo)-28(cal)-389(information)-389(related)-389(to)-389(the)]TJ 0 -13.549 Td [(submatrices)-362(\050see,)-369(e.g.,)-369([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -253.9509 -529.3831 cm -BT -/F15 10.9091 Tf 253.9509 529.3831 Td[(15)]TJ -ET -1 0 0 1 264.86 529.3831 cm + [(15)]TJ 0 g 0 G -1 0 0 1 -264.86 -529.3831 cm -BT -/F15 10.9091 Tf 264.86 529.3831 Td[(]\051.)-530(Th)1(e)-363(main)-361(m)-1(oti)1(v)55(at)1(ion)-362(f)1(or)-362(c)28(ho)-28(osing)-362(Ad)1(di)1(tiv)28(e)-362(Sc)27(h)29(w)27(arz)-362(p)1(re)-1(-)]TJ -123.1215 -13.5492 Td[(condi)1(tioners)-361(is)-362(t)1(heir)-361(in)29(trin)1(s)-1(ic)-361(par)1(allelism)-1(.)-527(A)-361(dr)1(a)27(wb)1(ac)27(k)-361(of)-361(th)1(e)-1(se)-362(p)1(rec)-1(on)1(dit)1(ioners)-361(is)-362(th)1(at)]TJ 0 -13.5492 Td[(th)1(e)-389(n)28(u)1(m)27(b)-27(e)-1(r)-388(of)-387(iteration)1(s)-389(of)-388(th)1(e)-389(p)1(rec)-1(on)1(diti)1(oned)-388(s)-1(ol)1(v)28(e)-1(r)1(s)-389(generally)-388(gr)1(o)27(ws)-388(w)-1(i)1(th)-388(th)1(e)-389(n)28(u)1(m)-1(-)]TJ 0 -13.5492 Td[(b)-27(e)-1(r)-370(of)-369(s)-1(u)1(bmatri)1(c)-1(es)-1(.)-554(T)-1(h)1(is)-370(m)-1(a)28(y)-370(b)-27(e)-371(a)-370(se)-1(r)1(ious)-370(limitation)-369(on)-370(p)1(arallel)-370(com)-1(p)1(uters,)-379(s)-1(in)1(c)-1(e)-370(the)]TJ 0 -13.5492 Td[(n)28(u)1(m)27(b)-27(e)-1(r)-403(of)-402(s)-1(u)1(bmatrices)-404(usual)1(ly)-403(m)-1(at)1(c)27(hes)-404(th)1(e)-404(n)28(u)1(m)27(b)-27(e)-1(r)-402(of)-403(a)28(v)55(ai)1(lable)-403(pr)1(o)-28(c)-1(ess)-1(ors.)-654(Op)1(timal)]TJ 0 -13.5492 Td[(con)28(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-262(rates,)-276(i.e.)-262(it)1(e)-1(rati)1(on)-262(n)29(um)28(b)-28(ers)-262(in)1(dep)-28(end)1(e)-1(n)28(t)-261(of)-262(t)1(he)-262(n)28(um)28(b)-27(e)-1(r)-261(of)-262(sub)1(m)-1(at)1(rice)-1(s,)-276(can)]TJ 0 -13.5492 Td[(b)-27(e)-370(obtai)1(ned)-369(b)28(y)-369(c)-1(or)1(re)-1(ctin)1(g)-370(th)1(e)-370(pr)1(e)-1(cond)1(ition)1(e)-1(r)-369(th)1(rou)1(gh)-369(a)-370(suit)1(able)-370(ap)1(pr)1(o)27(x)1(im)-1(at)1(ion)-369(of)-369(the)]TJ 0 -13.5492 Td[(ori)1(ginal)-323(l)1(inear)-323(syste)-1(m)-323(in)-322(a)-323(c)-1(oar)1(s)-1(e)-323(s)-1(p)1(ac)-1(e,)-325(whi)1(c)27(h)-323(gl)1(oball)1(y)-323(c)-1(ou)1(ples)-323(the)-323(inf)1(ormation)-322(related)]TJ 0 -13.5492 Td[(to)-333(the)-333(s)-1(in)1(gle)-334(sub)1(m)-1(atr)1(ice)-1(s.)]TJ/F20 10.9091 Tf 16.9365 -14.0113 Td[(Two-l)1(evel)-256(Schwarz)]TJ/F15 10.9091 Tf 90.3282 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-223(are)-222(obtain)1(e)-1(d)-221(b)28(y)-222(c)-1(om)28(bi)1(nin)1(g)-223(b)1(as)-1(i)1(c)-223(\050on)1(e)-1(-lev)28(e)-1(l\051)-222(S)1(c)27(h)28(w)28(arz)]TJ -107.2647 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-368(with)-366(a)-368(coarse)-1(-lev)28(e)-1(l)-366(c)-1(orr)1(e)-1(ction)1(.)-546(In)-367(t)1(his)-367(c)-1(on)28(t)1(e)-1(xt,)-375(th)1(e)-368(on)1(e)-1(-lev)28(e)-1(l)-367(p)1(rec)-1(on)1(di-)]TJ 0 -13.5492 Td[(tion)1(e)-1(r)-422(i)1(s)-423(oft)1(e)-1(n)-422(called)-422(`smo)-28(other')1(.)-711(Di\013e)-1(r)1(e)-1(n)28(t)-422(t)28(w)28(o-)-1(l)1(e)-1(v)28(el)-422(pr)1(e)-1(cond)1(ition)1(e)-1(rs)-422(are)-423(ob)1(tain)1(e)-1(d)-421(b)28(y)]TJ 0 -13.5492 Td[(v)56(aryi)1(ng)-310(t)1(he)-310(c)27(h)1(oice)-310(of)-310(t)1(he)-310(sm)-1(o)-28(ot)1(her)-310(an)1(d)-309(of)-309(the)-310(coarse)-1(-lev)28(e)-1(l)-309(c)-1(or)1(rec)-1(tion)1(,)-314(and)-309(th)1(e)-310(w)27(a)28(y)-309(they)]TJ 0 -13.5492 Td[(are)-399(com)27(b)1(in)1(e)-1(d)-398([)]TJ -ET -1 0 0 1 213.1882 352.7814 cm + [(]\051.)-530(The)-362(main)-362(motiv)55(ation)-361(for)-362(c)28(ho)-28(osing)-362(Additiv)28(e)-362(Sc)28(h)28(w)27(arz)-362(pre-)]TJ 0 -13.549 Td [(conditioners)-361(is)-361(their)-361(in)28(trinsic)-361(parallelism.)-528(A)-361(dra)28(wbac)28(k)-362(of)-361(these)-361(preconditioners)-361(is)-361(that)]TJ 0 -13.549 Td [(the)-388(n)28(um)27(b)-27(er)-388(of)-389(iterations)-388(of)-388(the)-388(preconditioned)-388(solv)28(ers)-388(ge)-1(n)1(e)-1(r)1(ally)-389(gro)28(ws)-388(with)-388(the)-388(n)28(um-)]TJ 0 -13.549 Td [(b)-28(er)-370(of)-370(submatrices.)-555(This)-370(ma)28(y)-370(b)-28(e)-370(a)-370(serious)-370(limitation)-370(on)-370(parallel)-370(computers,)-380(since)-370(the)]TJ 0 -13.55 Td [(n)28(um)28(b)-28(er)-403(of)-404(submatri)1(c)-1(es)-403(usually)-403(matc)28(hes)-403(the)-404(n)28(um)28(b)-28(er)-403(of)-403(a)28(v)55(ailable)-403(pro)-28(cessors.)-654(Optimal)]TJ 0 -13.549 Td [(con)28(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-261(rates,)-276(i.e.)-262(iteration)-262(n)28(um)28(b)-28(ers)-262(indep)-27(enden)27(t)-261(of)-262(the)-262(n)28(um)28(b)-28(er)-262(of)-261(submatrices)-1(,)-276(can)]TJ 0 -13.549 Td [(b)-28(e)-369(obtained)-370(b)28(y)-369(correcting)-370(t)1(he)-370(preconditioner)-369(through)-369(a)-370(suitable)-369(appro)28(ximation)-370(of)-369(the)]TJ 0 -13.549 Td [(original)-323(linear)-323(system)-323(in)-323(a)-323(coarse)-323(space,)-325(whic)28(h)-323(globally)-323(couples)-323(the)-323(infor)1(m)-1(ation)-322(related)]TJ 0 -13.549 Td [(to)-333(the)-334(single)-333(submatrices.)]TJ/F18 10.9091 Tf 16.937 -14.012 Td [(Two-level)-255(Schwarz)]TJ/F15 10.9091 Tf 90.328 0 Td [(preconditioners)-222(are)-222(obtained)-222(b)27(y)-222(com)28(bining)-222(basic)-222(\050one-lev)27(el\051)-222(Sc)28(h)28(w)27(arz)]TJ -107.265 -13.549 Td [(preconditioners)-367(with)-367(a)-367(coarse-lev)27(el)-367(correction.)-545(In)-367(this)-367(con)27(text,)-375(the)-367(one-lev)27(el)-367(precondi-)]TJ 0 -13.549 Td [(tioner)-422(is)-422(often)-423(called)-422(`smo)-28(other'.)-711(D)1(i\013)-1(eren)28(t)-422(t)28(w)28(o-lev)27(el)-422(preconditioners)-422(are)-422(obtained)-422(b)28(y)]TJ 0 -13.549 Td [(v)56(arying)-310(the)-309(c)27(hoice)-309(of)-310(the)-309(smo)-28(other)-310(and)-309(of)-310(the)-309(coarse-lev)27(el)-309(correction,)-314(and)-310(the)-309(w)27(a)28(y)-309(they)]TJ 0 -13.549 Td [(are)-398(com)27(bined)-398([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -213.1882 -352.7814 cm -BT -/F15 10.9091 Tf 213.1882 352.7814 Td[(15)]TJ -ET -1 0 0 1 224.0973 352.7814 cm + [(15)]TJ 0 g 0 G -1 0 0 1 -224.0973 -352.7814 cm -BT -/F15 10.9091 Tf 224.0973 352.7814 Td[(].)-639(The)-399(sam)-1(e)-398(re)-1(asoni)1(ng)-398(c)-1(an)-398(b)-27(e)-399(ap)1(pli)1(e)-1(d)-398(startin)1(g)-398(from)-398(the)-399(coarse)-1(-lev)28(e)-1(l)]TJ -82.3588 -13.5492 Td[(sys)-1(tem,)-495(i.)1(e)-1(.)-462(a)-462(c)-1(oarse-)-1(space)-463(c)-1(or)1(rec)-1(ti)1(on)-462(c)-1(an)-462(b)-27(e)-463(bu)1(ilt)-462(fr)1(om)-463(th)1(is)-463(sys)-1(tem,)-495(th)28(u)1(s)-463(ob)1(taini)1(ng)]TJ/F20 10.9091 Tf 0 -13.5492 Td[(mu)1(lti-l)1(evel)]TJ/F15 10.9091 Tf 53.8299 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-1(.)]TJ -36.8934 -14.0113 Td[(It)-443(is)-444(w)27(or)1(th)-443(noti)1(ng)-443(that)-443(opt)1(im)-1(al)-443(p)1(rec)-1(on)1(diti)1(oners)-444(do)-443(not)-443(n)1(e)-1(ce)-1(ss)-1(ar)1(ily)-443(c)-1(or)1(res)-1(p)-27(ond)-443(to)]TJ -16.9365 -13.5492 Td[(mini)1(m)27(um)-480(e)-1(x)1(e)-1(cuti)1(on)-480(time)-1(s.)-885(Ind)1(e)-1(ed,)-516(to)-480(obtain)-479(e)-1(\013e)-1(ctiv)28(e)-480(m)27(ul)1(ti-le)-1(v)28(el)-480(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-481(a)]TJ 0 -13.5492 Td[(trad)1(e)-1(o\013)-381(b)-27(e)-1(t)28(w)28(e)-1(en)-381(opti)1(m)-1(al)1(it)28(y)-381(of)-381(c)-1(on)29(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-382(an)1(d)-381(th)1(e)-382(cos)-1(t)-381(of)-381(b)1(uil)1(din)1(g)-382(an)1(d)-381(ap)1(plyi)1(ng)-381(the)]TJ 0 -13.5492 Td[(coars)-1(e-s)-1(p)1(ac)-1(e)-384(correc)-1(ti)1(ons)-384(m)27(u)1(s)-1(t)-383(b)-28(e)-384(ac)27(h)1(iev)28(e)-1(d)1(.)-596(The)-384(c)28(hoice)-384(of)-384(th)1(e)-384(n)28(um)28(b)-28(er)-384(of)-383(lev)28(e)-1(l)1(s)-1(,)-396(i.)1(e)-1(.)-383(of)]TJ 0 -13.5492 Td[(th)1(e)-380(coarse)-1(-space)-379(c)-1(orr)1(e)-1(ction)1(s)-1(,)-390(al)1(s)-1(o)-378(a\013)-1(ec)-1(ts)-379(th)1(e)-379(e)-1(\013ec)-1(tiv)28(eness)-380(of)-378(th)1(e)-379(pr)1(e)-1(cond)1(itioners.)-580(One)]TJ 0 -13.5492 Td[(more)-392(goal)-392(i)1(s)-392(to)-392(get)-392(con)28(v)28(e)-1(r)1(ge)-1(n)1(c)-1(e)-392(r)1(ate)-1(s)-392(as)-392(les)-1(s)-392(se)-1(n)1(s)-1(i)1(tiv)28(e)-392(as)-392(p)-28(ossible)-392(to)-391(v)56(ariation)1(s)-392(in)-391(the)]TJ 0 -13.5492 Td[(matrix)-333(co)-28(e\016)-1(cien)28(ts)-1(.)]TJ 16.9365 -14.0113 Td[(Tw)27(o)-303(main)-302(app)1(roac)27(h)1(e)-1(s)-303(c)-1(an)-302(b)-27(e)-304(u)1(s)-1(ed)-303(to)-303(b)1(ui)1(ld)-303(coarse)-1(-s)-1(p)1(ac)-1(e)-303(correc)-1(t)1(ions.)-434(T)-1(h)1(e)-304(geome)-1(tr)1(ic)]TJ -16.9365 -13.5492 Td[(app)1(roac)28(h)-412(app)1(lies)-413(c)-1(oar)1(s)-1(enin)1(g)-412(s)-1(tr)1(ate)-1(gies)-413(b)1(as)-1(ed)-412(on)-412(the)-412(kno)28(wledge)-413(of)-412(some)-413(ph)29(ys)-1(i)1(c)-1(al)-412(gri)1(d)]TJ 0 -13.5492 Td[(ass)-1(o)-28(ciated)-279(to)-280(th)1(e)-280(m)-1(at)1(rix)-279(and)-279(r)1(e)-1(qu)1(ires)-280(the)-280(u)1(s)-1(er)-279(to)-280(d)1(e)-1(\014)1(ne)-280(gr)1(id)-279(tran)1(s)-1(f)1(e)-1(r)-279(op)-27(e)-1(rat)1(ors)-280(fr)1(om)-280(the)]TJ 0 -13.5492 Td[(\014n)1(e)-394(to)-394(t)1(he)-394(coars)-1(e)-394(l)1(e)-1(v)28(els)-394(and)-393(v)1(ic)-1(e)-394(v)28(ersa.)-625(This)-394(ma)28(y)-394(r)1(e)-1(sul)1(t)-394(d)1(i\016)-1(cul)1(t)-394(f)1(or)-394(complex)-393(ge)-1(ome)-1(-)]TJ 0 -13.5492 Td[(tri)1(e)-1(s;)-464(f)1(urth)1(e)-1(r)1(m)-1(or)1(e)-1(,)-442(sui)1(table)-420(one-)-1(lev)28(el)-421(p)1(rec)-1(on)1(diti)1(oners)-421(ma)28(y)-420(b)-28(e)-421(r)1(e)-1(qu)1(ired)-420(to)-420(ge)-1(t)-420(e\016)-1(cien)28(t)]TJ 0 -13.5492 Td[(in)28(t)1(e)-1(rp)1(la)28(y)-381(b)-27(e)-1(t)28(w)28(e)-1(en)-381(\014n)1(e)-382(an)1(d)-381(coars)-1(e)-381(lev)28(e)-1(ls,)-393(e.g.)-381(when)-381(matrice)-1(s)-381(with)-381(h)1(ighl)1(y)-381(v)55(ar)1(yin)1(g)-381(c)-1(o)-28(ef-)]TJ 0 -13.5492 Td[(\014cien)28(ts)-417(are)-417(considered.)-694(The)-417(al)1(ge)-1(b)1(raic)-417(ap)1(proac)28(h)-417(b)1(ui)1(lds)-417(coarse)-1(-s)-1(p)1(ac)-1(e)-417(corr)1(e)-1(ctions)-417(u)1(s)-1(i)1(ng)]TJ 0 -13.5492 Td[(onl)1(y)-442(m)-1(at)1(rix)-442(i)1(nfor)1(m)-1(at)1(ion.)-770(It)-442(p)-28(erf)1(orms)-443(a)-442(f)1(ully)-441(automatic)-442(c)-1(oar)1(s)-1(enin)1(g)-442(and)-442(enf)1(orce)-1(s)-442(the)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [(].)-640(The)-398(same)-398(re)-1(asoni)1(ng)-399(can)-398(b)-28(e)-398(applied)-399(starting)-398(from)-398(the)-399(coarse-lev)28(el)]TJ 0 -13.55 Td [(system,)-495(i.e.)-462(a)-463(coarse-space)-462(correction)-463(can)-462(b)-28(e)-462(built)-463(from)-462(this)-462(system)-1(,)-494(th)28(us)-463(obtaining)]TJ/F18 10.9091 Tf 0 -13.549 Td [(multi-level)]TJ/F15 10.9091 Tf 53.83 0 Td [(preconditioners.)]TJ -36.893 -14.011 Td [(It)-443(is)-444(w)28(orth)-443(noting)-444(that)-443(optimal)-443(prec)-1(on)1(ditioners)-444(do)-443(not)-444(necessarily)-443(corresp)-28(ond)-443(to)]TJ -16.937 -13.549 Td [(minim)28(um)-480(exe)-1(cuti)1(on)-481(times.)-885(Indeed,)-517(to)-480(obtain)-480(e\013ectiv)28(e)-481(m)28(ulti-lev)28(el)-480(preconditioners)-480(a)]TJ 0 -13.549 Td [(tradeo\013)-381(b)-28(et)28(w)28(e)-1(en)-381(optimalit)28(y)-381(of)-381(con)28(v)27(ergence)-381(and)-381(the)-381(cost)-382(of)-381(building)-381(and)-381(applying)-381(the)]TJ 0 -13.55 Td [(coarse-space)-384(corrections)-384(m)28(ust)-384(b)-28(e)-383(ac)27(hiev)28(ed.)-596(The)-383(c)27(hoice)-383(of)-384(the)-384(n)28(um)28(b)-28(er)-384(of)-384(l)1(e)-1(v)28(els,)-396(i.e.)-384(of)]TJ 0 -13.549 Td [(the)-379(coarse-space)-379(corrections,)-390(also)-378(a\013ects)-379(the)-379(e\013ectiv)28(eness)-379(of)-378(the)-379(preconditioners.)-580(One)]TJ 0 -13.549 Td [(more)-392(goal)-391(is)-392(to)-392(get)-391(con)27(v)28(ergence)-392(r)1(ate)-1(s)-391(as)-392(less)-392(sensitiv)28(e)-392(as)-391(p)-28(ossible)-392(to)-391(v)55(ariations)-391(in)-392(the)]TJ 0 -13.549 Td [(matrix)-333(co)-28(e\016cien)28(ts)-1(.)]TJ 16.937 -14.012 Td [(Tw)28(o)-303(main)-303(approac)28(hes)-303(can)-303(b)-28(e)-303(used)-303(to)-303(build)-303(coarse-space)-303(corrections.)-434(The)-303(geometric)]TJ -16.937 -13.549 Td [(approac)28(h)-412(applies)-413(coarsening)-412(strategies)-413(based)-412(on)-412(the)-413(kn)1(o)27(wledge)-412(of)-412(some)-413(ph)28(ysical)-412(grid)]TJ 0 -13.549 Td [(asso)-28(ciated)-279(to)-280(the)-280(matri)1(x)-280(and)-279(requires)-280(the)-280(u)1(s)-1(er)-279(to)-280(de\014ne)-279(grid)-280(tr)1(ansfer)-280(op)-28(erators)-279(from)-280(the)]TJ 0 -13.549 Td [(\014ne)-394(to)-393(the)-394(coarse)-393(lev)27(els)-393(and)-394(vice)-393(v)28(ersa.)-626(This)-393(ma)28(y)-394(result)-393(di\016cult)-394(for)-393(complex)-394(geome-)]TJ 0 -13.549 Td [(tries;)-464(furthermore,)-442(suitable)-420(one-lev)27(el)-420(preconditioners)-420(ma)28(y)-421(b)-28(e)-420(required)-420(to)-421(get)-420(e\016cien)28(t)]TJ 0 -13.549 Td [(in)28(terpla)28(y)-381(b)-28(et)28(w)27(een)-381(\014ne)-381(and)-381(coarse)-381(lev)27(els,)-393(e.g.)-381(when)-381(matrices)-381(with)-381(highly)-381(v)55(arying)-381(co)-28(ef-)]TJ 0 -13.55 Td [(\014cien)28(ts)-417(are)-417(considered.)-694(The)-417(algebr)1(aic)-417(approac)28(h)-417(builds)-416(coarse-)-1(space)-416(corrections)-417(using)]TJ 0 -13.549 Td [(only)-442(matrix)-442(information.)-770(It)-443(p)-27(erforms)-442(a)-442(fully)-442(automatic)-442(coarse)-1(n)1(ing)-442(and)-442(enforces)-443(the)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -241 0 obj << +227 0 obj << /Type /Page -/Contents 242 0 R -/Resources 240 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 230 0 R -/Annots [ 244 0 R 245 0 R 246 0 R 247 0 R 248 0 R ] +/Contents 228 0 R +/Resources 226 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 210 0 R +/Annots [ 220 0 R 221 0 R 222 0 R 223 0 R 224 0 R ] >> endobj -244 0 obj << +220 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [492.2578 569.4965 499.7048 578.5193] +/Rect [492.258 569.496 499.705 578.519] /Subtype /Link /A << /S /GoTo /D (cite.Cai_Widlund_92) >> >> endobj -245 0 obj << +221 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [504.379 569.4965 511.8261 578.5193] +/Rect [504.379 569.496 511.826 578.519] /Subtype /Link /A << /S /GoTo /D (cite.dd1_94) >> >> endobj -246 0 obj << +222 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [516.5002 569.4965 529.4018 578.5193] +/Rect [516.5 569.496 529.402 578.519] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -247 0 obj << +223 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [252.9546 528.3868 265.8562 537.4096] +/Rect [252.955 528.387 265.856 537.41] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -248 0 obj << +224 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [212.192 351.7851 225.0936 360.808] +/Rect [212.192 351.785 225.094 360.808] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -243 0 obj << -/D [241 0 R /XYZ 141.7385 740.0018 null] +229 0 obj << +/D [227 0 R /XYZ 141.738 740.002 null] >> endobj 42 0 obj << -/D [241 0 R /XYZ 141.7385 715.0952 null] +/D [227 0 R /XYZ 141.738 715.095 null] >> endobj -240 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F19 105 0 R /F20 171 0 R >> +226 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F17 103 0 R /F18 163 0 R >> /ProcSet [ /PDF /Text ] >> endobj -253 0 obj << -/Length 18873 +246 0 obj << +/Length 14809 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(5)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(5)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Mul)66(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)23(gr)22(oun)-1(d)]TJ/F15 10.9091 Tf 391.3906 0 Td[(11)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Mul)67(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)22(gr)22(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(11)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F15 10.9091 Tf 93.9178 704.1363 Td[(in)28(t)1(e)-1(rp)1(la)28(y)-352(b)-27(et)28(w)27(ee)-1(n)-351(th)1(e)-353(\014)1(ne)-352(an)1(d)-352(coarse)-352(le)-1(v)28(els)-352(b)28(y)-351(s)-1(u)1(itab)1(ly)-352(c)28(ho)-28(osin)1(g)-352(the)-352(coarse)-352(s)-1(p)1(ac)-1(e)-352(an)1(d)]TJ 0 -13.5492 Td[(th)1(e)-334(c)-1(oar)1(s)-1(e-)-1(t)1(o-)-1(\014)1(ne)-334(i)1(n)28(te)-1(r)1(p)-28(ol)1(ation)-333([)]TJ -ET -1 0 0 1 247.3725 690.5871 cm + -401.542 -35.866 Td [(in)28(terpla)28(y)-352(b)-28(et)28(w)28(een)-352(the)-352(\014ne)-351(and)-352(coarse)-352(lev)28(els)-352(b)28(y)-351(suitably)-352(c)28(ho)-28(osing)-352(the)-351(coarse)-352(space)-352(and)]TJ 0 -13.549 Td [(the)-333(coarse-to-\014ne)-334(in)28(terp)-28(olation)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -247.3725 -690.5871 cm -BT -/F15 10.9091 Tf 247.3725 690.5871 Td[(17)]TJ -ET -1 0 0 1 258.2816 690.5871 cm + [(17)]TJ 0 g 0 G -1 0 0 1 -258.2816 -690.5871 cm -BT -/F15 10.9091 Tf 258.2816 690.5871 Td[(].)]TJ -147.4273 -13.6428 Td[(MLD2P)1(4)-255(uses)-256(a)-255(p)1(ur)1(e)-256(al)1(ge)-1(b)1(raic)-255(app)1(roac)27(h)-254(for)-254(bu)1(ild)1(ing)-255(t)1(he)-255(s)-1(equ)1(e)-1(n)1(c)-1(e)-255(of)-255(coarse)-256(matr)1(ic)-1(es)]TJ -16.9365 -13.5492 Td[(startin)1(g)-425(from)-425(the)-425(origi)1(nal)-425(matrix)1(.)-720(The)-426(al)1(ge)-1(b)1(raic)-425(app)1(roac)27(h)-425(i)1(s)-426(based)-425(on)-425(th)1(e)]TJ/F20 10.9091 Tf 369.2393 0 Td[(smo)51(othe)51(d)]TJ -369.2393 -13.5492 Td[(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 58.6124 0 Td[(algor)1(ithm)-402([)]TJ -ET -1 0 0 1 206.0396 649.8459 cm + [(].)]TJ 16.936 -13.643 Td [(MLD2P4)-255(uses)-255(a)-255(pur)1(e)-255(algebraic)-255(approac)28(h)-255(for)-255(building)-255(the)-254(sequence)-255(of)-255(coarse)-255(matrices)]TJ -16.936 -13.549 Td [(starting)-425(from)-425(the)-425(original)-425(matrix.)-720(The)-426(algebr)1(aic)-426(approac)28(h)-425(is)-425(based)-425(on)-425(the)]TJ/F18 10.9091 Tf 369.239 0 Td [(smo)51(othe)51(d)]TJ -369.239 -13.549 Td [(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 58.612 0 Td [(algorithm)-402([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -206.0396 -649.8459 cm -BT -/F15 10.9091 Tf 206.0396 649.8459 Td[(1)]TJ -ET -1 0 0 1 211.4942 649.8459 cm + [(1)]TJ 0 g 0 G -1 0 0 1 -211.4942 -649.8459 cm -BT -/F15 10.9091 Tf 211.4942 649.8459 Td[(,)]TJ -ET -1 0 0 1 218.9126 649.8459 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -218.9126 -649.8459 cm -BT -/F15 10.9091 Tf 218.9126 649.8459 Td[(19)]TJ -ET -1 0 0 1 229.8217 649.8459 cm + [-402(19)]TJ 0 g 0 G -1 0 0 1 -229.8217 -649.8459 cm -BT -/F15 10.9091 Tf 229.8217 649.8459 Td[(].)-651(A)-402(d)1(e)-1(coup)1(le)-1(d)-401(v)28(e)-1(rsion)-402(of)-401(this)-402(algorit)1(hm)-403(i)1(s)-403(impl)1(e)-1(me)-1(n)28(t)1(e)-1(d)1(,)]TJ -135.9039 -13.5492 Td[(where)-347(th)1(e)-348(smo)-28(othed)-346(aggregation)-346(is)-347(app)1(lied)-346(lo)-28(cally)-346(to)-347(eac)27(h)-346(s)-1(u)1(bmatri)1(x)-347([)]TJ -ET -1 0 0 1 430.4914 636.2967 cm + [(].)-652(A)-402(decoupled)-402(v)28(ersion)-402(of)-402(this)-403(algorithm)-402(is)-402(implemen)28(ted,)]TJ -58.612 -13.549 Td [(where)-347(the)-346(smo)-28(othed)-347(aggregation)-346(is)-347(applied)-347(l)1(o)-28(cally)-347(to)-347(eac)28(h)-346(submatrix)-347([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -430.4914 -636.2967 cm -BT -/F15 10.9091 Tf 430.4914 636.2967 Td[(18)]TJ -ET -1 0 0 1 441.4005 636.2967 cm + [(18)]TJ 0 g 0 G -1 0 0 1 -441.4005 -636.2967 cm -BT -/F15 10.9091 Tf 441.4005 636.2967 Td[(].)-484(In)-346(the)-347(n)1(e)-1(xt)]TJ -347.4827 -13.5492 Td[(t)28(w)27(o)-248(s)-1(u)1(bse)-1(ction)1(s)-250(w)28(e)-249(pr)1(o)27(v)1(ide)-249(a)-249(b)1(rief)-248(des)-1(crip)1(tion)-248(of)-248(the)-249(m)28(ulti)1(-)-1(lev)28(el)-249(Sc)28(h)28(w)28(arz)-249(pr)1(e)-1(cond)1(ition)1(e)-1(rs)]TJ 0 -13.5492 Td[(and)-389(of)-389(th)1(e)-390(s)-1(mo)-28(oth)1(e)-1(d)-389(aggr)1(e)-1(gati)1(on)-389(te)-1(c)28(hni)1(que)-390(as)-390(i)1(m)-1(p)1(lem)-1(en)28(ted)-389(in)-389(MLD2P)1(4.)-613(F)83(or)-389(f)1(ur)1(ther)]TJ 0 -13.5492 Td[(detail)1(s)-334(the)-333(use)-1(r)-333(is)-333(re)-1(f)1(e)-1(r)1(red)-333(to)-333([)]TJ -ET -1 0 0 1 238.1604 595.6491 cm + [(].)-484(In)-347(the)-347(n)1(e)-1(xt)]TJ 0 -13.549 Td [(t)28(w)28(o)-249(subsections)-249(w)28(e)-249(pro)28(vide)-249(a)-248(brief)-249(description)-249(of)-248(the)-249(m)28(ulti-lev)28(el)-249(Sc)28(h)27(w)28(arz)-249(p)1(rec)-1(on)1(ditioners)]TJ 0 -13.55 Td [(and)-389(of)-390(the)-389(smo)-28(othed)-390(aggregation)-389(tec)28(hnique)-390(as)-389(implemen)27(ted)-389(in)-390(M)1(LD2P4.)-613(F)83(or)-389(further)]TJ 0 -13.549 Td [(details)-333(the)-334(user)-333(is)-333(referred)-334(to)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -238.1604 -595.6491 cm -BT -/F15 10.9091 Tf 238.1604 595.6491 Td[(2)]TJ -ET -1 0 0 1 243.6149 595.6491 cm + [(2)]TJ 0 g 0 G -1 0 0 1 -243.6149 -595.6491 cm -BT -/F15 10.9091 Tf 243.6149 595.6491 Td[(,)]TJ -ET -1 0 0 1 250.2816 595.6491 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -250.2816 -595.6491 cm -BT -/F15 10.9091 Tf 250.2816 595.6491 Td[(3)]TJ -ET -1 0 0 1 255.7361 595.6491 cm + [-333(3)]TJ 0 g 0 G -1 0 0 1 -255.7361 -595.6491 cm -BT -/F15 10.9091 Tf 255.7361 595.6491 Td[(,)]TJ -ET -1 0 0 1 262.4028 595.6491 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -262.4028 -595.6491 cm -BT -/F15 10.9091 Tf 262.4028 595.6491 Td[(4)]TJ -ET -1 0 0 1 267.8574 595.6491 cm + [-334(4)]TJ 0 g 0 G -1 0 0 1 -267.8574 -595.6491 cm -BT -/F15 10.9091 Tf 267.8574 595.6491 Td[(,)]TJ -ET -1 0 0 1 274.524 595.6491 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -274.524 -595.6491 cm -BT -/F15 10.9091 Tf 274.524 595.6491 Td[(15)]TJ -ET -1 0 0 1 285.4331 595.6491 cm + [-333(15)]TJ 0 g 0 G -1 0 0 1 -285.4331 -595.6491 cm -BT -/F15 10.9091 Tf 285.4331 595.6491 Td[(].)]TJ/F19 11.9552 Tf -191.5153 -29.7481 Td[(5.)-1(1)-1125(M)-1(ult)-1(i-l)-1(ev)32(e)-1(l)-375(Sc)31(h)31(w)31(arz)-375(Pre)-1(condi)-1(ti)-1(oner)-1(s)]TJ/F15 10.9091 Tf 0 -20.7766 Td[(The)-270(Mu)1(ltil)1(e)-1(v)28(el)-270(p)1(rec)-1(on)1(diti)1(oners)-270(impleme)-1(n)28(ted)-269(in)-269(MLD2P)1(4)-270(are)-270(ob)1(tained)-269(b)28(y)-270(com)27(b)1(in)1(ing)-269(AS)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-316(with)-314(c)-1(oar)1(s)-1(e-)-1(space)-316(corr)1(e)-1(ctions;)-321(th)1(e)-1(refor)1(e)-316(w)28(e)-316(\014)1(rst)-315(pro)28(vi)1(de)-315(a)-315(s)-1(k)28(etc)27(h)-315(of)-314(the)]TJ 0 -13.5492 Td[(AS)-333(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-1(.)]TJ 16.9365 -13.6429 Td[(Giv)28(en)-302(th)1(e)-303(lin)1(e)-1(ar)-302(syste)-1(m)-302(\050)]TJ -ET -1 0 0 1 230.6386 504.3831 cm + [(].)]TJ/F17 11.9552 Tf 0 -29.748 Td [(5.1)-1125(Multi-lev)31(el)-375(Sc)31(h)32(w)31(arz)-375(Preconditioners)]TJ/F15 10.9091 Tf 0 -20.777 Td [(The)-270(Multilev)28(el)-270(p)1(rec)-1(on)1(ditioners)-270(implemen)28(ted)-270(in)-270(MLD2P4)-269(are)-270(obtained)-269(b)27(y)-269(com)27(binin)1(g)-270(AS)]TJ 0 -13.549 Td [(preconditioners)-315(with)-315(coarse-space)-315(corrections;)-321(therefore)-315(w)27(e)-315(\014rst)-315(pro)28(vide)-315(a)-315(sk)28(etc)27(h)-315(of)-315(the)]TJ 0 -13.549 Td [(AS)-333(preconditioners.)]TJ 16.936 -13.643 Td [(Giv)28(en)-303(the)-302(linear)-302(system)-303(\050)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -230.6386 -504.3831 cm -BT -/F15 10.9091 Tf 230.6386 504.3831 Td[(1)]TJ -ET -1 0 0 1 236.0931 504.3831 cm + [(1)]TJ 0 g 0 G -1 0 0 1 -236.0931 -504.3831 cm -BT -/F15 10.9091 Tf 236.0931 504.3831 Td[(\051,)-308(where)]TJ/F24 10.9091 Tf 41.8461 0 Td[(A)]TJ/F15 10.9091 Tf 11.212 0 Td[(=)-278(\050)]TJ/F24 10.9091 Tf 15.7576 0 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(ij)]TJ/F15 10.9091 Tf 7.2653 1.6364 Td[(\051)]TJ/F27 10.9091 Tf 7.2727 0 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F28 7.9701 Tf 5.1382 0 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 8.9346 -3.9588 Td[(is)-303(a)-302(n)1(onsingu)1(lar)-302(s)-1(p)1(arse)-303(matrix)]TJ -270.1365 -13.5492 Td[(with)-321(a)-321(symme)-1(tr)1(ic)-322(n)1(onze)-1(r)1(o)-321(pattern)1(,)-324(let)]TJ/F24 10.9091 Tf 184.5267 0 Td[(G)]TJ/F15 10.9091 Tf 11.6075 0 Td[(=)-278(\050)]TJ/F24 10.9091 Tf 15.7575 0 Td[(W)27(;)-166(E)]TJ/F15 10.9091 Tf 23.5303 0 Td[(\051)-321(b)-27(e)-322(th)1(e)-322(ad)1(jace)-1(n)1(c)-1(y)-321(gr)1(aph)-320(of)]TJ/F24 10.9091 Tf 134.3786 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(,)-323(w)-1(h)1(e)-1(r)1(e)]TJ/F24 10.9091 Tf -377.9824 -13.5492 Td[(W)]TJ/F15 10.9091 Tf 15.4193 0 Td[(=)]TJ/F27 10.9091 Tf 12.0859 0 Td[(f)]TJ/F15 10.9091 Tf 5.4546 0 Td[(1)]TJ/F24 10.9091 Tf 5.4545 0 Td[(;)]TJ/F15 10.9091 Tf 4.8485 0 Td[(2)]TJ/F24 10.9091 Tf 5.4546 0 Td[(;)-166(:)-167(:)-166(:)-167(;)-166(n)]TJ/F27 10.9091 Tf 30.7903 0 Td[(g)]TJ/F15 10.9091 Tf 9.4334 0 Td[(and)]TJ/F24 10.9091 Tf 21.5546 0 Td[(E)]TJ/F15 10.9091 Tf 12.2829 0 Td[(=)]TJ/F27 10.9091 Tf 12.086 0 Td[(f)]TJ/F15 10.9091 Tf 5.4545 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(i;)-166(j)]TJ/F15 10.9091 Tf 13.7236 0 Td[(\051)-330(:)]TJ/F24 10.9091 Tf 14.4749 0 Td[(a)]TJ/F25 7.9701 Tf 5.7665 -1.6364 Td[(ij)]TJ/F27 10.9091 Tf 10.8664 1.6364 Td[(6)]TJ/F15 10.9091 Tf 0 0 Td[(=)-330(0)]TJ/F27 10.9091 Tf 17.5405 0 Td[(g)]TJ/F15 10.9091 Tf 9.4334 0 Td[(are)-365(th)1(e)-365(v)28(e)-1(rt)1(e)-1(x)-364(s)-1(et)-365(an)1(d)-365(th)1(e)-365(e)-1(d)1(ge)-366(set)-365(of)]TJ/F24 10.9091 Tf 184.4767 0 Td[(G)]TJ/F15 10.9091 Tf 8.5772 0 Td[(,)]TJ -409.4208 -13.5492 Td[(res)-1(p)-27(ec)-1(ti)1(v)28(e)-1(ly)84(.)-466(T)-1(w)28(o)-341(v)28(erti)1(c)-1(es)-341(are)-341(c)-1(al)1(le)-1(d)-340(ad)1(jace)-1(n)28(t)-340(if)-340(there)-341(is)-341(an)-340(edge)-341(c)-1(on)1(nec)-1(t)1(ing)-340(them)-1(.)-466(F)84(or)]TJ 0 -13.5492 Td[(an)28(y)-238(in)29(te)-1(ger)]TJ/F24 10.9091 Tf 54.621 0 Td[(\016)-316(>)]TJ/F15 10.9091 Tf 19.8067 0 Td[(0,)-257(a)]TJ/F24 10.9091 Tf 19.3437 0 Td[(\016)]TJ/F15 10.9091 Tf 5.2614 0 Td[(-o)27(v)28(erl)1(ap)-238(par)1(tition)-237(of)]TJ/F24 10.9091 Tf 96.3406 0 Td[(W)]TJ/F15 10.9091 Tf 14.4165 0 Td[(can)-238(b)-28(e)-238(de\014n)1(e)-1(d)-237(re)-1(cur)1(s)-1(i)1(v)28(e)-1(ly)-238(as)-238(foll)1(o)27(ws.)-413(Gi)1(v)28(e)-1(n)]TJ -209.7899 -13.5492 Td[(a)-344(0-o)28(v)28(e)-1(r)1(lap)-343(\050or)-343(non-o)28(v)28(e)-1(r)1(lapp)1(in)1(g\051)-344(par)1(tition)-343(of)]TJ/F24 10.9091 Tf 216.2495 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-346(i.e.)-343(a)-344(se)-1(t)-343(of)]TJ/F24 10.9091 Tf 63.3773 0 Td[(m)]TJ/F15 10.9091 Tf 13.3269 0 Td[(di)1(s)-1(j)1(oin)28(t)-343(nonempt)28(y)-343(s)-1(ets)]TJ/F24 10.9091 Tf -304.7719 -13.5492 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9588 Td[(0)]TJ/F25 7.9701 Tf -1.5152 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 9.2778 3.0555 Td[(\032)]TJ/F24 10.9091 Tf 11.5151 0 Td[(W)]TJ/F15 10.9091 Tf 14.8569 0 Td[(suc)27(h)-278(th)1(at)]TJ/F27 10.9091 Tf 47.047 0 Td[([)]TJ/F25 7.9701 Tf 7.2728 3.9588 Td[(m)]TJ 0 -7.0143 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F24 10.9091 Tf 11.3188 3.0555 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9588 Td[(0)]TJ/F25 7.9701 Tf -1.5151 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 9.2777 3.0555 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-289(a)]TJ/F24 10.9091 Tf 14.6817 0 Td[(\016)]TJ/F15 10.9091 Tf 5.2614 0 Td[(-o)27(v)28(erl)1(ap)-279(p)1(arti)1(tion)-278(of)]TJ/F24 10.9091 Tf 97.6615 0 Td[(W)]TJ/F15 10.9091 Tf 14.8569 0 Td[(is)-279(ob)1(tained)-278(b)28(y)-278(c)-1(on)1(s)-1(i)1(derin)1(g)]TJ -289.8501 -13.5492 Td[(th)1(e)-307(s)-1(ets)]TJ/F24 10.9091 Tf 39.5379 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 9.0896 3.0555 Td[(\033)]TJ/F24 10.9091 Tf 11.5151 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 4.5878 Td[(\016)]TJ/F28 7.9701 Tf 4.046 0 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -12.1477 -7.8446 Td[(i)]TJ/F15 10.9091 Tf 20.2247 3.2568 Td[(obt)1(ained)-306(b)28(y)-307(i)1(nclud)1(ing)-306(the)-307(v)28(erti)1(c)-1(es)-307(that)-306(are)-307(adj)1(ac)-1(en)28(t)-306(to)-307(an)28(y)-306(v)28(ertex)]TJ -100.9733 -13.5492 Td[(in)]TJ/F24 10.9091 Tf 12.7273 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 4.5878 Td[(\016)]TJ/F28 7.9701 Tf 4.046 0 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -12.1477 -7.8446 Td[(i)]TJ/F15 10.9091 Tf 16.88 3.2568 Td[(.)]TJ -22.9738 -15.2694 Td[(Let)]TJ/F24 10.9091 Tf 18.79 0 Td[(n)]TJ/F25 7.9701 Tf 6.548 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 7.425 3.0555 Td[(b)-27(e)-265(th)1(e)-265(size)-265(of)]TJ/F24 10.9091 Tf 63.7053 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.9402 3.0555 Td[(and)]TJ/F24 10.9091 Tf 20.4566 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0842 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 7.6586 3.0555 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F28 7.9701 Tf 4.0895 2.5822 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 8.5172 -3.9588 Td[(th)1(e)-265(res)-1(t)1(riction)-264(op)-27(erator)-264(th)1(at)-264(maps)-265(a)-264(v)28(ec)-1(t)1(or)]TJ/F24 10.9091 Tf -211.5596 -14.9745 Td[(v)]TJ/F27 10.9091 Tf 8.9929 0 Td[(2)-303(<)]TJ/F25 7.9701 Tf 18.4651 3.9588 Td[(n)]TJ/F15 10.9091 Tf 9.4427 -3.9588 Td[(on)28(to)-349(t)1(he)-349(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 76.601 0 Td[(v)]TJ/F25 7.9701 Tf 5.6793 3.9588 Td[(\016)]TJ -0.3914 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 8.2491 3.0555 Td[(2)-303(<)]TJ/F25 7.9701 Tf 18.4651 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F15 10.9091 Tf 8.394 -1.3766 Td[(con)28(tain)1(ing)-349(th)1(e)-350(comp)-28(on)1(e)-1(n)29(ts)-350(of)]TJ/F24 10.9091 Tf 144.9832 0 Td[(v)]TJ/F15 10.9091 Tf 9.4857 0 Td[(corres)-1(p)-27(ond)1(in)1(g)-349(to)-349(the)]TJ -313.5049 -14.9745 Td[(v)28(ertice)-1(s)-369(in)]TJ/F24 10.9091 Tf 52.9901 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 6.0593 3.0555 Td[(.)-551(The)-369(transp)-27(os)-1(e)-369(of)]TJ/F24 10.9091 Tf 94.0006 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.6538 3.0555 Td[(is)-369(a)-369(pr)1(olongati)1(on)-369(op)-27(e)-1(r)1(ator)-369(fr)1(om)]TJ/F27 10.9091 Tf 155.4601 0 Td[(<)]TJ/F25 7.9701 Tf 7.8788 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F15 10.9091 Tf 8.613 -1.3766 Td[(to)]TJ/F27 10.9091 Tf 13.7223 0 Td[(<)]TJ/F25 7.9701 Tf 7.8788 3.9588 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(.)-551(The)]TJ -384.6175 -14.9745 Td[(matrix)]TJ/F24 10.9091 Tf 35.1334 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 7.5744 3.0555 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F24 10.9091 Tf 4.6284 3.0555 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 4.6284 3.0555 Td[(\051)]TJ/F25 7.9701 Tf 4.2424 3.9588 Td[(T)]TJ/F27 10.9091 Tf 9.6348 -3.9588 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F28 7.9701 Tf 4.0895 2.5822 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F15 10.9091 Tf 7.8725 -1.3766 Td[(can)-301(b)-27(e)-302(considered)-301(as)-302(a)-301(r)1(e)-1(striction)-300(of)]TJ/F24 10.9091 Tf 172.9636 0 Td[(A)]TJ/F15 10.9091 Tf 11.4666 0 Td[(corres)-1(p)-27(ond)1(in)1(g)]TJ -345.9661 -13.5492 Td[(to)-333(the)-333(s)-1(et)]TJ/F24 10.9091 Tf 49.1515 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 6.0593 3.0555 Td[(.)]TJ -48.5774 -13.6429 Td[(The)]TJ/F20 10.9091 Tf 22.4243 0 Td[(class)1(ic)51(al)-357(o)-1(ne-l)1(evel)-357(A)-1(S)]TJ/F15 10.9091 Tf 106.7234 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(i)1(s)-334(de\014n)1(e)-1(d)-333(b)29(y)]TJ/F24 10.9091 Tf -4.7921 -32.5163 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5879 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.022 Td[(AS)]TJ/F15 10.9091 Tf 15.5385 3.4341 Td[(=)]TJ/F25 7.9701 Tf 15.6487 13.6364 Td[(m)]TJ/F30 10.9091 Tf -4.1336 -3.2727 Td[(X)]TJ/F25 7.9701 Tf 1.0269 -23.4509 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F15 10.9091 Tf 11.8476 13.0872 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(\016)]TJ -0.0843 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.6284 2.6969 Td[(\051)]TJ/F25 7.9701 Tf 4.2424 4.5043 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -4.5043 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 4.5043 Td[(\016)]TJ 0 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.5441 2.6969 Td[(\051)]TJ/F28 7.9701 Tf 4.2424 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -4.5043 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(\016)]TJ -0.0843 -7.2012 Td[(i)]TJ/F24 10.9091 Tf 4.6284 2.6969 Td[(;)]TJ/F15 10.9091 Tf -268.1287 -35.9079 Td[(where)]TJ/F24 10.9091 Tf 32.3362 0 Td[(A)]TJ/F25 7.9701 Tf 8.1819 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.9712 3.0555 Td[(is)-406(ass)-1(u)1(m)-1(ed)-406(to)-405(b)-28(e)-406(non)1(s)-1(i)1(ngu)1(lar.)-662(Its)-406(ap)1(pli)1(c)-1(ation)-405(to)-406(a)-405(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 283.1864 0 Td[(v)]TJ/F27 10.9091 Tf 10.0275 0 Td[(2)-398(<)]TJ/F25 7.9701 Tf 19.4997 3.9588 Td[(n)]TJ/F15 10.9091 Tf 10.0635 -3.9588 Td[(with)1(in)-406(a)]TJ -372.2664 -13.5492 Td[(Kr)1(ylo)28(v)-333(s)-1(olv)28(er)-333(requ)1(ires)-334(the)-333(foll)1(o)27(win)1(g)-334(t)1(hree)-334(ste)-1(p)1(s)-1(:)]TJ -ET -1 0 0 1 93.9178 203.7409 cm + [(\051,)-308(where)]TJ/F22 10.9091 Tf 167.085 0 Td [(A)]TJ/F15 10.9091 Tf 11.212 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.636 Td [(ij)]TJ/F15 10.9091 Tf 7.266 1.636 Td [(\051)]TJ/F25 10.9091 Tf 7.272 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F26 7.9701 Tf 5.138 0 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F15 10.9091 Tf 8.934 -3.959 Td [(is)-302(a)-303(nonsingular)-302(sparse)-302(matrix)]TJ -270.136 -13.549 Td [(with)-321(a)-321(symmetric)-321(nonzero)-321(pattern,)-324(let)]TJ/F22 10.9091 Tf 184.526 0 Td [(G)]TJ/F15 10.9091 Tf 11.608 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(W)28(;)-167(E)]TJ/F15 10.9091 Tf 23.53 0 Td [(\051)-321(b)-28(e)-321(the)-321(adjacency)-321(graph)-321(of)]TJ/F22 10.9091 Tf 134.378 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)-324(wh)1(e)-1(re)]TJ/F22 10.9091 Tf -377.982 -13.549 Td [(W)]TJ/F15 10.9091 Tf 15.419 0 Td [(=)]TJ/F25 10.9091 Tf 12.086 0 Td [(f)]TJ/F15 10.9091 Tf 5.455 0 Td [(1)]TJ/F22 10.9091 Tf 5.454 0 Td [(;)]TJ/F15 10.9091 Tf 4.849 0 Td [(2)]TJ/F22 10.9091 Tf 5.454 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(n)]TJ/F25 10.9091 Tf 30.79 0 Td [(g)]TJ/F15 10.9091 Tf 9.434 0 Td [(and)]TJ/F22 10.9091 Tf 21.555 0 Td [(E)]TJ/F15 10.9091 Tf 12.282 0 Td [(=)]TJ/F25 10.9091 Tf 12.086 0 Td [(f)]TJ/F15 10.9091 Tf 5.455 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(i;)-167(j)]TJ/F15 10.9091 Tf 13.724 0 Td [(\051)-330(:)]TJ/F22 10.9091 Tf 14.475 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.637 Td [(ij)]TJ/F25 10.9091 Tf 10.867 1.637 Td [(6)]TJ/F15 10.9091 Tf 0 0 Td [(=)-330(0)]TJ/F25 10.9091 Tf 17.54 0 Td [(g)]TJ/F15 10.9091 Tf 9.434 0 Td [(are)-365(the)-364(v)27(ertex)-364(set)-365(and)-365(the)-365(edge)-364(set)-365(of)]TJ/F22 10.9091 Tf 184.476 0 Td [(G)]TJ/F15 10.9091 Tf 8.578 0 Td [(,)]TJ -409.421 -13.549 Td [(resp)-28(ectiv)28(ely)83(.)-466(Tw)28(o)-341(v)28(ertices)-341(are)-341(called)-340(adjacen)27(t)-340(if)-341(there)-340(is)-341(an)-341(edge)-341(conn)1(e)-1(ctin)1(g)-341(them.)-467(F)84(or)]TJ 0 -13.55 Td [(an)28(y)-238(in)28(te)-1(ger)]TJ/F22 10.9091 Tf 54.621 0 Td [(\016)-316(>)]TJ/F15 10.9091 Tf 19.807 0 Td [(0,)-257(a)]TJ/F22 10.9091 Tf 19.343 0 Td [(\016)]TJ/F15 10.9091 Tf 5.262 0 Td [(-o)28(v)28(erlap)-239(par)1(tition)-239(of)]TJ/F22 10.9091 Tf 96.34 0 Td [(W)]TJ/F15 10.9091 Tf 14.417 0 Td [(can)-238(b)-28(e)-238(de\014ned)-238(recursiv)28(ely)-239(as)-238(follo)28(ws.)-413(Giv)28(en)]TJ -209.79 -13.549 Td [(a)-344(0-o)28(v)28(erlap)-344(\050or)-343(non-o)28(v)27(erlapp)1(ing\051)-344(partition)-343(of)]TJ/F22 10.9091 Tf 216.249 0 Td [(W)]TJ/F15 10.9091 Tf 11.819 0 Td [(,)-346(i.e.)-344(a)-343(set)-344(of)]TJ/F22 10.9091 Tf 63.377 0 Td [(m)]TJ/F15 10.9091 Tf 13.327 0 Td [(disjoin)28(t)-344(nonempt)28(y)-343(se)-1(ts)]TJ/F22 10.9091 Tf -304.772 -13.549 Td [(W)]TJ/F20 7.9701 Tf 11.818 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.015 Td [(i)]TJ/F25 10.9091 Tf 9.278 3.056 Td [(\032)]TJ/F22 10.9091 Tf 11.515 0 Td [(W)]TJ/F15 10.9091 Tf 14.857 0 Td [(suc)28(h)-279(that)]TJ/F25 10.9091 Tf 47.047 0 Td [([)]TJ/F23 7.9701 Tf 7.272 3.959 Td [(m)]TJ 0 -7.015 Td [(i)]TJ/F20 7.9701 Tf 2.884 0 Td [(=1)]TJ/F22 10.9091 Tf 11.318 3.056 Td [(W)]TJ/F20 7.9701 Tf 11.819 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.015 Td [(i)]TJ/F15 10.9091 Tf 9.277 3.056 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(W)]TJ/F15 10.9091 Tf 11.819 0 Td [(,)-289(a)]TJ/F22 10.9091 Tf 14.681 0 Td [(\016)]TJ/F15 10.9091 Tf 5.262 0 Td [(-o)28(v)28(erlap)-279(partition)-278(of)]TJ/F22 10.9091 Tf 97.661 0 Td [(W)]TJ/F15 10.9091 Tf 14.857 0 Td [(is)-279(obtai)1(ned)-279(b)28(y)-279(considering)]TJ -289.85 -13.549 Td [(the)-307(sets)]TJ/F22 10.9091 Tf 39.538 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.015 Td [(i)]TJ/F25 10.9091 Tf 9.089 3.056 Td [(\033)]TJ/F22 10.9091 Tf 11.516 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 4.588 Td [(\016)]TJ/F26 7.9701 Tf 4.046 0 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -12.147 -7.845 Td [(i)]TJ/F15 10.9091 Tf 20.224 3.257 Td [(obtained)-307(b)28(y)-306(including)-307(the)-306(v)28(e)-1(r)1(tice)-1(s)-306(that)-307(are)-306(adjacen)27(t)-306(to)-307(an)28(y)-306(v)27(ertex)]TJ -100.973 -13.549 Td [(in)]TJ/F22 10.9091 Tf 12.727 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 4.587 Td [(\016)]TJ/F26 7.9701 Tf 4.046 0 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -12.148 -7.844 Td [(i)]TJ/F15 10.9091 Tf 16.88 3.257 Td [(.)]TJ -22.974 -15.27 Td [(Let)]TJ/F22 10.9091 Tf 18.79 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 3.959 Td [(\016)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 7.425 3.055 Td [(b)-28(e)-264(the)-264(size)-264(of)]TJ/F22 10.9091 Tf 63.706 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.94 3.055 Td [(and)]TJ/F22 10.9091 Tf 20.457 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F25 10.9091 Tf 7.658 3.055 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.813 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F26 7.9701 Tf 4.09 2.582 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F15 10.9091 Tf 8.518 -3.959 Td [(the)-264(restriction)-264(op)-28(erator)-264(that)-264(maps)-264(a)-264(v)28(ector)]TJ/F22 10.9091 Tf -211.56 -14.974 Td [(v)]TJ/F25 10.9091 Tf 8.993 0 Td [(2)-304(<)]TJ/F23 7.9701 Tf 18.465 3.959 Td [(n)]TJ/F15 10.9091 Tf 9.443 -3.959 Td [(on)28(to)-349(the)-349(v)28(ector)]TJ/F22 10.9091 Tf 76.601 0 Td [(v)]TJ/F23 7.9701 Tf 5.679 3.959 Td [(\016)]TJ -0.391 -7.015 Td [(i)]TJ/F25 10.9091 Tf 8.249 3.056 Td [(2)-304(<)]TJ/F23 7.9701 Tf 18.465 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.812 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F15 10.9091 Tf 8.394 -1.376 Td [(con)28(taining)-349(the)-349(comp)-28(onen)28(ts)-349(of)]TJ/F22 10.9091 Tf 144.983 0 Td [(v)]TJ/F15 10.9091 Tf 9.486 0 Td [(corresp)-28(onding)-349(to)-348(the)]TJ -313.505 -14.975 Td [(v)28(ertices)-369(in)]TJ/F22 10.9091 Tf 52.99 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.059 3.055 Td [(.)-551(The)-369(transp)-28(ose)-369(of)]TJ/F22 10.9091 Tf 94.001 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.654 3.055 Td [(is)-369(a)-369(prolongation)-369(op)-28(erator)-368(from)]TJ/F25 10.9091 Tf 155.46 0 Td [(<)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.813 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F15 10.9091 Tf 8.613 -1.377 Td [(to)]TJ/F25 10.9091 Tf 13.722 0 Td [(<)]TJ/F23 7.9701 Tf 7.879 3.959 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.959 Td [(.)-551(The)]TJ -384.617 -14.974 Td [(matrix)]TJ/F22 10.9091 Tf 35.133 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(\016)]TJ 0 -7.015 Td [(i)]TJ/F15 10.9091 Tf 7.575 3.056 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.015 Td [(i)]TJ/F22 10.9091 Tf 4.628 3.056 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(\016)]TJ -0.084 -7.015 Td [(i)]TJ/F15 10.9091 Tf 4.628 3.056 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.959 Td [(T)]TJ/F25 10.9091 Tf 9.635 -3.959 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.812 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F26 7.9701 Tf 4.09 2.583 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.812 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F15 10.9091 Tf 7.873 -1.376 Td [(can)-301(b)-28(e)-301(considered)-301(as)-301(a)-301(restriction)-301(of)]TJ/F22 10.9091 Tf 172.963 0 Td [(A)]TJ/F15 10.9091 Tf 11.467 0 Td [(corresp)-28(onding)]TJ -345.966 -13.549 Td [(to)-333(the)-334(set)]TJ/F22 10.9091 Tf 49.152 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.958 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.059 3.056 Td [(.)]TJ -48.578 -13.643 Td [(The)]TJ/F18 10.9091 Tf 22.425 0 Td [(classic)51(al)-357(o)-1(ne-)1(level)-358(AS)]TJ/F15 10.9091 Tf 106.723 0 Td [(preconditioner)-333(is)-334(de\014n)1(e)-1(d)-333(b)28(y)]TJ/F22 10.9091 Tf -4.792 -32.517 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(AS)]TJ/F15 10.9091 Tf 15.539 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.649 13.637 Td [(m)]TJ/F28 10.9091 Tf -4.134 -3.273 Td [(X)]TJ/F23 7.9701 Tf 1.027 -23.451 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.848 13.087 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.505 Td [(\016)]TJ -0.084 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.629 2.696 Td [(\051)]TJ/F23 7.9701 Tf 4.242 4.505 Td [(T)]TJ/F15 10.9091 Tf 6.605 -4.505 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 4.505 Td [(\016)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.544 2.696 Td [(\051)]TJ/F26 7.9701 Tf 4.242 4.505 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -4.505 Td [(R)]TJ/F23 7.9701 Tf 8.368 4.505 Td [(\016)]TJ -0.085 -7.201 Td [(i)]TJ/F22 10.9091 Tf 4.629 2.696 Td [(;)]TJ/F15 10.9091 Tf -268.129 -35.907 Td [(where)]TJ/F22 10.9091 Tf 32.336 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.958 Td [(\016)]TJ 0 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.971 3.056 Td [(is)-406(assumed)-406(to)-406(b)-27(e)-406(nonsingular.)-662(Its)-406(application)-405(to)-406(a)-406(v)28(ector)]TJ/F22 10.9091 Tf 283.187 0 Td [(v)]TJ/F25 10.9091 Tf 10.027 0 Td [(2)-399(<)]TJ/F23 7.9701 Tf 19.5 3.958 Td [(n)]TJ/F15 10.9091 Tf 10.063 -3.958 Td [(within)-406(a)]TJ -372.266 -13.55 Td [(Krylo)28(v)-333(solv)27(er)-333(requires)-333(the)-334(follo)28(wing)-333(three)-333(steps:)]TJ 0 g 0 G -1 0 0 1 -93.9178 -203.7409 cm -BT -/F15 10.9091 Tf 107.2512 203.7409 Td[(1.)]TJ -ET -1 0 0 1 115.736 203.7409 cm + 13.333 -22.89 Td [(1.)]TJ 0 g 0 G -1 0 0 1 -115.736 -203.7409 cm -BT -/F15 10.9091 Tf 121.1906 203.7409 Td[(res)-1(t)1(riction)-333(of)]TJ/F24 10.9091 Tf 64.6667 0 Td[(v)]TJ/F15 10.9091 Tf 9.3157 0 Td[(as)]TJ/F24 10.9091 Tf 13.3939 0 Td[(v)]TJ/F25 7.9701 Tf 5.2879 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 6.4115 1.6364 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F24 10.9091 Tf 4.6284 3.0555 Td[(v)]TJ/F15 10.9091 Tf 5.6793 0 Td[(,)]TJ/F24 10.9091 Tf 6.6667 0 Td[(i)]TJ/F15 10.9091 Tf 6.7885 0 Td[(=)-278(1)]TJ/F24 10.9091 Tf 16.9697 0 Td[(;)-166(:)-167(:)-166(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.8206 0 Td[(;)]TJ -ET -1 0 0 1 93.9178 180.8506 cm + [-500(restriction)-333(of)]TJ/F22 10.9091 Tf 78.607 0 Td [(v)]TJ/F15 10.9091 Tf 9.315 0 Td [(as)]TJ/F22 10.9091 Tf 13.394 0 Td [(v)]TJ/F23 7.9701 Tf 5.288 -1.636 Td [(i)]TJ/F15 10.9091 Tf 6.412 1.636 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F22 10.9091 Tf 4.628 3.055 Td [(v)]TJ/F15 10.9091 Tf 5.68 0 Td [(,)]TJ/F22 10.9091 Tf 6.666 0 Td [(i)]TJ/F15 10.9091 Tf 6.789 0 Td [(=)-278(1)]TJ/F22 10.9091 Tf 16.969 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.821 0 Td [(;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -180.8506 cm -BT -/F15 10.9091 Tf 107.2512 180.8506 Td[(2.)]TJ -ET -1 0 0 1 115.736 180.8506 cm + -207.367 -22.89 Td [(2.)]TJ 0 g 0 G -1 0 0 1 -115.736 -180.8506 cm -BT -/F15 10.9091 Tf 121.1906 180.8506 Td[(soluti)1(on)-333(of)-333(the)-333(linear)-333(sys)-1(tems)]TJ/F24 10.9091 Tf 143.3032 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 3.9588 Td[(\016)]TJ 0 -7.0143 Td[(i)]TJ/F24 10.9091 Tf 4.5441 3.0555 Td[(w)]TJ/F25 7.9701 Tf 7.81 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 6.4115 1.6364 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(v)]TJ/F25 7.9701 Tf 5.2879 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 3.3812 1.6364 Td[(,)]TJ/F24 10.9091 Tf 6.6667 0 Td[(i)]TJ/F15 10.9091 Tf 6.7886 0 Td[(=)-278(1)]TJ/F24 10.9091 Tf 16.9696 0 Td[(;)-166(:)-167(:)-166(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.8206 0 Td[(;)]TJ -ET -1 0 0 1 93.9178 157.9603 cm + [-500(solution)-333(of)-334(th)1(e)-334(linear)-333(systems)]TJ/F22 10.9091 Tf 157.243 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 3.959 Td [(\016)]TJ 0 -7.015 Td [(i)]TJ/F22 10.9091 Tf 4.544 3.056 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 6.411 1.637 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(v)]TJ/F23 7.9701 Tf 5.287 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.382 1.637 Td [(,)]TJ/F22 10.9091 Tf 6.666 0 Td [(i)]TJ/F15 10.9091 Tf 6.789 0 Td [(=)-278(1)]TJ/F22 10.9091 Tf 16.97 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(m)]TJ/F15 10.9091 Tf 33.82 0 Td [(;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -157.9603 cm -BT -/F15 10.9091 Tf 107.2512 157.9603 Td[(3.)]TJ -ET -1 0 0 1 115.736 157.9603 cm + -268.62 -22.89 Td [(3.)]TJ 0 g 0 G -1 0 0 1 -115.736 -157.9603 cm -BT -/F15 10.9091 Tf 121.1906 157.9603 Td[(pr)1(olongat)1(ion)-333(and)-333(sum)-333(of)-333(the)]TJ/F24 10.9091 Tf 139.182 0 Td[(w)]TJ/F25 7.9701 Tf 7.81 -1.6363 Td[(i)]TJ/F15 10.9091 Tf 3.3813 1.6363 Td[('s,)-333(i.e.)]TJ/F24 10.9091 Tf 32.7879 0 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F30 10.9091 Tf 11.5151 8.1819 Td[(P)]TJ/F25 7.9701 Tf 11.5152 -3.1548 Td[(m)]TJ 0 -8.2525 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F15 10.9091 Tf 11.3189 3.2254 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 4.6284 3.0555 Td[(\051)]TJ/F25 7.9701 Tf 4.2425 3.9588 Td[(T)]TJ/F24 10.9091 Tf 6.6044 -3.9588 Td[(w)]TJ/F25 7.9701 Tf 7.81 -1.6364 Td[(i)]TJ/F15 10.9091 Tf 3.3813 1.6364 Td[(.)]TJ -297.9922 -22.8903 Td[(Note)-473(th)1(at)-473(th)1(e)-473(lin)1(e)-1(ar)-472(sys)-1(t)1(e)-1(ms)-473(at)-473(step)-472(2)-473(are)-473(u)1(s)-1(u)1(ally)-472(solv)28(e)-1(d)-472(ap)1(pr)1(o)27(x)1(im)-1(at)1(e)-1(ly)84(,)-507(e)-1(.)1(g.)-473(u)1(s)-1(i)1(ng)]TJ 0 -13.5492 Td[(in)1(c)-1(ompl)1(e)-1(te)-334(LU)-333(f)1(ac)-1(tor)1(iz)-1(ati)1(ons)-334(suc)28(h)-333(as)-334(ILU\050)]TJ/F24 10.9091 Tf 202.6366 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-333(MILU\050)]TJ/F24 10.9091 Tf 44.091 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051)-333(and)-333(ILU\050)]TJ/F24 10.9091 Tf 52.2728 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051)-333([)]TJ -ET -1 0 0 1 429.081 121.5209 cm + [-500(prolongation)-333(and)-333(sum)-334(of)-333(the)]TJ/F22 10.9091 Tf 153.122 0 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.381 1.637 Td [('s,)-333(i.e.)]TJ/F22 10.9091 Tf 32.788 0 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F28 10.9091 Tf 11.515 8.181 Td [(P)]TJ/F23 7.9701 Tf 11.515 -3.154 Td [(m)]TJ 0 -8.253 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.319 3.226 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.958 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 4.628 3.056 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.958 Td [(T)]TJ/F22 10.9091 Tf 6.605 -3.958 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 3.381 1.637 Td [(.)]TJ -297.992 -22.891 Td [(Note)-473(th)1(at)-473(the)-472(linear)-473(systems)-473(at)-472(step)-473(2)-472(are)-473(usually)-472(solv)28(ed)-473(appro)28(ximately)83(,)-507(e.g.)-472(using)]TJ 0 -13.549 Td [(incomplete)-333(LU)-334(factorizations)-333(suc)28(h)-334(as)-333(ILU\050)]TJ/F22 10.9091 Tf 202.637 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-333(MILU\050)]TJ/F22 10.9091 Tf 44.091 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051)-333(and)-334(ILU\050)]TJ/F22 10.9091 Tf 52.273 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -429.081 -121.5209 cm -BT -/F15 10.9091 Tf 429.081 121.5209 Td[(14)]TJ -ET -1 0 0 1 439.9901 121.5209 cm + [(14)]TJ 0 g 0 G -1 0 0 1 -439.9901 -121.5209 cm -BT -/F15 10.9091 Tf 439.9901 121.5209 Td[(,)-333(Chap)1(te)-1(r)-333(10].)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [(,)-334(Chapter)-333(10].)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -252 0 obj << +245 0 obj << /Type /Page -/Contents 253 0 R -/Resources 251 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 230 0 R -/Annots [ 255 0 R 256 0 R 257 0 R 258 0 R 259 0 R 260 0 R 261 0 R 262 0 R 263 0 R 264 0 R 283 0 R ] +/Contents 246 0 R +/Resources 244 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 210 0 R +/Annots [ 243 0 R 225 0 R 232 0 R 233 0 R 234 0 R 235 0 R 236 0 R 237 0 R 238 0 R 239 0 R 240 0 R ] >> endobj -255 0 obj << +243 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -256 0 obj << +225 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [246.3762 689.5909 259.2779 698.6137] +/Rect [246.376 689.591 259.278 698.614] /Subtype /Link /A << /S /GoTo /D (cite.StubenGMD69_99) >> >> endobj -257 0 obj << +232 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [205.0434 648.8496 212.4905 657.8724] +/Rect [205.043 648.85 212.49 657.872] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -258 0 obj << +233 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [217.9163 648.8496 230.818 657.8724] +/Rect [217.916 648.85 230.818 657.872] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -259 0 obj << +234 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [429.4951 635.3004 442.3967 644.3232] +/Rect [429.495 635.3 442.397 644.323] /Subtype /Link /A << /S /GoTo /D (cite.TUMINARO_TONG) >> >> endobj -260 0 obj << +235 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [237.1641 594.6528 244.6112 603.6756] +/Rect [237.164 594.653 244.611 603.676] /Subtype /Link /A << /S /GoTo /D (cite.para_04) >> >> endobj -261 0 obj << +236 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [249.2853 594.6528 256.7324 603.6756] +/Rect [249.285 594.653 256.732 603.676] /Subtype /Link /A << /S /GoTo /D (cite.aaecc_07) >> >> endobj -262 0 obj << +237 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [261.4065 594.6528 268.8536 603.6756] +/Rect [261.407 594.653 268.854 603.676] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -263 0 obj << +238 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [273.5278 594.6528 286.4294 603.6756] +/Rect [273.528 594.653 286.429 603.676] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -264 0 obj << +239 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [229.6423 500.6596 237.0894 513.5612] +/Rect [229.642 500.66 237.089 513.561] /Subtype /Link /A << /S /GoTo /D (equation.1) >> >> endobj -283 0 obj << +240 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [428.0847 120.5246 440.9864 129.5474] +/Rect [428.085 120.525 440.986 129.547] /Subtype /Link /A << /S /GoTo /D (cite.Saad_book) >> >> endobj -254 0 obj << -/D [252 0 R /XYZ 93.9178 740.0018 null] +247 0 obj << +/D [245 0 R /XYZ 93.918 740.002 null] >> endobj 46 0 obj << -/D [252 0 R /XYZ 93.9178 577.2151 null] +/D [245 0 R /XYZ 93.918 577.215 null] >> endobj -280 0 obj << -/D [252 0 R /XYZ 93.9178 219.8394 null] +253 0 obj << +/D [245 0 R /XYZ 93.918 219.839 null] >> endobj -281 0 obj << -/D [252 0 R /XYZ 93.9178 196.0148 null] +254 0 obj << +/D [245 0 R /XYZ 93.918 196.015 null] >> endobj -282 0 obj << -/D [252 0 R /XYZ 93.9178 173.1245 null] +255 0 obj << +/D [245 0 R /XYZ 93.918 173.125 null] >> endobj -251 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F20 171 0 R /F19 105 0 R /F24 176 0 R /F25 267 0 R /F27 179 0 R /F28 270 0 R /F22 273 0 R /F26 276 0 R /F30 279 0 R >> +244 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F18 163 0 R /F17 103 0 R /F22 165 0 R /F23 248 0 R /F25 166 0 R /F26 249 0 R /F20 250 0 R /F24 251 0 R /F28 252 0 R >> /ProcSet [ /PDF /Text ] >> endobj -292 0 obj << -/Length 16057 +266 0 obj << +/Length 13812 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(12)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(12)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F15 10.9091 Tf 158.675 704.1363 Td[(A)-318(v)56(ari)1(an)28(t)-318(of)-317(the)-318(class)-1(ical)-318(AS)-317(p)1(rec)-1(on)1(diti)1(oner)-318(th)1(at)-318(out)1(p)-28(erf)1(orms)-319(i)1(t)-318(in)-317(terms)-319(of)-317(con)28(v)28(e)-1(r)1(-)]TJ -16.9365 -13.5492 Td[(gence)-266(rate)-265(and)-265(of)-265(compu)1(tation)-265(an)1(d)-265(c)-1(omm)28(uni)1(c)-1(ati)1(on)-265(time)-266(on)-265(p)1(arallel)-265(di)1(s)-1(tr)1(ibu)1(te)-1(d)1(-m)-1(em)-1(or)1(y)]TJ 0 -13.5492 Td[(com)-1(p)1(uters)-387(is)-387(the)-387(s)-1(o-called)]TJ/F20 10.9091 Tf 129.2159 0 Td[(R)51(estricte)51(d)-407(AS)-408(\050)1(R)-1(AS\051)]TJ/F15 10.9091 Tf 105.9938 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-386([)]TJ -ET -1 0 0 1 452.7446 677.0379 cm +/F15 10.9091 Tf -186.328 -35.866 Td [(A)-318(v)56(arian)28(t)-318(of)-318(the)-317(class)-1(i)1(c)-1(al)-317(AS)-318(preconditioner)-317(that)-318(outp)-28(erforms)-318(it)-317(in)-318(terms)-318(of)-317(con)27(v)28(er-)]TJ -16.937 -13.549 Td [(gence)-265(rate)-266(and)-265(of)-265(computation)-265(and)-265(comm)27(uni)1(c)-1(ation)-265(time)-265(on)-265(parallel)-265(distributed-memory)]TJ 0 -13.549 Td [(computers)-387(is)-387(the)-387(so-called)]TJ/F18 10.9091 Tf 129.216 0 Td [(R)51(estricte)51(d)-407(AS)-407(\050RAS\051)]TJ/F15 10.9091 Tf 105.994 0 Td [(preconditioner)-387([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -452.7446 -677.0379 cm -BT -/F15 10.9091 Tf 452.7446 677.0379 Td[(5)]TJ -ET -1 0 0 1 458.1992 677.0379 cm + [(5)]TJ 0 g 0 G -1 0 0 1 -458.1992 -677.0379 cm -BT -/F15 10.9091 Tf 458.1992 677.0379 Td[(,)]TJ -ET -1 0 0 1 465.4501 677.0379 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -465.4501 -677.0379 cm -BT -/F15 10.9091 Tf 465.4501 677.0379 Td[(10)]TJ -ET -1 0 0 1 476.3592 677.0379 cm + [-387(10)]TJ 0 g 0 G -1 0 0 1 -476.3592 -677.0379 cm -BT -/F15 10.9091 Tf 476.3592 677.0379 Td[(].)-605(It)-387(i)1(s)-388(ob)1(tain)1(e)-1(d)]TJ -334.6207 -13.5492 Td[(b)28(y)-407(z)-1(eroi)1(ng)-408(t)1(he)-408(com)-1(p)-27(onen)28(ts)-408(of)]TJ/F24 10.9091 Tf 148.0779 0 Td[(w)]TJ/F25 7.9701 Tf 7.8101 -1.6363 Td[(i)]TJ/F15 10.9091 Tf 7.8271 1.6363 Td[(corres)-1(p)-27(ond)1(in)1(g)-408(to)-407(the)-408(o)28(v)28(e)-1(r)1(lapp)1(in)1(g)-408(v)28(ertice)-1(s)-408(wh)1(e)-1(n)-407(ap)1(-)]TJ -163.7151 -13.5492 Td[(pl)1(yin)1(g)-349(the)-349(pr)1(olongat)1(ion.)-490(T)-1(h)1(e)-1(r)1(e)-1(f)1(ore,)-353(RAS)-348(di\013e)-1(r)1(s)-349(from)-349(clas)-1(sical)-349(AS)-348(b)28(y)-349(t)1(he)-349(pr)1(olongati)1(on)]TJ 0 -13.5492 Td[(op)-27(e)-1(r)1(ators,)-401(whi)1(c)27(h)-387(ar)1(e)-388(s)-1(u)1(bstitu)1(te)-1(d)-386(b)28(y)-387(\050)]TJ 182.6914 2.7576 Td[(~)]TJ/F24 10.9091 Tf -2.3655 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 3.9588 Td[(0)]TJ/F25 7.9701 Tf -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 4.8166 3.0555 Td[(\051)]TJ/F25 7.9701 Tf 4.2425 3.9588 Td[(T)]TJ/F27 10.9091 Tf 10.6135 -3.9588 Td[(2)-367(<)]TJ/F25 7.9701 Tf 19.1606 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 2.8128 Td[(\016)]TJ 0 -5.395 Td[(i)]TJ/F28 7.9701 Tf 4.0895 2.5822 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(,)-400(w)-1(h)1(e)-1(r)1(e)]TJ 41.8991 2.7576 Td[(~)]TJ/F24 10.9091 Tf -2.3655 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 3.9588 Td[(0)]TJ/F25 7.9701 Tf -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 9.0403 3.0555 Td[(is)-387(obtain)1(e)-1(d)-386(b)28(y)-387(z)-1(eroi)1(ng)]TJ -305.7498 -13.5492 Td[(th)1(e)-334(ro)28(ws)-334(of)]TJ/F24 10.9091 Tf 56.4546 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(\016)]TJ -0.0843 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 8.2648 3.0555 Td[(corres)-1(p)-27(ond)1(in)1(g)-334(to)-333(th)1(e)-334(v)28(e)-1(r)1(tice)-1(s)-334(i)1(n)]TJ/F24 10.9091 Tf 154.4547 0 Td[(W)]TJ/F25 7.9701 Tf 11.8182 3.9588 Td[(\016)]TJ -1.5152 -7.0143 Td[(i)]TJ/F27 10.9091 Tf 6.0593 3.0555 Td[(n)]TJ/F24 10.9091 Tf 5.4546 0 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9588 Td[(0)]TJ/F25 7.9701 Tf -1.5152 -7.0143 Td[(i)]TJ/F15 10.9091 Tf 6.2475 3.0555 Td[(:)]TJ/F24 10.9091 Tf -127.8046 -29.6348 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5879 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7758 -8.022 Td[(R)-6(AS)]TJ/F15 10.9091 Tf 21.8944 3.4341 Td[(=)]TJ/F25 7.9701 Tf 15.6487 13.6364 Td[(m)]TJ/F30 10.9091 Tf -4.1336 -3.2727 Td[(X)]TJ/F25 7.9701 Tf 1.0269 -23.4509 Td[(i)]TJ/F22 7.9701 Tf 2.8831 0 Td[(=1)]TJ/F15 10.9091 Tf 11.8476 13.0872 Td[(\050)]TJ 6.608 2.7576 Td[(~)]TJ/F24 10.9091 Tf -2.3655 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 4.5043 Td[(0)]TJ/F25 7.9701 Tf -0.0843 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.8166 2.6969 Td[(\051)]TJ/F25 7.9701 Tf 4.2424 4.5043 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -4.5043 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 4.5043 Td[(\016)]TJ 0 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.5441 2.6969 Td[(\051)]TJ/F28 7.9701 Tf 4.2424 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -4.5043 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(\016)]TJ -0.0843 -7.2012 Td[(i)]TJ/F24 10.9091 Tf 4.6284 2.6969 Td[(:)]TJ/F15 10.9091 Tf -271.4008 -30.7803 Td[(Anal)1(ogously)83(,)-333(th)1(e)-334(AS)-333(v)56(ari)1(an)28(t)-333(c)-1(all)1(e)-1(d)]TJ/F20 10.9091 Tf 168.5759 0 Td[(AS)-358(w)-1(i)1(t)-1(h)-358(Harm)1(o)-1(ni)1(c)-358(extension)-358(\050AS)-1(H\051)]TJ/F15 10.9091 Tf 176.6079 0 Td[(is)-334(d)1(e)-1(\014)1(ned)-333(b)28(y)]TJ/F24 10.9091 Tf -207.7353 -29.3065 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5879 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.022 Td[(AS)-56(H)]TJ/F15 10.9091 Tf 23.0374 3.4341 Td[(=)]TJ/F25 7.9701 Tf 15.6487 13.6364 Td[(m)]TJ/F30 10.9091 Tf -4.1335 -3.2727 Td[(X)]TJ/F25 7.9701 Tf 1.0268 -23.4509 Td[(i)]TJ/F22 7.9701 Tf 2.8832 0 Td[(=1)]TJ/F15 10.9091 Tf 11.8476 13.0872 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 4.5043 Td[(\016)]TJ -0.0842 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.6283 2.6969 Td[(\051)]TJ/F25 7.9701 Tf 4.2425 4.5043 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -4.5043 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 4.5043 Td[(\016)]TJ 0 -7.2012 Td[(i)]TJ/F15 10.9091 Tf 4.5441 2.6969 Td[(\051)]TJ/F28 7.9701 Tf 4.2425 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 7.0979 -1.7467 Td[(~)]TJ/F24 10.9091 Tf -2.3656 -2.7576 Td[(R)]TJ/F22 7.9701 Tf 8.3674 4.5043 Td[(0)]TJ/F25 7.9701 Tf -0.0842 -7.2012 Td[(i)]TJ/F24 10.9091 Tf 4.8165 2.6969 Td[(:)]TJ/F15 10.9091 Tf -271.9722 -30.1742 Td[(W)84(e)-336(n)1(ote)-335(that)-334(for)]TJ/F24 10.9091 Tf 83.4217 0 Td[(\016)]TJ/F15 10.9091 Tf 8.3157 0 Td[(=)-280(0)-334(the)-335(th)1(re)-1(e)-335(v)56(ari)1(an)28(ts)-335(of)-334(the)-335(AS)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)-334(are)-335(all)-334(e)-1(q)1(ual)-334(to)-335(th)1(e)]TJ -91.7375 -13.5492 Td[(bl)1(o)-28(c)27(k-Jacobi)-333(p)1(re)-1(cond)1(ition)1(e)-1(r)1(.)]TJ 16.9365 -13.5492 Td[(As)-359(al)1(re)-1(ad)1(y)-358(obse)-1(r)1(v)28(e)-1(d)1(,)-365(t)1(he)-359(con)28(v)28(erge)-1(n)1(c)-1(e)-358(rate)-358(of)-358(the)-358(one-)-1(lev)28(el)-358(Sc)27(h)29(w)27(arz)-358(precondi)1(tioned)]TJ -16.9365 -13.5492 Td[(iterati)1(v)28(e)-359(s)-1(ol)1(v)28(e)-1(rs)-358(dete)-1(r)1(iorates)-359(as)-359(t)1(he)-359(n)28(u)1(m)27(b)-27(er)]TJ/F24 10.9091 Tf 211.4221 0 Td[(m)]TJ/F15 10.9091 Tf 13.487 0 Td[(of)-358(p)1(artiti)1(ons)-359(of)]TJ/F24 10.9091 Tf 75.4535 0 Td[(W)]TJ/F15 10.9091 Tf 15.7269 0 Td[(in)1(c)-1(r)1(e)-1(ase)-1(s)-359([)]TJ -ET -1 0 0 1 506.7366 462.2978 cm + [(].)-605(It)-387(is)-386(obtained)]TJ -235.21 -13.549 Td [(b)28(y)-408(zeroing)-407(the)-408(comp)-28(onen)28(ts)-407(of)]TJ/F22 10.9091 Tf 148.078 0 Td [(w)]TJ/F23 7.9701 Tf 7.81 -1.637 Td [(i)]TJ/F15 10.9091 Tf 7.827 1.637 Td [(corresp)-28(onding)-407(to)-408(the)-407(o)27(v)28(erlapping)-407(v)28(ertices)-408(when)-407(ap-)]TJ -163.715 -13.549 Td [(plying)-349(the)-349(p)1(rolongation.)-491(Therefore,)-353(RAS)-349(di\013ers)-349(f)1(rom)-349(classical)-349(AS)-349(b)28(y)-349(the)-349(prolongation)]TJ 0 -13.55 Td [(op)-28(erators,)-400(whic)27(h)-387(are)-387(substituted)-387(b)28(y)-387(\050)]TJ 182.692 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.366 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.368 3.959 Td [(0)]TJ/F23 7.9701 Tf -0.085 -7.014 Td [(i)]TJ/F15 10.9091 Tf 4.817 3.055 Td [(\051)]TJ/F23 7.9701 Tf 4.242 3.959 Td [(T)]TJ/F25 10.9091 Tf 10.614 -3.959 Td [(2)-367(<)]TJ/F23 7.9701 Tf 19.161 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 2.813 Td [(\016)]TJ 0 -5.395 Td [(i)]TJ/F26 7.9701 Tf 4.089 2.582 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.959 Td [(,)-401(where)]TJ 41.899 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.365 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.367 3.959 Td [(0)]TJ/F23 7.9701 Tf -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 9.04 3.055 Td [(is)-387(obtained)-387(b)28(y)-388(zeroing)]TJ -305.75 -13.549 Td [(the)-333(ro)27(ws)-333(of)]TJ/F22 10.9091 Tf 56.455 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(\016)]TJ -0.084 -7.014 Td [(i)]TJ/F15 10.9091 Tf 8.265 3.055 Td [(corresp)-28(onding)-333(to)-333(the)-334(v)28(ertices)-333(in)]TJ/F22 10.9091 Tf 154.455 0 Td [(W)]TJ/F23 7.9701 Tf 11.818 3.959 Td [(\016)]TJ -1.515 -7.014 Td [(i)]TJ/F25 10.9091 Tf 6.059 3.055 Td [(n)]TJ/F22 10.9091 Tf 5.454 0 Td [(W)]TJ/F20 7.9701 Tf 11.819 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 6.247 3.055 Td [(:)]TJ/F22 10.9091 Tf -127.805 -29.635 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(R)-6(AS)]TJ/F15 10.9091 Tf 21.894 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.649 13.637 Td [(m)]TJ/F28 10.9091 Tf -4.134 -3.273 Td [(X)]TJ/F23 7.9701 Tf 1.027 -23.451 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.848 13.087 Td [(\050)]TJ 6.608 2.758 Td [(~)]TJ/F22 10.9091 Tf -2.366 -2.758 Td [(R)]TJ/F20 7.9701 Tf 8.368 4.505 Td [(0)]TJ/F23 7.9701 Tf -0.084 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.816 2.696 Td [(\051)]TJ/F23 7.9701 Tf 4.243 4.505 Td [(T)]TJ/F15 10.9091 Tf 6.604 -4.505 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(A)]TJ/F23 7.9701 Tf 8.181 4.505 Td [(\016)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.544 2.696 Td [(\051)]TJ/F26 7.9701 Tf 4.243 4.505 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -4.505 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.505 Td [(\016)]TJ -0.084 -7.201 Td [(i)]TJ/F22 10.9091 Tf 4.628 2.696 Td [(:)]TJ/F15 10.9091 Tf -271.401 -30.78 Td [(Analogously)83(,)-333(the)-333(AS)-334(v)56(arian)28(t)-333(called)]TJ/F18 10.9091 Tf 168.576 0 Td [(AS)-358(with)-358(Harmonic)-357(extension)-358(\050ASH\051)]TJ/F15 10.9091 Tf 176.608 0 Td [(is)-333(de\014ned)-334(b)28(y)]TJ/F22 10.9091 Tf -207.735 -29.306 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(AS)-56(H)]TJ/F15 10.9091 Tf 23.038 3.434 Td [(=)]TJ/F23 7.9701 Tf 15.648 13.636 Td [(m)]TJ/F28 10.9091 Tf -4.133 -3.273 Td [(X)]TJ/F23 7.9701 Tf 1.027 -23.451 Td [(i)]TJ/F20 7.9701 Tf 2.883 0 Td [(=1)]TJ/F15 10.9091 Tf 11.847 13.088 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.504 Td [(\016)]TJ -0.084 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.628 2.697 Td [(\051)]TJ/F23 7.9701 Tf 4.243 4.504 Td [(T)]TJ/F15 10.9091 Tf 6.604 -4.504 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 4.504 Td [(\016)]TJ 0 -7.201 Td [(i)]TJ/F15 10.9091 Tf 4.544 2.697 Td [(\051)]TJ/F26 7.9701 Tf 4.242 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 7.098 -1.747 Td [(~)]TJ/F22 10.9091 Tf -2.366 -2.757 Td [(R)]TJ/F20 7.9701 Tf 8.367 4.504 Td [(0)]TJ/F23 7.9701 Tf -0.084 -7.201 Td [(i)]TJ/F22 10.9091 Tf 4.817 2.697 Td [(:)]TJ/F15 10.9091 Tf -271.973 -30.174 Td [(W)83(e)-334(note)-335(that)-335(for)]TJ/F22 10.9091 Tf 83.422 0 Td [(\016)]TJ/F15 10.9091 Tf 8.316 0 Td [(=)-280(0)-335(the)-334(three)-335(v)56(arian)28(ts)-335(of)-335(the)-334(AS)-335(preconditioner)-335(are)-334(all)-335(equal)-335(t)1(o)-335(the)]TJ -91.738 -13.55 Td [(blo)-28(c)28(k-Jacobi)-333(preconditioner.)]TJ 16.937 -13.549 Td [(As)-358(already)-358(obse)-1(r)1(v)27(ed,)-364(the)-358(con)27(v)28(ergence)-358(rate)-358(of)-359(the)-358(one-lev)28(el)-358(Sc)27(h)28(w)28(arz)-358(preconditioned)]TJ -16.937 -13.549 Td [(iterativ)28(e)-359(solv)28(ers)-358(deteriorates)-358(as)-359(the)-358(n)28(um)28(b)-28(er)]TJ/F22 10.9091 Tf 211.422 0 Td [(m)]TJ/F15 10.9091 Tf 13.488 0 Td [(of)-358(partitions)-358(of)]TJ/F22 10.9091 Tf 75.453 0 Td [(W)]TJ/F15 10.9091 Tf 15.727 0 Td [(increases)-358([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -506.7366 -462.2978 cm -BT -/F15 10.9091 Tf 506.7366 462.2978 Td[(7)]TJ -ET -1 0 0 1 512.1912 462.2978 cm + [(7)]TJ 0 g 0 G -1 0 0 1 -512.1912 -462.2978 cm -BT -/F15 10.9091 Tf 512.1912 462.2978 Td[(,)]TJ -ET -1 0 0 1 519.1302 462.2978 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -519.1302 -462.2978 cm -BT -/F15 10.9091 Tf 519.1302 462.2978 Td[(15)]TJ -ET -1 0 0 1 530.0393 462.2978 cm + [-359(15)]TJ 0 g 0 G -1 0 0 1 -530.0393 -462.2978 cm -BT -/F15 10.9091 Tf 530.0393 462.2978 Td[(].)-519(T)83(o)]TJ -388.3008 -13.5492 Td[(redu)1(c)-1(e)-308(th)1(e)-309(d)1(e)-1(p)-27(e)-1(n)1(dency)-308(of)-307(the)-308(n)28(u)1(m)27(b)-27(e)-1(r)-307(of)-308(iterati)1(ons)-308(on)-308(th)1(e)-308(degre)-1(e)-308(of)-307(paral)1(le)-1(l)1(is)-1(m)-308(w)28(e)-309(ma)28(y)]TJ 0 -13.5492 Td[(in)28(t)1(ro)-28(d)1(uce)-276(a)-276(glob)1(al)-275(c)-1(ou)1(plin)1(g)-276(amon)1(g)-276(th)1(e)-276(o)27(v)28(erl)1(appi)1(ng)-275(part)1(ition)1(s)-276(b)28(y)-275(de\014ni)1(ng)-275(a)-276(coarse)-1(-s)-1(p)1(ac)-1(e)]TJ 0 -13.5492 Td[(app)1(ro)28(ximation)]TJ/F24 10.9091 Tf 72.1198 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.0953 1.6887 Td[(of)-274(the)-275(matrix)]TJ/F24 10.9091 Tf 64.7833 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(.)-425(In)-274(a)-275(pu)1(re)-275(algebrai)1(c)-276(se)-1(tt)1(ing,)]TJ/F24 10.9091 Tf 137.1498 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.0953 1.6887 Td[(is)-275(usual)1(ly)-275(b)1(uilt)-274(with)]TJ -318.7889 -13.5492 Td[(a)-375(Gal)1(e)-1(r)1(kin)-374(app)1(roac)27(h)1(.)-569(Giv)28(en)-374(a)-375(s)-1(et)]TJ/F24 10.9091 Tf 166.3185 0 Td[(W)]TJ/F25 7.9701 Tf 10.303 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 11.1858 1.6887 Td[(of)]TJ/F20 10.9091 Tf 12.877 0 Td[(c)51(o)51(arse)-395(vertic)51(es)]TJ/F15 10.9091 Tf 68.9977 0 Td[(,)-385(with)-374(s)-1(i)1(z)-1(e)]TJ/F24 10.9091 Tf 53.653 0 Td[(n)]TJ/F25 7.9701 Tf 6.548 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-385(and)-374(a)-375(suit)1(able)]TJ -336.9798 -13.5492 Td[(res)-1(t)1(riction)-333(op)-27(e)-1(r)1(ator)]TJ/F24 10.9091 Tf 96.2425 0 Td[(R)]TJ/F25 7.9701 Tf 8.2832 -1.6887 Td[(C)]TJ/F27 10.9091 Tf 10.127 1.6887 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F26 5.9776 Tf 5.1382 -1.3394 Td[(C)]TJ/F28 7.9701 Tf 6.1942 1.3394 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 5.6364 -3.9588 Td[(,)]TJ/F24 10.9091 Tf 6.6666 0 Td[(A)]TJ/F25 7.9701 Tf 8.1819 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.7331 1.6887 Td[(is)-334(d)1(e)-1(\014)1(ned)-333(as)]TJ/F24 10.9091 Tf -10.1287 -20.9733 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.127 1.6887 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(R)]TJ/F25 7.9701 Tf 8.2831 -1.6887 Td[(C)]TJ/F24 10.9091 Tf 7.0968 1.6887 Td[(AR)]TJ/F25 7.9701 Tf 16.5493 4.5043 Td[(T)]TJ -0.0843 -7.2012 Td[(C)]TJ/F15 10.9091 Tf -233.5116 -18.2764 Td[(and)-495(the)-497(coarse)-1(-lev)28(e)-1(l)-496(corr)1(e)-1(ction)-496(matri)1(x)-496(to)-497(b)-27(e)-497(com)27(b)1(ined)-496(with)-496(a)-496(generic)-496(one-)-1(lev)28(el)-496(AS)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)]TJ/F24 10.9091 Tf 72.1819 0 Td[(M)]TJ/F22 7.9701 Tf 10.5833 -1.6887 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 9.8935 1.6887 Td[(is)-334(ob)1(tain)1(e)-1(d)-333(as)]TJ/F24 10.9091 Tf 63.8687 -20.9733 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 15.5384 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 4.5043 Td[(T)]TJ -0.0843 -7.2012 Td[(C)]TJ/F24 10.9091 Tf 7.0968 2.6969 Td[(A)]TJ/F28 7.9701 Tf 8.1818 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -6.5865 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 11.3188 3.4341 Td[(R)]TJ/F25 7.9701 Tf 8.2832 -1.6887 Td[(C)]TJ/F24 10.9091 Tf 7.0968 1.6887 Td[(;)]TJ/F15 10.9091 Tf -248.6591 -20.9733 Td[(where)]TJ/F24 10.9091 Tf 31.9095 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 11.0973 1.6887 Td[(is)-367(ass)-1(u)1(m)-1(ed)-366(to)-367(b)-27(e)-367(nonsin)1(gular)1(.)-545(The)-367(ap)1(pli)1(c)-1(ati)1(on)-367(of)]TJ/F24 10.9091 Tf 240.8833 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 16.5086 3.4341 Td[(to)-367(a)-366(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 56.2741 0 Td[(v)]TJ/F15 10.9091 Tf 9.6797 0 Td[(corre-)]TJ -385.1177 -13.5492 Td[(sp)-28(on)1(ds)-325(to)-326(a)-325(r)1(e)-1(striction)1(,)-327(a)-325(soluti)1(on)-325(and)-324(a)-326(p)1(rolon)1(gation)-324(s)-1(tep;)-327(the)-326(solu)1(tion)-325(step,)-327(i)1(n)28(v)28(olvi)1(ng)]TJ 0 -13.5492 Td[(th)1(e)-334(m)-1(at)1(rix)]TJ/F24 10.9091 Tf 54.2728 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-333(ma)27(y)-333(b)-27(e)-334(carri)1(e)-1(d)-333(ou)1(t)-334(al)1(s)-1(o)-333(app)1(ro)28(ximately)83(.)]TJ -52.6149 -13.5492 Td[(The)-309(c)-1(om)28(bin)1(ation)-309(of)]TJ/F24 10.9091 Tf 96.1762 0 Td[(M)]TJ/F25 7.9701 Tf 10.5833 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.4687 1.6887 Td[(and)]TJ/F24 10.9091 Tf 20.9476 0 Td[(M)]TJ/F22 7.9701 Tf 10.5833 -1.6887 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 9.629 1.6887 Td[(ma)27(y)-308(b)-28(e)-309(p)-28(erf)1(orme)-1(d)-308(in)-309(eith)1(e)-1(r)-309(an)-308(add)1(itiv)28(e)-309(or)-309(a)-309(m)27(u)1(l-)]TJ -179.5588 -13.5492 Td[(tip)1(licativ)28(e)-275(framew)27(ork)1(.)-425(In)-275(th)1(e)-276(f)1(orme)-1(r)-274(c)-1(ase)-1(,)-286(the)]TJ/F20 10.9091 Tf 217.1915 0 Td[(tw)-1(o-l)1(evel)-304(additive)]TJ/F15 10.9091 Tf 85.1983 0 Td[(Sc)28(h)28(w)28(arz)-276(p)1(rec)-1(on)1(diti)1(oner)]TJ -302.3899 -13.5492 Td[(is)-334(ob)1(tain)1(e)-1(d)1(:)]TJ/F24 10.9091 Tf 153.9707 -13.5492 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(LA)]TJ/F15 10.9091 Tf 15.6304 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 14.9324 3.4341 Td[(+)]TJ/F24 10.9091 Tf 10.9091 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(:)]TJ/F15 10.9091 Tf -255.4501 -18.2575 Td[(App)1(lyi)1(ng)]TJ/F24 10.9091 Tf 48.2012 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F28 7.9701 Tf 5.759 0 Td[(\000)]TJ/F25 7.9701 Tf 6.5865 0 Td[(A)]TJ/F15 10.9091 Tf 11.4059 3.4341 Td[(to)-418(a)-419(v)28(ec)-1(tor)]TJ/F24 10.9091 Tf 57.9672 0 Td[(v)]TJ/F15 10.9091 Tf 10.2441 0 Td[(with)1(in)-418(a)-419(K)1(rylo)28(v)-418(s)-1(ol)1(v)28(e)-1(r)-418(corres)-1(p)-27(on)1(ds)-419(to)-418(app)1(lyin)1(g)]TJ/F24 10.9091 Tf 234.3781 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf -399.9429 -11.5506 Td[(and)]TJ/F24 10.9091 Tf 21.2121 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 11.9103 3.4341 Td[(to)]TJ/F24 10.9091 Tf 13.3334 0 Td[(v)]TJ/F15 10.9091 Tf 9.3156 0 Td[(in)1(dep)-28(end)1(e)-1(n)29(tly)-333(and)-333(th)1(e)-1(n)-332(s)-1(u)1(m)-1(min)1(g)-334(u)1(p)-333(the)-333(re)-1(sul)1(ts)-1(.)]TJ -53.6525 -13.5492 Td[(In)-355(t)1(he)-355(m)27(u)1(ltip)1(licativ)28(e)-355(c)-1(ase)-1(,)-360(th)1(e)-356(com)27(b)1(in)1(ation)-355(can)-354(b)-28(e)-355(p)-27(e)-1(r)1(formed)-355(b)28(y)-354(\014rst)-355(ap)1(ply)1(ing)-355(th)1(e)]TJ -16.9365 -13.5492 Td[(sm)-1(o)-28(ot)1(her)]TJ/F24 10.9091 Tf 47.6667 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7758 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2341 0 Td[(L)]TJ/F15 10.9091 Tf 11.9104 3.4341 Td[(and)-332(then)-333(the)-333(c)-1(oarse-)-1(lev)28(el)-334(corr)1(e)-1(ction)-333(op)-27(e)-1(r)1(ator)]TJ/F24 10.9091 Tf 217.4851 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 12.5082 3.4341 Td[(:)]TJ/F24 10.9091 Tf -164.4656 -21.5786 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7758 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2341 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(v)-36(;)]TJ -45.7404 -13.7889 Td[(z)]TJ/F15 10.9091 Tf 8.5833 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(w)]TJ/F15 10.9091 Tf 10.5278 0 Td[(+)]TJ/F24 10.9091 Tf 10.909 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7758 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 12.5081 3.4341 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(v)]TJ/F27 10.9091 Tf 8.1035 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(Aw)]TJ/F15 10.9091 Tf 16.2854 0 Td[(\051;)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [(].)-519(T)83(o)]TJ -316.09 -13.549 Td [(reduce)-308(the)-308(dep)-28(endency)-308(of)-307(the)-308(n)28(um)27(b)-27(er)-308(of)-308(iterations)-308(on)-308(the)-308(degree)-308(of)-308(parallelism)-308(w)28(e)-308(ma)28(y)]TJ 0 -13.549 Td [(in)28(tro)-28(duce)-275(a)-276(global)-275(coupling)-276(among)-275(the)-276(o)28(v)28(erlapping)-275(partitions)-276(b)28(y)-275(de\014ning)-276(a)-275(coarse-space)]TJ 0 -13.55 Td [(appro)28(ximation)]TJ/F22 10.9091 Tf 72.12 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.095 1.688 Td [(of)-275(the)-275(matrix)]TJ/F22 10.9091 Tf 64.784 0 Td [(A)]TJ/F15 10.9091 Tf 8.181 0 Td [(.)-425(In)-275(a)-275(pure)-274(algebraic)-275(setting,)]TJ/F22 10.9091 Tf 137.15 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.095 1.688 Td [(is)-275(usually)-275(built)-274(with)]TJ -318.789 -13.549 Td [(a)-375(Galerkin)-375(approac)28(h.)-569(Giv)28(en)-375(a)-374(s)-1(et)]TJ/F22 10.9091 Tf 166.319 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.186 1.689 Td [(of)]TJ/F18 10.9091 Tf 12.877 0 Td [(c)51(o)51(arse)-396(vertic)52(es)]TJ/F15 10.9091 Tf 68.997 0 Td [(,)-385(with)-375(size)]TJ/F22 10.9091 Tf 53.653 0 Td [(n)]TJ/F23 7.9701 Tf 6.548 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(,)-385(and)-375(a)-375(suitable)]TJ -336.98 -13.549 Td [(restriction)-333(op)-28(erator)]TJ/F22 10.9091 Tf 96.243 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F25 10.9091 Tf 10.127 1.689 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.182 3.959 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.34 Td [(C)]TJ/F26 7.9701 Tf 6.194 1.34 Td [(\002)]TJ/F23 7.9701 Tf 6.587 0 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.959 Td [(,)]TJ/F22 10.9091 Tf 6.667 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(is)-333(de\014ned)-334(as)]TJ/F22 10.9091 Tf -10.129 -20.973 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.689 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F22 10.9091 Tf 7.097 1.689 Td [(AR)]TJ/F23 7.9701 Tf 16.549 4.504 Td [(T)]TJ -0.084 -7.201 Td [(C)]TJ/F15 10.9091 Tf -233.512 -18.277 Td [(and)-496(the)-496(c)-1(oar)1(s)-1(e-lev)28(el)-496(correction)-496(matrix)-497(to)-496(b)-28(e)-496(com)28(bined)-496(with)-497(a)-496(generic)-496(one-lev)28(el)-497(AS)]TJ 0 -13.549 Td [(preconditioner)]TJ/F22 10.9091 Tf 72.182 0 Td [(M)]TJ/F20 7.9701 Tf 10.584 -1.688 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 9.893 1.688 Td [(is)-333(obtained)-334(as)]TJ/F22 10.9091 Tf 63.869 -20.973 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 15.539 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 4.504 Td [(T)]TJ -0.084 -7.201 Td [(C)]TJ/F22 10.9091 Tf 7.097 2.697 Td [(A)]TJ/F26 7.9701 Tf 8.182 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -6.586 -8.022 Td [(C)]TJ/F22 10.9091 Tf 11.319 3.434 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F22 10.9091 Tf 7.097 1.689 Td [(;)]TJ/F15 10.9091 Tf -248.66 -20.973 Td [(where)]TJ/F22 10.9091 Tf 31.91 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.097 1.689 Td [(is)-367(assumed)-367(to)-366(b)-28(e)-367(nonsingular)1(.)-545(The)-367(application)-366(of)]TJ/F22 10.9091 Tf 240.883 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 16.508 3.434 Td [(to)-367(a)-366(v)27(ector)]TJ/F22 10.9091 Tf 56.274 0 Td [(v)]TJ/F15 10.9091 Tf 9.68 0 Td [(corre-)]TJ -385.118 -13.549 Td [(sp)-28(onds)-325(to)-325(a)-325(restriction,)-327(a)-325(solution)-325(and)-325(a)-325(prolongation)-325(step;)-328(the)-325(solution)-325(step,)-327(in)28(v)27(olvi)1(ng)]TJ 0 -13.55 Td [(the)-333(matrix)]TJ/F22 10.9091 Tf 54.273 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.688 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.688 Td [(,)-333(ma)27(y)-333(b)-28(e)-333(carried)-333(out)-334(also)-333(appro)28(ximately)83(.)]TJ -52.615 -13.549 Td [(The)-309(com)28(bination)-309(of)]TJ/F22 10.9091 Tf 96.176 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.469 1.689 Td [(and)]TJ/F22 10.9091 Tf 20.948 0 Td [(M)]TJ/F20 7.9701 Tf 10.583 -1.689 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 9.629 1.689 Td [(ma)28(y)-309(b)-28(e)-309(p)-28(erformed)-309(in)-309(either)-309(an)-309(additiv)28(e)-309(or)-309(a)-309(m)27(ul-)]TJ -179.559 -13.549 Td [(tiplicativ)28(e)-275(framew)28(ork.)-425(In)-275(the)-275(former)-275(c)-1(ase,)-286(the)]TJ/F18 10.9091 Tf 217.192 0 Td [(two-level)-304(additive)]TJ/F15 10.9091 Tf 85.198 0 Td [(Sc)28(h)28(w)27(arz)-275(preconditioner)]TJ -302.39 -13.549 Td [(is)-333(obtained:)]TJ/F22 10.9091 Tf 153.971 -13.549 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.235 0 Td [(LA)]TJ/F15 10.9091 Tf 15.63 3.435 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 14.933 3.435 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.435 Td [(:)]TJ/F15 10.9091 Tf -255.45 -18.258 Td [(Applying)]TJ/F22 10.9091 Tf 48.202 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F26 7.9701 Tf 5.759 0 Td [(\000)]TJ/F23 7.9701 Tf 6.587 0 Td [(A)]TJ/F15 10.9091 Tf 11.406 3.434 Td [(to)-418(a)-419(v)28(ector)]TJ/F22 10.9091 Tf 57.967 0 Td [(v)]TJ/F15 10.9091 Tf 10.244 0 Td [(within)-418(a)-419(Krylo)28(v)-418(solv)27(er)-418(corresp)-28(onds)-418(to)-419(appl)1(ying)]TJ/F22 10.9091 Tf 234.378 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf -399.943 -11.551 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 11.91 3.434 Td [(to)]TJ/F22 10.9091 Tf 13.334 0 Td [(v)]TJ/F15 10.9091 Tf 9.315 0 Td [(indep)-28(enden)28(tly)-333(and)-333(then)-334(summing)-333(up)-333(the)-334(results.)]TJ -53.652 -13.549 Td [(In)-355(the)-355(m)28(ultiplicativ)28(e)-355(case,)-360(the)-355(com)28(bination)-355(can)-355(b)-28(e)-355(p)-27(erformed)-355(b)28(y)-355(\014rst)-355(applying)-355(the)]TJ -16.937 -13.549 Td [(smo)-28(other)]TJ/F22 10.9091 Tf 47.667 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.235 0 Td [(L)]TJ/F15 10.9091 Tf 11.91 3.434 Td [(and)-333(then)-334(th)1(e)-334(coarse-lev)28(el)-334(correction)-333(op)-28(erator)]TJ/F22 10.9091 Tf 217.485 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 12.509 3.434 Td [(:)]TJ/F22 10.9091 Tf -164.466 -21.579 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(v)-36(;)]TJ -45.74 -13.789 Td [(z)]TJ/F15 10.9091 Tf 8.583 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(w)]TJ/F15 10.9091 Tf 10.528 0 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 12.509 3.434 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(v)]TJ/F25 10.9091 Tf 8.104 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(Aw)]TJ/F15 10.9091 Tf 16.285 0 Td [(\051;)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -291 0 obj << +265 0 obj << /Type /Page -/Contents 292 0 R -/Resources 290 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 230 0 R -/Annots [ 294 0 R 295 0 R 296 0 R 297 0 R ] +/Contents 266 0 R +/Resources 264 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 210 0 R +/Annots [ 241 0 R 242 0 R 262 0 R 263 0 R ] >> endobj -294 0 obj << +241 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [451.7484 676.0417 459.1954 685.0645] +/Rect [451.748 676.042 459.195 685.065] /Subtype /Link /A << /S /GoTo /D (cite.CAI_SARKIS) >> >> endobj -295 0 obj << +242 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [464.4538 676.0417 477.3555 685.0645] +/Rect [464.454 676.042 477.355 685.065] /Subtype /Link /A << /S /GoTo /D (cite.EFSTATHIOU) >> >> endobj -296 0 obj << +262 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [505.7404 461.3016 513.1874 470.3244] +/Rect [505.74 461.302 513.187 470.324] /Subtype /Link /A << /S /GoTo /D (cite.dd1_94) >> >> endobj -297 0 obj << +263 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [518.1339 461.3016 531.0355 470.3244] +/Rect [518.134 461.302 531.036 470.324] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -293 0 obj << -/D [291 0 R /XYZ 141.7385 740.0018 null] +267 0 obj << +/D [265 0 R /XYZ 141.738 740.002 null] >> endobj -290 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F20 171 0 R /F24 176 0 R /F25 267 0 R /F22 273 0 R /F27 179 0 R /F26 276 0 R /F28 270 0 R /F30 279 0 R >> +264 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F18 163 0 R /F22 165 0 R /F23 248 0 R /F20 250 0 R /F25 166 0 R /F24 251 0 R /F26 249 0 R /F28 252 0 R >> /ProcSet [ /PDF /Text ] >> endobj -302 0 obj << -/Length 14455 +278 0 obj << +/Length 11465 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(5)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(5)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Mul)66(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)23(gr)22(oun)-1(d)]TJ/F15 10.9091 Tf 391.3906 0 Td[(13)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Mul)67(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)22(gr)22(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(13)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F15 10.9091 Tf 93.9178 704.1363 Td[(th)1(is)-279(corresp)-28(on)1(ds)-278(to)-279(t)1(he)-279(f)1(ollo)28(win)1(g)]TJ/F20 10.9091 Tf 156.3223 0 Td[(tw)-1(o-l)1(evel)-307(hy)1(brid)-307(pr)52(e-smo)51(othe)51(d)]TJ/F15 10.9091 Tf 143.0037 0 Td[(Sc)28(h)28(w)28(arz)-279(p)1(rec)-1(on)1(diti)1(oner:)]TJ/F24 10.9091 Tf -190.113 -24.5723 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(LH)]TJ/F28 7.9701 Tf 13.3293 0 Td[(\000)]TJ/F25 7.9701 Tf 6.5866 0 Td[(P)-147(R)-7(E)]TJ/F15 10.9091 Tf 23.1536 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F15 10.9091 Tf 14.9324 3.4341 Td[(+)]TJ/F30 10.9091 Tf 10.9091 8.8364 Td[(\000)]TJ/F24 10.9091 Tf 5 -8.8364 Td[(I)]TJ/F27 10.9091 Tf 8.0757 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 12.5082 3.4341 Td[(A)]TJ/F30 10.9091 Tf 8.1818 8.8364 Td[(\001)]TJ/F24 10.9091 Tf 6.8182 -8.8364 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(:)]TJ/F15 10.9091 Tf -300.2078 -24.5724 Td[(On)-368(th)1(e)-369(other)-368(han)1(d,)-377(b)28(y)-368(app)1(lyi)1(ng)-369(t)1(he)-369(sm)-1(o)-27(other)-369(af)1(ter)-369(t)1(he)-369(coars)-1(e-le)-1(v)28(el)-368(c)-1(or)1(rec)-1(tion)1(,)-377(i.e.)-368(b)28(y)]TJ 0 -13.5492 Td[(com)-1(p)1(utin)1(g)]TJ/F24 10.9091 Tf 150.5056 -12.9058 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7758 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 12.5081 3.4341 Td[(v)-36(;)]TJ -45.7404 -13.7889 Td[(z)]TJ/F15 10.9091 Tf 8.5833 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(w)]TJ/F15 10.9091 Tf 10.5278 0 Td[(+)]TJ/F24 10.9091 Tf 10.909 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 8.274 3.4341 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(v)]TJ/F27 10.9091 Tf 8.1035 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(Aw)]TJ/F15 10.9091 Tf 16.2854 0 Td[(\051)]TJ/F24 10.9091 Tf 4.2424 0 Td[(;)]TJ/F15 10.9091 Tf -258.9152 -19.1875 Td[(th)1(e)]TJ/F20 10.9091 Tf 18.7879 0 Td[(tw)-1(o-l)1(evel)-357(h)-1(y)1(bri)1(d)-358(p)51(ost-smo)51(othe)51(d)]TJ/F15 10.9091 Tf 148.7565 0 Td[(Sc)28(h)28(w)28(arz)-334(p)1(re)-1(cond)1(ition)1(e)-1(r)-333(i)1(s)-334(obtai)1(ned:)]TJ/F24 10.9091 Tf -60.9726 -24.5723 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(2)]TJ/F25 7.9701 Tf 4.2342 0 Td[(LH)]TJ/F28 7.9701 Tf 13.3293 0 Td[(\000)]TJ/F25 7.9701 Tf 6.5866 0 Td[(P)-147(O)-30(S)-56(T)]TJ/F15 10.9091 Tf 28.4361 3.4341 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 10.6982 3.4341 Td[(+)]TJ/F30 10.9091 Tf 10.9091 8.8364 Td[(\000)]TJ/F24 10.9091 Tf 5 -8.8364 Td[(I)]TJ/F27 10.9091 Tf 8.0757 0 Td[(\000)]TJ/F24 10.9091 Tf 10.9091 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ -7.7759 -8.0219 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F24 10.9091 Tf 8.274 3.4341 Td[(A)]TJ/F30 10.9091 Tf 8.1818 8.8364 Td[(\001)]TJ/F24 10.9091 Tf 6.8182 -8.8364 Td[(M)]TJ/F28 7.9701 Tf 11.7727 4.5878 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F25 7.9701 Tf -7.7759 -8.0219 Td[(C)]TJ/F24 10.9091 Tf 12.5082 3.4341 Td[(:)]TJ/F15 10.9091 Tf -302.8491 -24.5724 Td[(On)1(e)-223(more)-223(v)56(ari)1(an)28(t)-222(of)-222(t)28(w)27(o-lev)28(e)-1(l)-222(h)29(ybr)1(id)-222(p)1(re)-1(cond)1(ition)1(e)-1(r)-221(is)-223(ob)1(tained)-222(b)28(y)-222(ap)1(ply)1(ing)-222(th)1(e)-223(s)-1(mo)-28(oth)1(e)-1(r)]TJ 0 -13.5492 Td[(b)-27(e)-1(f)1(ore)-240(an)1(d)-239(aft)1(e)-1(r)-239(th)1(e)-240(coars)-1(e-le)-1(v)28(el)-239(correc)-1(ti)1(on.)-413(In)-239(th)1(is)-240(case)-1(,)-258(th)1(e)-240(p)1(re)-1(cond)1(ition)1(e)-1(r)-238(is)-240(symm)-1(etric)]TJ 0 -13.5492 Td[(if)]TJ/F24 10.9091 Tf 10 0 Td[(A)]TJ/F15 10.9091 Tf 8.1819 0 Td[(,)]TJ/F24 10.9091 Tf 6.6666 0 Td[(M)]TJ/F22 7.9701 Tf 10.5834 -1.6887 Td[(1)]TJ/F25 7.9701 Tf 4.2342 0 Td[(L)]TJ/F15 10.9091 Tf 9.8935 1.6887 Td[(and)]TJ/F24 10.9091 Tf 21.2121 0 Td[(M)]TJ/F25 7.9701 Tf 10.5834 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.7331 1.6887 Td[(are)-333(s)-1(ymme)-1(tr)1(ic)-1(.)]TJ -75.1517 -13.5706 Td[(As)-533(pr)1(e)-1(v)1(iously)-532(noted,)-582(on)-532(p)1(arallel)-532(c)-1(ompu)1(te)-1(r)1(s)-533(the)-533(n)29(um)27(b)-27(er)-532(of)-533(sub)1(matrice)-1(s)-533(u)1(s)-1(u)1(ally)]TJ -16.9365 -13.5492 Td[(matc)27(h)1(e)-1(s)-307(the)-307(n)28(u)1(m)27(b)-27(e)-1(r)-306(of)-307(a)28(v)56(ailab)1(le)-307(pr)1(o)-28(c)-1(ess)-1(ors.)-435(When)-307(th)1(e)-307(s)-1(ize)-307(of)-307(th)1(e)-307(s)-1(ystem)-308(to)-306(b)-28(e)-307(pr)1(e)-1(con-)]TJ 0 -13.5492 Td[(di)1(tioned)-300(i)1(s)-301(v)28(e)-1(r)1(y)-300(large,)-307(t)1(he)-301(u)1(s)-1(e)-300(of)-300(man)28(y)-300(p)1(ro)-28(ce)-1(ss)-1(or)1(s)-1(,)-306(i.e.)-300(of)-300(man)28(y)-300(sm)-1(all)-299(s)-1(u)1(bmatrice)-1(s,)-307(of)1(ten)]TJ 0 -13.5492 Td[(leads)-314(to)-314(a)-314(large)-314(coars)-1(e-le)-1(v)28(el)-314(sys)-1(t)1(e)-1(m,)-318(whose)-315(solu)1(tion)-314(ma)28(y)-314(b)-27(e)-315(comput)1(ational)1(ly)-314(exp)-28(ensiv)28(e.)]TJ 0 -13.5492 Td[(On)-384(th)1(e)-386(ot)1(her)-385(h)1(and)1(,)-398(th)1(e)-385(use)-385(of)-385(f)1(e)-1(w)-385(p)1(ro)-28(ces)-1(sors)-385(often)-384(le)-1(ad)1(s)-385(to)-385(lo)-27(c)-1(al)-384(s)-1(u)1(m)-1(at)1(rice)-1(s)-385(th)1(at)-385(are)]TJ 0 -13.5492 Td[(to)-28(o)-424(exp)-27(e)-1(n)1(s)-1(i)1(v)28(e)-425(to)-424(b)-27(e)-425(p)1(ro)-28(ces)-1(se)-1(d)-423(on)-424(single)-424(pr)1(o)-28(ce)-1(ss)-1(or)1(s)-1(,)-446(b)-28(ec)-1(au)1(s)-1(e)-424(of)-424(mem)-1(or)1(y)-424(and)1(/or)-424(com)-1(-)]TJ 0 -13.5492 Td[(pu)1(tin)1(g)-324(requi)1(re)-1(men)28(ts.)-442(Th)1(e)-1(r)1(e)-1(f)1(ore)-1(,)-325(it)-324(se)-1(ems)-325(n)1(atur)1(al)-324(to)-324(u)1(s)-1(e)-324(a)-324(rec)-1(u)1(rsiv)28(e)-324(appr)1(oac)27(h)1(,)-326(in)-323(whic)28(h)]TJ 0 -13.5492 Td[(th)1(e)-395(c)-1(oar)1(s)-1(e-)-1(l)1(e)-1(v)28(el)-394(c)-1(orr)1(e)-1(ction)-394(is)-394(re)-1(-ap)1(plied)-394(startin)1(g)-395(f)1(rom)-395(t)1(he)-395(curr)1(e)-1(n)29(t)-395(coarse)-1(-lev)28(e)-1(l)-394(sys)-1(t)1(e)-1(m.)]TJ 0 -13.5492 Td[(The)-321(c)-1(or)1(res)-1(p)-27(ond)1(ing)-321(p)1(rec)-1(on)1(dit)1(ioners,)-323(c)-1(all)1(e)-1(d)]TJ/F20 10.9091 Tf 202.455 0 Td[(mu)1(lti-l)1(evel)]TJ/F15 10.9091 Tf 53.6944 0 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-1(,)-323(can)-321(signi)1(\014can)28(tly)]TJ -256.1494 -13.5492 Td[(redu)1(c)-1(e)-282(the)-283(com)-1(p)1(utat)1(ional)-282(cos)-1(t)-282(of)-282(pr)1(e)-1(cond)1(ition)1(ing)-282(with)-282(r)1(e)-1(sp)-28(ec)-1(t)-282(to)-282(the)-282(t)28(w)27(o-lev)28(e)-1(l)-282(c)-1(ase)-283(\050se)-1(e)]TJ 0 -13.5492 Td[([)]TJ -ET -1 0 0 1 96.9481 370.2545 cm + -401.542 -35.866 Td [(this)-278(corresp)-28(onds)-278(to)-278(the)-278(follo)28(wing)]TJ/F18 10.9091 Tf 156.322 0 Td [(two-level)-307(hybrid)-307(pr)51(e-smo)51(othe)52(d)]TJ/F15 10.9091 Tf 143.004 0 Td [(Sc)28(h)28(w)27(arz)-278(preconditioner:)]TJ/F22 10.9091 Tf -190.113 -24.572 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(LH)]TJ/F26 7.9701 Tf 13.33 0 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(P)-148(R)-6(E)]TJ/F15 10.9091 Tf 23.154 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F15 10.9091 Tf 14.933 3.434 Td [(+)]TJ/F28 10.9091 Tf 10.909 8.836 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(I)]TJ/F25 10.9091 Tf 8.076 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F22 10.9091 Tf 12.508 3.434 Td [(A)]TJ/F28 10.9091 Tf 8.182 8.836 Td [(\001)]TJ/F22 10.9091 Tf 6.818 -8.836 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.235 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(:)]TJ/F15 10.9091 Tf -300.208 -24.572 Td [(On)-368(the)-369(other)-368(hand,)-377(b)27(y)-368(applying)-368(the)-369(smo)-28(other)-368(after)-369(the)-368(coarse-lev)27(el)-368(correction,)-377(i.e.)-369(b)28(y)]TJ 0 -13.55 Td [(computing)]TJ/F22 10.9091 Tf 150.505 -12.905 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.587 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.021 Td [(C)]TJ/F22 10.9091 Tf 12.508 3.434 Td [(v)-36(;)]TJ -45.741 -13.789 Td [(z)]TJ/F15 10.9091 Tf 8.584 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(w)]TJ/F15 10.9091 Tf 10.528 0 Td [(+)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 8.274 3.434 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(v)]TJ/F25 10.9091 Tf 8.103 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(Aw)]TJ/F15 10.9091 Tf 16.286 0 Td [(\051)]TJ/F22 10.9091 Tf 4.242 0 Td [(;)]TJ/F15 10.9091 Tf -258.915 -19.188 Td [(the)]TJ/F18 10.9091 Tf 18.788 0 Td [(two-level)-358(hybrid)-357(p)51(ost-smo)51(othe)51(d)]TJ/F15 10.9091 Tf 148.756 0 Td [(Sc)28(h)28(w)27(arz)-333(preconditioner)-333(is)-334(obt)1(ained:)]TJ/F22 10.9091 Tf -60.972 -24.572 Td [(M)]TJ/F26 7.9701 Tf 11.772 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ -7.776 -8.022 Td [(2)]TJ/F23 7.9701 Tf 4.234 0 Td [(LH)]TJ/F26 7.9701 Tf 13.33 0 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(P)-148(O)-29(S)-56(T)]TJ/F15 10.9091 Tf 28.436 3.434 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.775 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 10.698 3.434 Td [(+)]TJ/F28 10.9091 Tf 10.909 8.836 Td [(\000)]TJ/F22 10.9091 Tf 5 -8.836 Td [(I)]TJ/F25 10.9091 Tf 8.076 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ -7.776 -8.022 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F22 10.9091 Tf 8.274 3.434 Td [(A)]TJ/F28 10.9091 Tf 8.182 8.836 Td [(\001)]TJ/F22 10.9091 Tf 6.818 -8.836 Td [(M)]TJ/F26 7.9701 Tf 11.773 4.588 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F23 7.9701 Tf -7.776 -8.022 Td [(C)]TJ/F22 10.9091 Tf 12.508 3.434 Td [(:)]TJ/F15 10.9091 Tf -302.849 -24.572 Td [(One)-222(more)-222(v)55(arian)28(t)-222(of)-222(t)27(w)28(o-lev)28(el)-222(h)27(yb)1(rid)-223(precondit)1(ioner)-223(is)-222(obtained)-222(b)28(y)-222(applying)-222(the)-223(smo)-27(other)]TJ 0 -13.55 Td [(b)-28(efore)-239(and)-239(after)-239(the)-240(coarse-lev)28(el)-239(correction.)-413(In)-239(this)-240(case,)-258(the)-239(preconditioner)-239(is)-239(symme)-1(tr)1(ic)]TJ 0 -13.549 Td [(if)]TJ/F22 10.9091 Tf 10 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(,)]TJ/F22 10.9091 Tf 6.666 0 Td [(M)]TJ/F20 7.9701 Tf 10.584 -1.688 Td [(1)]TJ/F23 7.9701 Tf 4.234 0 Td [(L)]TJ/F15 10.9091 Tf 9.893 1.688 Td [(and)]TJ/F22 10.9091 Tf 21.213 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.688 Td [(are)-333(symmetric.)]TJ -75.152 -13.57 Td [(As)-533(previou)1(s)-1(l)1(y)-533(noted,)-582(on)-533(parallel)-532(computers)-533(the)-532(n)28(um)27(b)-27(er)-533(of)-532(submatrices)-533(usually)]TJ -16.936 -13.55 Td [(matc)28(hes)-307(the)-307(n)28(um)28(b)-28(er)-307(of)-307(a)28(v)56(ailable)-307(pro)-28(cessors.)-436(When)-307(t)1(he)-307(size)-307(of)-307(the)-307(system)-307(to)-307(b)-28(e)-306(precon-)]TJ 0 -13.549 Td [(ditioned)-300(is)-300(v)28(ery)-300(large,)-307(the)-300(use)-301(of)-300(man)28(y)-300(pro)-28(cessors,)-307(i.e.)-300(of)-300(man)28(y)-300(small)-300(submatrices,)-307(often)]TJ 0 -13.549 Td [(leads)-314(to)-314(a)-314(large)-314(coarse-lev)28(el)-314(syste)-1(m,)-317(whose)-314(s)-1(olu)1(tion)-314(ma)27(y)-314(b)-27(e)-314(com)-1(p)1(utationally)-314(exp)-28(ensiv)28(e.)]TJ 0 -13.549 Td [(On)-385(the)-384(other)-385(hand,)-397(the)-385(use)-385(of)-384(few)-385(pro)-28(cessors)-385(often)-384(leads)-385(to)-385(lo)-27(cal)-385(sumatrices)-385(that)-384(are)]TJ 0 -13.549 Td [(to)-28(o)-424(exp)-28(ensiv)28(e)-424(to)-424(b)-28(e)-424(pro)-27(cesse)-1(d)-423(on)-424(single)-424(pro)-28(cessors,)-447(b)-28(ecause)-424(of)-424(memory)-424(and/or)-424(com-)]TJ 0 -13.55 Td [(puting)-324(requiremen)28(ts.)-441(Therefore,)-326(it)-324(seems)-324(natural)-324(to)-324(use)-324(a)-323(re)-1(cur)1(s)-1(i)1(v)27(e)-324(approac)28(h,)-326(i)1(n)-324(whic)27(h)]TJ 0 -13.549 Td [(the)-394(coarse-)-1(lev)28(el)-394(correction)-395(is)-394(re-applied)-394(starting)-395(from)-394(the)-394(curren)27(t)-394(coarse-lev)28(el)-395(system.)]TJ 0 -13.549 Td [(The)-321(corresp)-28(onding)-320(prec)-1(on)1(ditioners,)-324(called)]TJ/F18 10.9091 Tf 202.455 0 Td [(multi-level)]TJ/F15 10.9091 Tf 53.694 0 Td [(preconditioners,)-323(can)-321(signi\014can)28(tly)]TJ -256.149 -13.549 Td [(reduce)-282(the)-283(computational)-282(cost)-282(of)-283(preconditioning)-282(with)-282(resp)-28(ect)-283(to)-282(the)-282(t)28(w)27(o-lev)28(el)-282(case)-283(\050see)]TJ 0 -13.549 Td [([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -96.9481 -370.2545 cm -BT -/F15 10.9091 Tf 96.9481 370.2545 Td[(15)]TJ -ET -1 0 0 1 107.8572 370.2545 cm + [(15)]TJ 0 g 0 G -1 0 0 1 -107.8572 -370.2545 cm -BT -/F15 10.9091 Tf 107.8572 370.2545 Td[(,)-320(Chap)1(te)-1(r)-317(3])1(\051.)-439(Add)1(itiv)28(e)-317(and)-316(h)28(ybr)1(id)-317(m)28(ult)1(ilev)28(e)-1(l)-317(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-318(ar)1(e)-318(obt)1(ained)-317(as)-317(dir)1(e)-1(ct)]TJ -13.9394 -13.5492 Td[(exte)-1(n)1(s)-1(i)1(ons)-359(of)-359(th)1(e)-360(t)28(w)28(o-)-1(lev)28(el)-359(c)-1(ou)1(n)28(terpar)1(ts)-1(.)-521(F)84(or)-359(a)-359(detailed)-359(d)1(e)-1(sc)-1(r)1(ition)-358(of)-359(th)1(e)-1(m,)-365(the)-359(reader)]TJ 0 -13.5492 Td[(is)-321(referred)-321(to)-321([)]TJ -ET -1 0 0 1 161.2428 343.1561 cm + [(,)-320(Chapter)-317(3]\051.)-439(Additiv)28(e)-318(and)-317(h)28(ybrid)-317(m)28(ultilev)28(el)-317(preconditioners)-317(are)-317(obtained)-317(as)-318(direct)]TJ 0 -13.549 Td [(extensions)-359(of)-359(the)-359(t)28(w)27(o-lev)28(el)-359(coun)28(terparts.)-522(F)84(or)-359(a)-359(detailed)-359(descrition)-359(of)-359(them,)-366(the)-359(reader)]TJ 0 -13.55 Td [(is)-321(referred)-321(to)-321([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -161.2428 -343.1561 cm -BT -/F15 10.9091 Tf 161.2428 343.1561 Td[(15)]TJ -ET -1 0 0 1 172.1519 343.1561 cm + [(15)]TJ 0 g 0 G -1 0 0 1 -172.1519 -343.1561 cm -BT -/F15 10.9091 Tf 172.1519 343.1561 Td[(,)-323(Chapter)-321(3])1(.)-441(Th)1(e)-322(algor)1(ith)1(m)-322(f)1(or)-321(the)-321(app)1(lication)-320(of)-321(a)-321(m)27(u)1(lti-lev)28(e)-1(l)-320(h)28(ybr)1(id)]TJ -78.2341 -13.5492 Td[(p)-27(os)-1(t-sm)-1(o)-28(ot)1(hed)-335(pr)1(e)-1(cond)1(ition)1(e)-1(r)]TJ/F24 10.9091 Tf 145.6759 0 Td[(M)]TJ/F15 10.9091 Tf 15.4287 0 Td[(to)-335(a)-335(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 55.2408 0 Td[(v)]TJ/F15 10.9091 Tf 5.6793 0 Td[(,)-335(i.e.)-335(for)-335(th)1(e)-336(comput)1(ation)-335(of)]TJ/F24 10.9091 Tf 135.9109 0 Td[(w)]TJ/F15 10.9091 Tf 11.1665 0 Td[(=)]TJ/F24 10.9091 Tf 11.5479 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(v)]TJ/F15 10.9091 Tf 5.6793 0 Td[(,)]TJ -409.4208 -13.5492 Td[(is)-311(rep)-27(orted,)-315(f)1(or)-311(example,)-315(in)-310(Figu)1(re)]TJ -ET -1 0 0 1 260.1405 316.0577 cm + [(,)-324(Chap)1(ter)-322(3])1(.)-441(The)-321(algorithm)-321(for)-321(the)-321(application)-321(of)-321(a)-321(m)28(ulti-lev)28(el)-321(h)28(ybrid)]TJ 0 -13.549 Td [(p)-28(ost-smo)-28(othed)-335(preconditioner)]TJ/F22 10.9091 Tf 145.676 0 Td [(M)]TJ/F15 10.9091 Tf 15.428 0 Td [(to)-335(a)-335(v)27(ector)]TJ/F22 10.9091 Tf 55.241 0 Td [(v)]TJ/F15 10.9091 Tf 5.68 0 Td [(,)-336(i.)1(e)-1(.)-335(for)-335(the)-335(computation)-335(of)]TJ/F22 10.9091 Tf 135.91 0 Td [(w)]TJ/F15 10.9091 Tf 11.167 0 Td [(=)]TJ/F22 10.9091 Tf 11.548 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(v)]TJ/F15 10.9091 Tf 5.68 0 Td [(,)]TJ -409.421 -13.549 Td [(is)-311(rep)-27(orted,)-316(for)-310(example,)-315(in)-311(Figure)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -260.1405 -316.0577 cm -BT -/F15 10.9091 Tf 260.1405 316.0577 Td[(1)]TJ -ET -1 0 0 1 265.5951 316.0577 cm + [-311(1)]TJ 0 g 0 G -1 0 0 1 -265.5951 -316.0577 cm -BT -/F15 10.9091 Tf 265.5951 316.0577 Td[(.)-437(Here)-311(th)1(e)-311(n)28(um)28(b)-28(er)-311(of)-310(lev)28(els)-311(is)-311(denoted)-310(b)28(y)]TJ/F24 10.9091 Tf 199.0322 0 Td[(nl)-20(ev)]TJ/F15 10.9091 Tf 24.1658 0 Td[(and)]TJ -394.8753 -13.5492 Td[(th)1(e)-360(le)-1(v)28(els)-360(ar)1(e)-360(n)28(um)28(b)-27(e)-1(red)-359(in)-359(i)1(nc)-1(r)1(e)-1(asin)1(g)-360(or)1(der)-360(start)1(ing)-359(fr)1(om)-360(the)-360(\014)1(nes)-1(t)-359(on)1(e)-1(,)-366(i)1(.e)-1(.)-359(th)1(e)-360(\014n)1(e)-1(st)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)-392(is)-392(le)-1(v)28(el)-392(1;)-422(th)1(e)-393(c)-1(oar)1(s)-1(e)-392(m)-1(atr)1(ix)-392(and)-392(th)1(e)-393(corres)-1(p)-27(ond)1(in)1(g)-393(b)1(as)-1(ic)-392(prec)-1(on)1(di)1(tioner)-392(at)-392(e)-1(ac)28(h)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)]TJ/F24 10.9091 Tf 24.8485 0 Td[(l)]TJ/F15 10.9091 Tf 7.1061 0 Td[(are)-333(denoted)-333(b)28(y)]TJ/F24 10.9091 Tf 74.5758 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.7772 Td[(l)]TJ/F15 10.9091 Tf 6.7566 1.7772 Td[(and)]TJ/F24 10.9091 Tf 21.2122 0 Td[(M)]TJ/F25 7.9701 Tf 10.5833 -1.7772 Td[(l)]TJ/F15 10.9091 Tf 3.1203 1.7772 Td[(,)-333(res)-1(p)-27(ec)-1(tiv)28(ely)84(,)-333(w)-1(i)1(th)]TJ/F24 10.9091 Tf 93.1213 0 Td[(A)]TJ/F22 7.9701 Tf 8.1818 -1.6363 Td[(1)]TJ/F15 10.9091 Tf 7.7626 1.6363 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(.)]TJ/F19 11.9552 Tf -285.1472 -29.3352 Td[(5.)-1(2)-1125(Sm)-1(o)-32(ot)-1(hed)-375(Agg)-1(reg)-1(ati)-1(on)]TJ/F15 10.9091 Tf 0 -20.6362 Td[(In)-411(or)1(der)-411(to)-411(d)1(e)-1(\014)1(ne)-411(the)-411(res)-1(tr)1(ic)-1(t)1(ion)-411(op)-27(e)-1(r)1(ator)]TJ/F24 10.9091 Tf 207.9903 0 Td[(R)]TJ/F25 7.9701 Tf 8.2832 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-430(whic)28(h)-411(is)-411(use)-1(d)-410(to)-411(com)-1(p)1(ute)-411(the)-411(c)-1(oar)1(s)-1(e-)]TJ -223.3703 -13.5492 Td[(lev)28(e)-1(l)-280(m)-1(atr)1(ix)]TJ/F24 10.9091 Tf 59.1879 0 Td[(A)]TJ/F25 7.9701 Tf 8.1819 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(,)-291(MLD2P)1(4)-281(use)-1(s)-281(th)1(e)]TJ/F20 10.9091 Tf 93.5509 0 Td[(smo)51(othe)51(d)-310(aggr)52(e)51(gation)]TJ/F15 10.9091 Tf 103.8759 0 Td[(algor)1(ithm)-281(d)1(e)-1(sc)-1(r)1(ib)-28(ed)-280(in)-281([)]TJ -ET -1 0 0 1 477.8507 211.8895 cm + [(.)-437(Here)-310(the)-311(n)28(um)28(b)-28(er)-311(of)-310(lev)27(els)-310(is)-311(denoted)-311(b)28(y)]TJ/F22 10.9091 Tf 370.709 0 Td [(nl)-20(ev)]TJ/F15 10.9091 Tf 24.166 0 Td [(and)]TJ -394.875 -13.549 Td [(the)-359(lev)27(els)-359(are)-360(n)28(um)28(b)-28(ered)-359(in)-360(i)1(ncre)-1(asin)1(g)-360(order)-359(starting)-360(from)-359(the)-359(\014nest)-360(one,)-366(i.e.)-359(the)-360(\014nest)]TJ 0 -13.549 Td [(lev)28(el)-393(is)-392(lev)28(el)-393(1;)-421(the)-393(coarse)-392(matrix)-393(and)-392(the)-392(corresp)-28(onding)-392(basic)-393(precondit)1(ioner)-393(at)-392(eac)28(h)]TJ 0 -13.55 Td [(lev)28(el)]TJ/F22 10.9091 Tf 24.848 0 Td [(l)]TJ/F15 10.9091 Tf 7.106 0 Td [(are)-333(denoted)-334(b)28(y)]TJ/F22 10.9091 Tf 74.576 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.777 Td [(l)]TJ/F15 10.9091 Tf 6.757 1.777 Td [(and)]TJ/F22 10.9091 Tf 21.212 0 Td [(M)]TJ/F23 7.9701 Tf 10.583 -1.777 Td [(l)]TJ/F15 10.9091 Tf 3.12 1.777 Td [(,)-333(resp)-28(ectiv)28(ely)83(,)-333(with)]TJ/F22 10.9091 Tf 93.122 0 Td [(A)]TJ/F20 7.9701 Tf 8.182 -1.636 Td [(1)]TJ/F15 10.9091 Tf 7.762 1.636 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(.)]TJ/F17 11.9552 Tf -285.147 -29.335 Td [(5.2)-1125(Smo)-31(othed)-375(Aggregation)]TJ/F15 10.9091 Tf 0 -20.636 Td [(In)-411(order)-411(to)-411(de\014ne)-411(the)-411(restriction)-411(op)-27(erator)]TJ/F22 10.9091 Tf 207.99 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(,)-430(whic)27(h)-411(is)-411(used)-411(to)-411(compu)1(te)-412(th)1(e)-411(c)-1(oar)1(s)-1(e-)]TJ -223.37 -13.549 Td [(lev)28(el)-281(matrix)]TJ/F22 10.9091 Tf 59.188 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.096 1.689 Td [(,)-291(MLD2P4)-281(uses)-281(the)]TJ/F18 10.9091 Tf 93.551 0 Td [(smo)51(othe)51(d)-309(aggr)51(e)51(gation)]TJ/F15 10.9091 Tf 103.876 0 Td [(algorithm)-281(describ)-28(ed)-280(in)-281([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -477.8507 -211.8895 cm -BT -/F15 10.9091 Tf 477.8507 211.8895 Td[(1)]TJ -ET -1 0 0 1 483.3053 211.8895 cm + [(1)]TJ 0 g 0 G -1 0 0 1 -483.3053 -211.8895 cm -BT -/F15 10.9091 Tf 483.3053 211.8895 Td[(,)]TJ -ET -1 0 0 1 489.3992 211.8895 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -489.3992 -211.8895 cm -BT -/F15 10.9091 Tf 489.3992 211.8895 Td[(19)]TJ -ET -1 0 0 1 500.3083 211.8895 cm + [-281(19)]TJ 0 g 0 G -1 0 0 1 -500.3083 -211.8895 cm -BT -/F15 10.9091 Tf 500.3083 211.8895 Td[(].)]TJ -406.3905 -13.5492 Td[(The)-443(b)1(as)-1(ic)-443(id)1(e)-1(a)-442(of)-442(this)-443(al)1(gorith)1(m)-443(is)-443(to)-443(b)1(uil)1(d)-443(a)-442(c)-1(oar)1(s)-1(e)-443(se)-1(t)-442(of)-443(v)28(erti)1(c)-1(es)]TJ/F24 10.9091 Tf 335.9388 0 Td[(W)]TJ/F25 7.9701 Tf 10.303 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 11.9257 1.6887 Td[(b)28(y)-442(s)-1(u)1(itab)1(ly)]TJ -358.1675 -13.5492 Td[(grou)1(pin)1(g)-330(th)1(e)-330(v)28(e)-1(r)1(tice)-1(s)-330(of)]TJ/F24 10.9091 Tf 116.0198 0 Td[(W)]TJ/F15 10.9091 Tf 15.414 0 Td[(in)28(t)1(o)-330(di)1(s)-1(j)1(oin)28(t)-329(s)-1(u)1(bse)-1(ts)-330(\050aggr)1(e)-1(gates)-1(\051,)-330(an)1(d)-329(to)-330(d)1(e)-1(\014)1(ne)-330(the)-330(coarse)-1(-)]TJ -131.4338 -13.5492 Td[(to-\014n)1(e)-254(s)-1(p)1(ac)-1(e)-254(tr)1(ansfer)-253(op)-28(erator)]TJ/F24 10.9091 Tf 144.0312 0 Td[(R)]TJ/F25 7.9701 Tf 8.3675 3.9588 Td[(T)]TJ -0.0843 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 9.8621 3.2328 Td[(b)28(y)-253(app)1(lyin)1(g)-254(a)-253(suitab)1(le)-254(sm)-1(o)-28(ot)1(her)-254(t)1(o)-254(a)-253(s)-1(impl)1(e)-254(piec)-1(ewise)]TJ -162.1765 -13.5492 Td[(constan)28(t)-333(prol)1(ongation)-332(op)-28(erator)1(,)-334(t)1(o)-334(imp)1(ro)28(v)28(e)-334(the)-333(qual)1(it)28(y)-333(of)-333(the)-334(coarse)-1(-space)-334(c)-1(or)1(rec)-1(ti)1(on.)]TJ 16.9365 -13.5706 Td[(Thr)1(e)-1(e)-334(main)-333(steps)-334(can)-333(b)-27(e)-334(iden)28(ti)1(\014ed)-333(in)-333(th)1(e)-334(s)-1(mo)-28(oth)1(e)-1(d)-333(aggr)1(e)-1(gati)1(on)-333(pr)1(o)-28(c)-1(edu)1(re:)]TJ -ET -1 0 0 1 93.9178 121.5209 cm + [(].)]TJ -271.893 -13.549 Td [(The)-443(basic)-442(idea)-443(of)-443(this)-442(algorithm)-443(is)-442(to)-443(build)-443(a)-442(coarse)-443(set)-443(of)-442(v)27(erti)1(c)-1(es)]TJ/F22 10.9091 Tf 335.939 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 11.925 1.689 Td [(b)28(y)-443(suitably)]TJ -358.167 -13.55 Td [(grouping)-329(the)-330(v)28(ertices)-330(of)]TJ/F22 10.9091 Tf 116.02 0 Td [(W)]TJ/F15 10.9091 Tf 15.414 0 Td [(in)28(to)-330(disjoin)28(t)-329(subsets)-330(\050aggregates\051,)-331(an)1(d)-330(to)-330(de\014ne)-329(the)-330(coarse-)]TJ -131.434 -13.549 Td [(to-\014ne)-253(space)-254(transfer)-253(op)-28(erator)]TJ/F22 10.9091 Tf 144.031 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(T)]TJ -0.084 -7.192 Td [(C)]TJ/F15 10.9091 Tf 9.862 3.233 Td [(b)28(y)-254(applyin)1(g)-254(a)-253(s)-1(u)1(itable)-254(smo)-28(other)-253(to)-254(a)-253(simple)-254(piecewise)]TJ -162.176 -13.549 Td [(constan)28(t)-334(p)1(rolongation)-334(op)-27(erator,)-334(to)-333(impro)28(v)28(e)-334(the)-333(qualit)28(y)-333(of)-334(the)-333(coarse-space)-334(correction.)]TJ 16.936 -13.571 Td [(Three)-333(main)-334(steps)-333(can)-333(b)-28(e)-334(id)1(e)-1(n)28(ti\014ed)-333(in)-333(the)-334(smo)-27(othed)-334(aggregation)-333(pro)-28(cedure:)]TJ 0 g 0 G -1 0 0 1 -93.9178 -121.5209 cm -BT -/F15 10.9091 Tf 107.2512 121.5209 Td[(1.)]TJ -ET -1 0 0 1 115.736 121.5209 cm + -3.603 -22.601 Td [(1.)]TJ 0 g 0 G -1 0 0 1 -115.736 -121.5209 cm -BT -/F15 10.9091 Tf 121.1906 121.5209 Td[(coars)-1(eni)1(ng)-333(of)-333(the)-333(v)28(e)-1(r)1(te)-1(x)-333(se)-1(t)]TJ/F24 10.9091 Tf 134.7274 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-333(to)-333(obtain)]TJ/F24 10.9091 Tf 53.9395 0 Td[(W)]TJ/F25 7.9701 Tf 10.303 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(;)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [-500(coarsening)-333(of)-334(the)-333(v)28(ertex)-333(s)-1(et)]TJ/F22 10.9091 Tf 148.667 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-333(to)-334(obtain)]TJ/F22 10.9091 Tf 53.94 0 Td [(W)]TJ/F23 7.9701 Tf 10.303 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.096 1.689 Td [(;)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -301 0 obj << +277 0 obj << /Type /Page -/Contents 302 0 R -/Resources 300 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 311 0 R -/Annots [ 304 0 R 305 0 R 306 0 R 307 0 R 308 0 R 309 0 R ] +/Contents 278 0 R +/Resources 276 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 281 0 R +/Annots [ 275 0 R 270 0 R 271 0 R 272 0 R 273 0 R 274 0 R ] >> endobj -304 0 obj << +275 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -305 0 obj << +270 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [95.9519 369.2582 108.8535 378.2811] +/Rect [95.952 369.258 108.853 378.281] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -306 0 obj << +271 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [160.2465 342.1598 173.1481 351.1827] +/Rect [160.247 342.16 173.148 351.183] /Subtype /Link /A << /S /GoTo /D (cite.dd2_96) >> >> endobj -307 0 obj << +272 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [259.1443 312.9402 266.5913 324.6297] +/Rect [259.144 312.94 266.591 324.63] /Subtype /Link /A << /S /GoTo /D (figure.1) >> >> endobj -308 0 obj << +273 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [476.8545 210.8932 484.3015 219.9161] +/Rect [476.854 210.893 484.302 219.916] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -309 0 obj << +274 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [488.4029 210.8932 501.3046 219.9161] +/Rect [488.403 210.893 501.305 219.916] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -303 0 obj << -/D [301 0 R /XYZ 93.9178 740.0018 null] +279 0 obj << +/D [277 0 R /XYZ 93.918 740.002 null] >> endobj 50 0 obj << -/D [301 0 R /XYZ 93.9178 257.9228 null] +/D [277 0 R /XYZ 93.918 257.923 null] >> endobj -310 0 obj << -/D [301 0 R /XYZ 93.9178 137.4749 null] +280 0 obj << +/D [277 0 R /XYZ 93.918 137.475 null] >> endobj -300 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F20 171 0 R /F24 176 0 R /F28 270 0 R /F22 273 0 R /F25 267 0 R /F30 279 0 R /F27 179 0 R /F19 105 0 R >> +276 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F18 163 0 R /F22 165 0 R /F26 249 0 R /F20 250 0 R /F23 248 0 R /F28 252 0 R /F25 166 0 R /F17 103 0 R >> /ProcSet [ /PDF /Text ] >> endobj -315 0 obj << -/Length 12725 +290 0 obj << +/Length 10087 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(14)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(14)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 66.6128 -138.7337 cm 0 g 0 G 0 g 0 G -1 0 0 1 5.4546 138.3352 cm +0 g 0 G +0 g 0 G +/F22 9.9626 Tf -124.174 -45.783 Td [(v)]TJ/F7 6.9738 Tf 4.83 -1.495 Td [(1)]TJ/F15 9.9626 Tf 7.236 1.495 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(v)]TJ/F15 9.9626 Tf 5.187 0 Td [(;)]TJ/F39 9.9626 Tf -27.769 -17.625 Td [(for)]TJ/F22 9.9626 Tf 17.767 0 Td [(l)]TJ/F15 9.9626 Tf 5.936 0 Td [(=)-278(2)]TJ/F22 9.9626 Tf 15.498 0 Td [(;)-167(nl)-19(ev)]TJ/F39 9.9626 Tf 27.22 0 Td [(do)]TJ/F15 9.9626 Tf -56.458 -14.789 Td [(!)-444(transfer)]TJ/F22 9.9626 Tf 44.113 0 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.495 Td [(l)]TJ/F13 6.9738 Tf 2.56 0 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F15 9.9626 Tf 7.79 1.495 Td [(to)-333(the)-334(next)-333(coarser)-333(lev)27(el)]TJ/F22 9.9626 Tf -65.518 -11.956 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.826 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(R)]TJ/F10 6.9738 Tf 7.564 -1.494 Td [(l)]TJ/F22 9.9626 Tf 3.058 1.494 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.494 Td [(l)]TJ/F13 6.9738 Tf 2.56 0 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F39 9.9626 Tf -55.372 -13.295 Td [(endfor)]TJ/F15 9.9626 Tf 0 -17.625 Td [(!)-444(apply)-334(the)-333(coarsest-lev)28(el)-334(correction)]TJ/F22 9.9626 Tf 0 -15.177 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(nl)-6(ev)]TJ/F15 9.9626 Tf 18.765 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(A)]TJ/F13 6.9738 Tf 7.472 4.262 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F10 6.9738 Tf -6.227 -7.267 Td [(nl)-6(ev)]TJ/F22 9.9626 Tf 15.998 3.005 Td [(v)]TJ/F10 6.9738 Tf 4.83 -1.494 Td [(nl)-6(ev)]TJ/F39 9.9626 Tf -62.466 -16.131 Td [(for)]TJ/F22 9.9626 Tf 17.767 0 Td [(l)]TJ/F15 9.9626 Tf 5.936 0 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(nl)-20(ev)]TJ/F25 9.9626 Tf 21.188 0 Td [(\000)]TJ/F15 9.9626 Tf 9.963 0 Td [(1)]TJ/F22 9.9626 Tf 4.981 0 Td [(;)]TJ/F15 9.9626 Tf 4.428 0 Td [(1)]TJ/F22 9.9626 Tf 4.981 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(\000)]TJ/F15 9.9626 Tf 7.749 0 Td [(1)]TJ/F39 9.9626 Tf 8.8 0 Td [(do)]TJ/F15 9.9626 Tf -90.774 -14.789 Td [(!)-444(transfer)]TJ/F22 9.9626 Tf 44.112 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.495 Td [(l)]TJ/F7 6.9738 Tf 2.56 0 Td [(+1)]TJ/F15 9.9626 Tf 13.906 1.495 Td [(to)-333(the)-334(next)-333(\014ner)-333(lev)28(e)-1(l)]TJ/F22 9.9626 Tf -65.463 -11.968 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(R)]TJ/F10 6.9738 Tf 7.641 3.616 Td [(T)]TJ -0.076 -6.437 Td [(l)]TJ/F7 6.9738 Tf 2.559 0 Td [(+1)]TJ/F22 9.9626 Tf 10.586 2.821 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(l)]TJ/F7 6.9738 Tf 2.56 0 Td [(+1)]TJ/F15 9.9626 Tf 10.585 1.494 Td [(;)]TJ -59.965 -14.855 Td [(!)-444(com)-1(p)1(ute)-334(the)-333(residual)-333(at)-334(the)-333(curren)28(t)-334(lev)28(el)]TJ/F22 9.9626 Tf 0 -12.342 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.495 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.495 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(v)]TJ/F10 6.9738 Tf 4.829 -1.495 Td [(l)]TJ/F25 9.9626 Tf 5.272 1.495 Td [(\000)]TJ/F22 9.9626 Tf 9.963 0 Td [(A)]TJ/F13 6.9738 Tf 7.472 4.262 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F10 6.9738 Tf -6.226 -7.268 Td [(l)]TJ/F22 9.9626 Tf 10.696 3.006 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(l)]TJ/F15 9.9626 Tf 3.058 1.495 Td [(;)]TJ -67.01 -14.79 Td [(!)-444(apply)-334(the)-333(basic)-333(Sc)27(h)28(w)28(arz)-333(preconditioner)-334(to)-333(the)-333(residual)]TJ/F22 9.9626 Tf 0 -12.343 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(M)]TJ/F13 6.9738 Tf 10.752 4.262 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F10 6.9738 Tf -7.313 -7.267 Td [(l)]TJ/F22 9.9626 Tf 11.783 3.005 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.494 Td [(l)]TJ/F15 9.9626 Tf -46.778 -13.295 Td [(!)-444(up)-28(date)]TJ/F22 9.9626 Tf 40.681 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(l)]TJ/F22 9.9626 Tf -45.565 -10.461 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.825 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(l)]TJ/F15 9.9626 Tf 5.272 1.494 Td [(+)]TJ/F22 9.9626 Tf 9.963 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(l)]TJ/F39 9.9626 Tf -55.803 -10.461 Td [(endfor)]TJ/F22 9.9626 Tf 0 -14.79 Td [(w)]TJ/F15 9.9626 Tf 10.168 0 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(y)]TJ/F7 6.9738 Tf 4.885 -1.494 Td [(1)]TJ/F15 9.9626 Tf 4.469 1.494 Td [(;)]TJ +ET q -[]0 d -0 J -0.3985 w -0 0.1992 m -268.3164 0.1992 l -S +1 0 0 1 213.806 714.896 cm +[]0 d 0 J 0.398 w 0 0 m 268.316 0 l S Q -1 0 0 1 0 -271.2158 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 271.2158 l -S +1 0 0 1 214.005 443.282 cm +[]0 d 0 J 0.398 w 0 0 m 0 271.614 l S Q -1 0 0 1 1.5691 259.8584 cm -0 g 0 G -0 g 0 G -1 0 0 1 -215.375 -703.3393 cm -BT -/F24 9.9626 Tf 220.8295 694.2188 Td[(v)]TJ/F7 6.9738 Tf 4.8291 -1.4944 Td[(1)]TJ/F15 9.9626 Tf 7.2367 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(v)]TJ/F15 9.9626 Tf 5.1866 0 Td[(;)]TJ/F41 9.9626 Tf -27.7685 -17.6244 Td[(for)]TJ/F24 9.9626 Tf 17.7666 0 Td[(l)]TJ/F15 9.9626 Tf 5.936 0 Td[(=)-278(2)]TJ/F24 9.9626 Tf 15.4974 0 Td[(;)-166(n)-1(l)-20(e)1(v)]TJ/F41 9.9626 Tf 27.2209 0 Td[(do)]TJ/F15 9.9626 Tf -56.4583 -14.7898 Td[(!)-444(tran)1(s)-1(f)1(e)-1(r)]TJ/F24 9.9626 Tf 44.1125 0 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F13 6.9738 Tf 2.5599 0 Td[(\000)]TJ/F7 6.9738 Tf 6.2266 0 Td[(1)]TJ/F15 9.9626 Tf 7.7903 1.4944 Td[(to)-333(the)-333(next)-333(c)-1(oarser)-333(le)-1(v)28(el)]TJ/F24 9.9626 Tf -65.5183 -11.9552 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(R)]TJ/F10 6.9738 Tf 7.5645 -1.4944 Td[(l)]TJ/F24 9.9626 Tf 3.058 1.4944 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F13 6.9738 Tf 2.5599 0 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F41 9.9626 Tf -55.3714 -13.2954 Td[(endfor)]TJ/F15 9.9626 Tf 0 -17.6244 Td[(!)-444(app)1(ly)-333(the)-333(c)-1(oarses)-1(t-lev)28(e)-1(l)-333(correc)-1(ti)1(on)]TJ/F24 9.9626 Tf 0 -15.1773 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(nl)-6(ev)]TJ/F15 9.9626 Tf 18.7654 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(A)]TJ/F13 6.9738 Tf 7.472 4.2618 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F10 6.9738 Tf -6.2267 -7.2671 Td[(nl)-6(ev)]TJ/F24 9.9626 Tf 15.9981 3.0053 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(nl)-6(ev)]TJ/F41 9.9626 Tf -62.4652 -16.13 Td[(for)]TJ/F24 9.9626 Tf 17.7666 0 Td[(l)]TJ/F15 9.9626 Tf 5.936 0 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(nl)-20(ev)]TJ/F27 9.9626 Tf 21.1879 0 Td[(\000)]TJ/F15 9.9626 Tf 9.9626 0 Td[(1)]TJ/F24 9.9626 Tf 4.9813 0 Td[(;)]TJ/F15 9.9626 Tf 4.4278 0 Td[(1)]TJ/F24 9.9626 Tf 4.9814 0 Td[(;)]TJ/F27 9.9626 Tf 4.4278 0 Td[(\000)]TJ/F15 9.9626 Tf 7.7487 0 Td[(1)]TJ/F41 9.9626 Tf 8.8003 0 Td[(do)]TJ/F15 9.9626 Tf -90.7739 -14.7898 Td[(!)-444(tran)1(s)-1(f)1(e)-1(r)]TJ/F24 9.9626 Tf 44.1124 0 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F7 6.9738 Tf 2.5599 0 Td[(+1)]TJ/F15 9.9626 Tf 13.9062 1.4944 Td[(to)-333(the)-333(next)-333(\014ner)-333(lev)28(e)-1(l)]TJ/F24 9.9626 Tf -65.463 -11.9674 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(R)]TJ/F10 6.9738 Tf 7.6415 3.6153 Td[(T)]TJ -0.077 -6.4368 Td[(l)]TJ/F7 6.9738 Tf 2.5599 0 Td[(+1)]TJ/F24 9.9626 Tf 10.5854 2.8215 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F7 6.9738 Tf 2.5598 0 Td[(+1)]TJ/F15 9.9626 Tf 10.5854 1.4944 Td[(;)]TJ -59.9654 -14.855 Td[(!)-444(c)-1(ompu)1(te)-334(th)1(e)-334(res)-1(i)1(du)1(al)-334(at)-333(th)1(e)-334(c)-1(u)1(rr)1(e)-1(n)28(t)-333(lev)28(e)-1(l)]TJ/F24 9.9626 Tf 0 -12.3426 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(v)]TJ/F10 6.9738 Tf 4.8291 -1.4944 Td[(l)]TJ/F27 9.9626 Tf 5.2719 1.4944 Td[(\000)]TJ/F24 9.9626 Tf 9.9626 0 Td[(A)]TJ/F13 6.9738 Tf 7.472 4.2618 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F10 6.9738 Tf -6.2267 -7.2671 Td[(l)]TJ/F24 9.9626 Tf 10.696 3.0053 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 3.058 1.4944 Td[(;)]TJ -67.0102 -14.7898 Td[(!)-444(app)1(ly)-333(the)-333(basic)-334(Sc)28(h)28(w)28(arz)-334(p)1(re)-1(cond)1(ition)1(e)-1(r)-333(to)-333(th)1(e)-334(res)-1(i)1(dual)]TJ/F24 9.9626 Tf 0 -12.3426 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(M)]TJ/F13 6.9738 Tf 10.7513 4.2618 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F10 6.9738 Tf -7.3128 -7.2671 Td[(l)]TJ/F24 9.9626 Tf 11.7822 3.0053 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F15 9.9626 Tf -46.7782 -13.2954 Td[(!)-444(up)-27(date)]TJ/F24 9.9626 Tf 40.6809 0 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F24 9.9626 Tf -45.5654 -10.4608 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.8253 1.4944 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(y)]TJ/F10 6.9738 Tf 4.8845 -1.4944 Td[(l)]TJ/F15 9.9626 Tf 5.2719 1.4944 Td[(+)]TJ/F24 9.9626 Tf 9.9626 0 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(l)]TJ/F41 9.9626 Tf -55.8022 -10.4608 Td[(endfor)]TJ/F24 9.9626 Tf 0 -14.7898 Td[(w)]TJ/F15 9.9626 Tf 10.1678 0 Td[(=)]TJ/F24 9.9626 Tf 10.5161 0 Td[(y)]TJ/F7 6.9738 Tf 4.8845 -1.4944 Td[(1)]TJ/F15 9.9626 Tf 4.4694 1.4944 Td[(;)]TJ -ET -1 0 0 1 481.7238 443.4809 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 271.2158 l -S +1 0 0 1 481.923 443.282 cm +[]0 d 0 J 0.398 w 0 0 m 0 271.614 l S Q -1 0 0 1 -267.9179 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -268.3164 0.1992 l -S +1 0 0 1 213.806 443.282 cm +[]0 d 0 J 0.398 w 0 0 m 268.316 0 l S Q -1 0 0 1 -51.4936 -18.5347 cm 0 g 0 G -1 0 0 1 -162.3123 -424.5477 cm BT -/F15 10.9091 Tf 162.3123 424.5477 Td[(Figu)1(re)-334(1:)-444(Ap)1(pli)1(c)-1(ation)-332(of)-333(the)-334(m)28(ul)1(ti-le)-1(v)28(el)-333(h)28(yb)1(rid)-333(p)-27(ost-)-1(smo)-28(othed)-333(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ -ET -1 0 0 1 533.6158 424.5477 cm +/F15 10.9091 Tf 162.312 424.548 Td [(Figure)-333(1:)-445(Application)-333(of)-333(the)-333(m)27(ulti-lev)28(el)-333(h)28(ybrid)-334(p)-27(ost-sm)-1(o)-27(othed)-334(pr)1(e)-1(cond)1(itioner.)]TJ 0 g 0 G -1 0 0 1 -391.8773 -14.0763 cm 0 g 0 G -1 0 0 1 0 -32.1522 cm 0 g 0 G -1 0 0 1 -141.7385 -378.3192 cm -BT -/F15 10.9091 Tf 155.0719 378.3192 Td[(2.)]TJ -ET -1 0 0 1 163.5567 378.3192 cm + -7.24 -46.229 Td [(2.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -378.3192 cm -BT -/F15 10.9091 Tf 169.0113 378.3192 Td[(construction)-333(of)-332(the)-334(p)1(rolon)1(gator)]TJ/F24 10.9091 Tf 152.5759 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(T)]TJ -0.0842 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 7.0968 3.2328 Td[(;)]TJ -ET -1 0 0 1 141.7385 353.2676 cm + [-500(construction)-333(of)-334(th)1(e)-334(prolongator)]TJ/F22 10.9091 Tf 166.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.368 3.959 Td [(T)]TJ -0.085 -7.192 Td [(C)]TJ/F15 10.9091 Tf 7.097 3.233 Td [(;)]TJ 0 g 0 G -1 0 0 1 -141.7385 -353.2676 cm -BT -/F15 10.9091 Tf 155.0719 353.2676 Td[(3.)]TJ -ET -1 0 0 1 163.5567 353.2676 cm + -181.895 -25.051 Td [(3.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -353.2676 cm -BT -/F15 10.9091 Tf 169.0113 353.2676 Td[(app)1(lication)-333(of)]TJ/F24 10.9091 Tf 68.7879 0 Td[(R)]TJ/F25 7.9701 Tf 8.2832 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.7331 1.6887 Td[(and)]TJ/F24 10.9091 Tf 21.2122 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(T)]TJ -0.0843 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 10.7332 3.2328 Td[(to)-333(bu)1(ild)]TJ/F24 10.9091 Tf 41.2122 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 7.0968 1.6887 Td[(.)]TJ -194.8598 -25.0516 Td[(T)83(o)-426(p)-28(erf)1(orm)-426(the)-427(coarse)-1(n)1(ing)-426(ste)-1(p)1(,)-449(w)27(e)-427(h)1(a)28(v)28(e)-427(impleme)-1(n)28(t)1(e)-1(d)-426(th)1(e)-427(aggregation)-426(al)1(gorith)1(m)]TJ -16.9365 -13.5492 Td[(sk)28(e)-1(tc)28(hed)-389(i)1(n)-388([)]TJ -ET -1 0 0 1 202.6998 314.6668 cm + [-500(application)-333(of)]TJ/F22 10.9091 Tf 82.727 0 Td [(R)]TJ/F23 7.9701 Tf 8.283 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(and)]TJ/F22 10.9091 Tf 21.213 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.958 Td [(T)]TJ -0.084 -7.191 Td [(C)]TJ/F15 10.9091 Tf 10.733 3.233 Td [(to)-333(build)]TJ/F22 10.9091 Tf 41.212 0 Td [(A)]TJ/F23 7.9701 Tf 8.182 -1.689 Td [(C)]TJ/F15 10.9091 Tf 7.097 1.689 Td [(.)]TJ -194.86 -25.052 Td [(T)83(o)-426(p)-28(erform)-426(the)-426(coarsening)-426(s)-1(tep,)-449(w)28(e)-427(ha)28(v)28(e)-426(implemen)27(ted)-426(the)-426(aggregation)-426(algorithm)]TJ -16.937 -13.549 Td [(sk)28(etc)27(hed)-388(in)-388([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -202.6998 -314.6668 cm -BT -/F15 10.9091 Tf 202.6998 314.6668 Td[(4)]TJ -ET -1 0 0 1 208.1543 314.6668 cm + [(4)]TJ 0 g 0 G -1 0 0 1 -208.1543 -314.6668 cm -BT -/F15 10.9091 Tf 208.1543 314.6668 Td[(].)-610(Accordi)1(ng)-388(to)-389([)]TJ -ET -1 0 0 1 290.2848 314.6668 cm + [(].)-610(According)-389(to)-388([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -290.2848 -314.6668 cm -BT -/F15 10.9091 Tf 290.2848 314.6668 Td[(19)]TJ -ET -1 0 0 1 301.1939 314.6668 cm + [(19)]TJ 0 g 0 G -1 0 0 1 -301.1939 -314.6668 cm -BT -/F15 10.9091 Tf 301.1939 314.6668 Td[(],)-402(a)-388(m)-1(o)-27(di\014)1(c)-1(ati)1(on)-389(of)-388(t)1(his)-389(algor)1(ith)1(m)-389(has)-389(b)-27(e)-1(en)-388(actuall)1(y)]TJ -159.4554 -13.5492 Td[(considered,)-256(in)-237(whic)28(h)-237(e)-1(ac)28(h)-237(aggre)-1(gat)1(e)]TJ/F24 10.9091 Tf 169.0404 0 Td[(N)]TJ/F25 7.9701 Tf 8.7651 -1.6364 Td[(r)]TJ/F15 10.9091 Tf 7.1452 1.6364 Td[(is)-238(made)-237(of)-237(v)28(e)-1(rt)1(ic)-1(es)-238(of)]TJ/F24 10.9091 Tf 99.1645 0 Td[(W)]TJ/F15 10.9091 Tf 14.4087 0 Td[(th)1(at)-238(ar)1(e)]TJ/F20 10.9091 Tf 39.7567 0 Td[(str)51(ongly)-269(c)51(ou)1(ple)51(d)]TJ/F15 10.9091 Tf -338.2806 -13.5492 Td[(to)-333(a)-334(certain)-333(r)1(o)-28(ot)-333(v)28(e)-1(r)1(te)-1(x)]TJ/F24 10.9091 Tf 115.2426 0 Td[(r)]TJ/F27 10.9091 Tf 8.255 0 Td[(2)]TJ/F24 10.9091 Tf 10.303 0 Td[(W)]TJ/F15 10.9091 Tf 11.8182 0 Td[(,)-333(i.e.)]TJ/F24 10.9091 Tf -39.6838 -28.5239 Td[(N)]TJ/F25 7.9701 Tf 8.7651 -1.6364 Td[(r)]TJ/F15 10.9091 Tf 7.585 1.6364 Td[(=)]TJ/F30 10.9091 Tf 11.5151 12.1092 Td[(n)]TJ/F24 10.9091 Tf 7.2728 -12.1092 Td[(s)]TJ/F27 10.9091 Tf 8.1438 0 Td[(2)]TJ/F24 10.9091 Tf 10.303 0 Td[(W)]TJ/F15 10.9091 Tf 14.8485 0 Td[(:)]TJ/F27 10.9091 Tf 6.0605 0 Td[(j)]TJ/F24 10.9091 Tf 3.0303 0 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(r)-30(s)]TJ/F27 10.9091 Tf 8.4707 1.6364 Td[(j)]TJ/F24 10.9091 Tf 6.0606 0 Td[(>)-278(\022)]TJ/F30 10.9091 Tf 16.9393 9.8599 Td[(p)]TJ + [(],)-403(a)-388(mo)-28(di\014cation)-388(of)-389(this)-388(algorithm)-389(has)-388(b)-28(een)-388(actually)]TJ 0 -13.549 Td [(considered,)-257(in)-237(whic)28(h)-238(eac)28(h)-237(aggregate)]TJ/F22 10.9091 Tf 169.041 0 Td [(N)]TJ/F23 7.9701 Tf 8.765 -1.637 Td [(r)]TJ/F15 10.9091 Tf 7.145 1.637 Td [(is)-237(m)-1(ad)1(e)-238(of)-237(v)27(ertices)-237(of)]TJ/F22 10.9091 Tf 99.165 0 Td [(W)]TJ/F15 10.9091 Tf 14.408 0 Td [(that)-237(are)]TJ/F18 10.9091 Tf 39.757 0 Td [(str)51(ongly)-269(c)51(ouple)51(d)]TJ/F15 10.9091 Tf -338.281 -13.55 Td [(to)-333(a)-334(certain)-333(ro)-28(ot)-333(v)28(ertex)]TJ/F22 10.9091 Tf 115.243 0 Td [(r)]TJ/F25 10.9091 Tf 8.255 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(W)]TJ/F15 10.9091 Tf 11.818 0 Td [(,)-333(i.e.)]TJ/F22 10.9091 Tf -39.684 -28.523 Td [(N)]TJ/F23 7.9701 Tf 8.766 -1.637 Td [(r)]TJ/F15 10.9091 Tf 7.585 1.637 Td [(=)]TJ/F28 10.9091 Tf 11.515 12.109 Td [(n)]TJ/F22 10.9091 Tf 7.272 -12.109 Td [(s)]TJ/F25 10.9091 Tf 8.144 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(W)]TJ/F15 10.9091 Tf 14.849 0 Td [(:)]TJ/F25 10.9091 Tf 6.06 0 Td [(j)]TJ/F22 10.9091 Tf 3.031 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.637 Td [(r)-29(s)]TJ/F25 10.9091 Tf 8.471 1.637 Td [(j)]TJ/F22 10.9091 Tf 6.06 0 Td [(>)-278(\022)]TJ/F28 10.9091 Tf 16.94 9.859 Td [(p)]TJ ET -1 0 0 1 373.3437 268.9044 cm q -[]0 d -0 J -0.4364 w -0 0.2182 m -34.5348 0.2182 l -S +1 0 0 1 373.344 269.123 cm +[]0 d 0 J 0.436 w 0 0 m 34.535 0 l S Q -1 0 0 1 -373.3437 -268.9044 cm BT -/F27 10.9091 Tf 373.3437 259.0445 Td[(j)]TJ/F24 10.9091 Tf 3.0303 0 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(r)-30(r)]TJ/F24 10.9091 Tf 8.6114 1.6364 Td[(a)]TJ/F25 7.9701 Tf 5.7664 -1.6364 Td[(ss)]TJ/F27 10.9091 Tf 8.33 1.6364 Td[(j)]TJ/F30 10.9091 Tf 3.0303 12.1091 Td[(o)]TJ/F27 10.9091 Tf 9.6969 -12.1091 Td[([)-222(f)]TJ/F24 10.9091 Tf 15.1515 0 Td[(r)]TJ/F27 10.9091 Tf 5.2248 0 Td[(g)]TJ/F24 10.9091 Tf 7.2727 0 Td[(;)]TJ/F15 10.9091 Tf -303.4859 -29.1301 Td[(for)-340(a)-341(giv)28(en)]TJ/F24 10.9091 Tf 54.5168 0 Td[(\022)]TJ/F27 10.9091 Tf 8.5901 0 Td[(2)]TJ/F15 10.9091 Tf 10.4386 0 Td[([0)]TJ/F24 10.9091 Tf 8.4849 0 Td[(;)]TJ/F15 10.9091 Tf 4.8484 0 Td[(1].)-466(Sin)1(c)-1(e)-341(th)1(is)-341(algorith)1(m)-341(has)-341(a)-341(se)-1(q)1(uen)28(tial)-340(natu)1(re)-1(,)-342(a)]TJ/F20 10.9091 Tf 242.9761 0 Td[(de)51(c)51(oupl)1(e)51(d)]TJ/F15 10.9091 Tf 49.1719 0 Td[(v)28(ers)-1(i)1(on)]TJ -379.0268 -13.5492 Td[(of)-398(it)-399(has)-399(b)-27(e)-1(en)-399(c)28(hose)-1(n)1(,)-415(w)-1(h)1(e)-1(r)1(e)-400(eac)27(h)-398(pro)-27(c)-1(es)-1(sor)]TJ/F24 10.9091 Tf 216.2363 0 Td[(i)]TJ/F15 10.9091 Tf 8.1102 0 Td[(in)1(dep)-28(end)1(e)-1(n)29(tly)-399(ap)1(pli)1(e)-1(s)-399(the)-399(algori)1(thm)-399(to)]TJ -224.3465 -13.5492 Td[(th)1(e)-422(se)-1(t)-420(of)-421(v)28(ertice)-1(s)]TJ/F24 10.9091 Tf 91.547 0 Td[(W)]TJ/F22 7.9701 Tf 11.8182 3.9589 Td[(0)]TJ/F25 7.9701 Tf -1.5152 -7.0144 Td[(i)]TJ/F15 10.9091 Tf 10.8388 3.0555 Td[(ass)-1(ign)1(e)-1(d)-420(to)-421(it)-420(in)-421(t)1(he)-421(ini)1(tial)-421(d)1(ata)-421(di)1(s)-1(tr)1(ibu)1(tion.)-706(T)-1(h)1(is)-421(v)28(e)-1(r)1(s)-1(ion)-420(is)]TJ -112.6888 -13.5492 Td[(em)27(bar)1(rass)-1(in)1(gly)-250(p)1(arallel,)-267(sin)1(c)-1(e)-250(it)-250(do)-28(es)-251(n)1(ot)-250(re)-1(q)1(uir)1(e)-251(an)28(y)-250(d)1(ata)-250(c)-1(omm)27(u)1(nication)1(.)-417(On)-249(the)-250(other)]TJ 0 -13.5492 Td[(han)1(d,)-311(it)-306(ma)27(y)-306(p)1(ro)-28(d)1(uce)-307(non)1(-)-1(u)1(ni)1(form)-306(aggregate)-1(s)-306(near)-306(b)-28(ou)1(nd)1(ary)-306(v)28(e)-1(r)1(tice)-1(s,)-312(i.)1(e)-1(.)-306(n)1(e)-1(ar)-306(v)28(ertice)-1(s)]TJ 0 -13.5492 Td[(adj)1(ac)-1(en)28(t)-403(to)-403(v)28(ertices)-404(in)-402(other)-403(pr)1(o)-28(c)-1(es)-1(sors,)-420(and)-403(i)1(s)-404(strongl)1(y)-403(dep)-28(end)1(e)-1(n)29(t)-403(on)-403(th)1(e)-404(n)28(u)1(m)27(b)-27(e)-1(r)-402(of)]TJ 0 -13.5492 Td[(pr)1(o)-28(ce)-1(ss)-1(or)1(s)-315(and)-313(on)-314(th)1(e)-315(in)1(itial)-313(parti)1(tioni)1(ng)-314(of)-314(th)1(e)-315(matri)1(x)]TJ/F24 10.9091 Tf 263.5655 0 Td[(A)]TJ/F15 10.9091 Tf 8.1818 0 Td[(.)-438(Nev)28(e)-1(r)1(theles)-1(s,)-318(thi)1(s)-315(algor)1(ithm)]TJ -271.7473 -13.5492 Td[(has)-260(b)-27(ee)-1(n)-259(c)27(h)1(os)-1(en)-259(for)-259(the)-260(imp)1(le)-1(men)28(tation)-259(in)-259(MLD)1(2P4,)-274(s)-1(i)1(nce)-261(i)1(t)-260(h)1(as)-260(b)-28(ee)-1(n)-259(sho)28(wn)-260(t)1(o)-260(pr)1(o)-28(du)1(c)-1(e)]TJ 0 -13.5492 Td[(go)-28(o)-28(d)-332(re)-1(sul)1(ts)-334(in)-333(p)1(ractice)-334([)]TJ -ET -1 0 0 1 260.1022 121.5209 cm +/F25 10.9091 Tf 373.344 259.044 Td [(j)]TJ/F22 10.9091 Tf 3.03 0 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.636 Td [(r)-30(r)]TJ/F22 10.9091 Tf 8.612 1.636 Td [(a)]TJ/F23 7.9701 Tf 5.766 -1.636 Td [(ss)]TJ/F25 10.9091 Tf 8.33 1.636 Td [(j)]TJ/F28 10.9091 Tf 3.03 12.11 Td [(o)]TJ/F25 10.9091 Tf 9.697 -12.11 Td [([)-222(f)]TJ/F22 10.9091 Tf 15.152 0 Td [(r)]TJ/F25 10.9091 Tf 5.225 0 Td [(g)]TJ/F22 10.9091 Tf 7.272 0 Td [(;)]TJ/F15 10.9091 Tf -303.486 -29.13 Td [(for)-341(a)-341(giv)28(en)]TJ/F22 10.9091 Tf 54.517 0 Td [(\022)]TJ/F25 10.9091 Tf 8.59 0 Td [(2)]TJ/F15 10.9091 Tf 10.439 0 Td [([0)]TJ/F22 10.9091 Tf 8.485 0 Td [(;)]TJ/F15 10.9091 Tf 4.848 0 Td [(1].)-467(Since)-341(this)-340(algorithm)-341(has)-341(a)-341(sequen)28(tial)-341(natur)1(e)-1(,)-342(a)]TJ/F18 10.9091 Tf 242.976 0 Td [(de)51(c)51(ouple)51(d)]TJ/F15 10.9091 Tf 49.172 0 Td [(v)28(ersion)]TJ -379.027 -13.549 Td [(of)-399(it)-399(has)-399(b)-27(e)-1(en)-398(c)27(hosen,)-415(where)-399(eac)28(h)-399(pro)-28(cessor)]TJ/F22 10.9091 Tf 216.237 0 Td [(i)]TJ/F15 10.9091 Tf 8.11 0 Td [(indep)-28(enden)28(tly)-399(applies)-399(the)-399(al)1(gorithm)-399(to)]TJ -224.347 -13.549 Td [(the)-421(set)-421(of)-421(v)28(ertices)]TJ/F22 10.9091 Tf 91.547 0 Td [(W)]TJ/F20 7.9701 Tf 11.819 3.959 Td [(0)]TJ/F23 7.9701 Tf -1.515 -7.014 Td [(i)]TJ/F15 10.9091 Tf 10.838 3.055 Td [(assigned)-421(to)-421(it)-421(in)-420(the)-421(initial)-421(data)-421(distribution.)-707(This)-420(v)27(ersion)-421(is)]TJ -112.689 -13.549 Td [(em)28(barrassingly)-250(parallel,)-267(since)-250(it)-251(do)-27(es)-251(not)-250(require)-250(an)28(y)-250(data)-251(comm)28(unication.)-416(On)-251(the)-250(other)]TJ 0 -13.549 Td [(hand,)-312(it)-306(ma)28(y)-306(pro)-28(duce)-306(non-uniform)-307(aggregates)-306(near)-306(b)-28(oundary)-306(v)28(ertices,)-312(i.e.)-306(near)-307(v)28(ertices)]TJ 0 -13.55 Td [(adjacen)28(t)-403(to)-403(v)27(ertices)-403(in)-403(other)-403(pro)-28(cessors,)-420(and)-403(is)-404(strongly)-403(dep)-27(enden)27(t)-403(on)-403(the)-403(n)28(um)28(b)-28(er)-403(of)]TJ 0 -13.549 Td [(pro)-28(cessors)-314(and)-314(on)-314(the)-314(initial)-314(partitioning)-314(of)-314(the)-314(matrix)]TJ/F22 10.9091 Tf 263.566 0 Td [(A)]TJ/F15 10.9091 Tf 8.182 0 Td [(.)-438(Nev)28(ertheless,)-318(this)-314(algorithm)]TJ -271.748 -13.549 Td [(has)-260(b)-27(ee)-1(n)-259(c)28(hosen)-260(for)-260(the)-259(implemen)28(tation)-260(in)-260(MLD2P)1(4,)-275(since)-260(it)-259(has)-260(b)-28(een)-259(sho)28(wn)-260(to)-260(pro)-27(duce)]TJ 0 -13.549 Td [(go)-28(o)-28(d)-333(results)-333(in)-334(p)1(ractic)-1(e)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -260.1022 -121.5209 cm -BT -/F15 10.9091 Tf 260.1022 121.5209 Td[(3)]TJ -ET -1 0 0 1 265.5568 121.5209 cm + [(3)]TJ 0 g 0 G -1 0 0 1 -265.5568 -121.5209 cm -BT -/F15 10.9091 Tf 265.5568 121.5209 Td[(,)]TJ -ET -1 0 0 1 272.2235 121.5209 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -272.2235 -121.5209 cm -BT -/F15 10.9091 Tf 272.2235 121.5209 Td[(4)]TJ -ET -1 0 0 1 277.678 121.5209 cm + [-333(4)]TJ 0 g 0 G -1 0 0 1 -277.678 -121.5209 cm -BT -/F15 10.9091 Tf 277.678 121.5209 Td[(,)]TJ -ET -1 0 0 1 284.3447 121.5209 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -284.3447 -121.5209 cm -BT -/F15 10.9091 Tf 284.3447 121.5209 Td[(18)]TJ -ET -1 0 0 1 295.2538 121.5209 cm + [-333(18)]TJ 0 g 0 G -1 0 0 1 -295.2538 -121.5209 cm -BT -/F15 10.9091 Tf 295.2538 121.5209 Td[(].)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [(].)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -314 0 obj << +289 0 obj << /Type /Page -/Contents 315 0 R -/Resources 313 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 311 0 R -/Annots [ 328 0 R 329 0 R 330 0 R 331 0 R 332 0 R ] +/Contents 290 0 R +/Resources 288 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 281 0 R +/Annots [ 283 0 R 284 0 R 285 0 R 286 0 R 287 0 R ] >> endobj -328 0 obj << +283 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [201.7035 313.6705 209.1506 322.6933] +/Rect [201.703 313.671 209.151 322.693] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -329 0 obj << +284 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [289.2885 313.6705 302.1901 322.6933] +/Rect [289.288 313.671 302.19 322.693] /Subtype /Link /A << /S /GoTo /D (cite.VANEK_MANDEL_BREZINA) >> >> endobj -330 0 obj << +285 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [259.106 120.5246 266.5531 129.5474] +/Rect [259.106 120.525 266.553 129.547] /Subtype /Link /A << /S /GoTo /D (cite.aaecc_07) >> >> endobj -331 0 obj << +286 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [271.2272 120.5246 278.6743 129.5474] +/Rect [271.227 120.525 278.674 129.547] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -332 0 obj << +287 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [283.3484 120.5246 296.25 129.5474] +/Rect [283.348 120.525 296.25 129.547] /Subtype /Link /A << /S /GoTo /D (cite.TUMINARO_TONG) >> >> endobj -316 0 obj << -/D [314 0 R /XYZ 141.7385 740.0018 null] +291 0 obj << +/D [289 0 R /XYZ 141.738 740.002 null] >> endobj -312 0 obj << -/D [314 0 R /XYZ 210.0699 438.097 null] +282 0 obj << +/D [289 0 R /XYZ 210.07 438.097 null] >> endobj -326 0 obj << -/D [314 0 R /XYZ 141.7385 389.2781 null] +295 0 obj << +/D [289 0 R /XYZ 141.738 389.278 null] >> endobj -327 0 obj << -/D [314 0 R /XYZ 141.7385 369.3352 null] +296 0 obj << +/D [289 0 R /XYZ 141.738 369.335 null] >> endobj -313 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F24 176 0 R /F7 319 0 R /F41 126 0 R /F10 322 0 R /F13 325 0 R /F27 179 0 R /F25 267 0 R /F20 171 0 R /F30 279 0 R /F22 273 0 R >> +288 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F22 165 0 R /F7 292 0 R /F39 116 0 R /F10 293 0 R /F13 294 0 R /F25 166 0 R /F23 248 0 R /F18 163 0 R /F28 252 0 R /F20 250 0 R >> /ProcSet [ /PDF /Text ] >> endobj -335 0 obj << -/Length 5485 +303 0 obj << +/Length 3920 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(5)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(5)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Mul)66(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)23(gr)22(oun)-1(d)]TJ/F15 10.9091 Tf 391.3906 0 Td[(15)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Mul)67(ti-level)-378(Domain)-378(Decomp)1(osition)-378(Ba)22(ck)22(gr)22(ound)]TJ/F15 10.9091 Tf 401.542 0 Td [(15)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F15 10.9091 Tf 110.8543 704.1363 Td[(The)-277(pr)1(olongat)1(or)]TJ/F24 10.9091 Tf 80.0384 0 Td[(P)]TJ/F25 7.9701 Tf 7.0038 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.127 1.6887 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(R)]TJ/F25 7.9701 Tf 8.3674 3.9588 Td[(T)]TJ -0.0843 -7.1916 Td[(C)]TJ/F15 10.9091 Tf 10.116 3.2328 Td[(is)-277(bu)1(ilt)-276(s)-1(tar)1(ting)-276(fr)1(om)-278(a)]TJ/F20 10.9091 Tf 109.5201 0 Td[(tent)-1(ative)-305(pr)51(olongator)]TJ/F24 10.9091 Tf 102.5945 0 Td[(P)]TJ/F27 10.9091 Tf 11.5492 0 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F28 7.9701 Tf 5.1382 0 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F26 5.9776 Tf 5.1382 -1.3394 Td[(C)]TJ/F15 10.9091 Tf 6.6924 -2.6194 Td[(,)]TJ -409.4208 -13.5492 Td[(de\014n)1(e)-1(d)-332(as)]TJ/F24 10.9091 Tf 114.8185 -17.8186 Td[(P)]TJ/F15 10.9091 Tf 11.5491 0 Td[(=)-278(\050)]TJ/F24 10.9091 Tf 15.7576 0 Td[(p)]TJ/F25 7.9701 Tf 5.4886 -1.6364 Td[(ij)]TJ/F15 10.9091 Tf 7.2653 1.6364 Td[(\051)]TJ/F24 10.9091 Tf 4.2425 0 Td[(;)-1166(p)]TJ/F25 7.9701 Tf 21.2462 -1.6364 Td[(ij)]TJ/F15 10.9091 Tf 10.2955 1.6364 Td[(=)]TJ/F30 10.9091 Tf 11.5151 15.3819 Td[(\032)]TJ/F15 10.9091 Tf 13.1632 -9.1358 Td[(1)-1913(if)]TJ/F24 10.9091 Tf 35.7202 0 Td[(i)]TJ/F27 10.9091 Tf 6.7886 0 Td[(2)]TJ/F24 10.9091 Tf 10.3029 0 Td[(V)]TJ/F25 7.9701 Tf 8.7879 5.3073 Td[(j)]TJ -2.4242 -8.7414 Td[(C)]TJ/F15 10.9091 Tf -59.1754 -10.1151 Td[(0)-1913(otherwise)]TJ/F24 10.9091 Tf 79.2607 7.3031 Td[(:)]TJ -ET -1 0 0 1 492.4295 672.7685 cm + -384.606 -35.866 Td [(The)-277(prolongator)]TJ/F22 10.9091 Tf 80.039 0 Td [(P)]TJ/F23 7.9701 Tf 7.003 -1.688 Td [(C)]TJ/F15 10.9091 Tf 10.128 1.688 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(R)]TJ/F23 7.9701 Tf 8.367 3.959 Td [(T)]TJ -0.084 -7.191 Td [(C)]TJ/F15 10.9091 Tf 10.116 3.232 Td [(is)-277(built)-276(starting)-277(from)-277(a)]TJ/F18 10.9091 Tf 109.52 0 Td [(tentative)-306(pr)51(olongator)]TJ/F22 10.9091 Tf 102.594 0 Td [(P)]TJ/F25 10.9091 Tf 11.55 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.181 3.959 Td [(n)]TJ/F26 7.9701 Tf 5.139 0 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F24 5.9776 Tf 5.138 -1.339 Td [(C)]TJ/F15 10.9091 Tf 6.693 -2.62 Td [(,)]TJ -409.421 -13.549 Td [(de\014ned)-333(as)]TJ/F22 10.9091 Tf 114.818 -17.818 Td [(P)]TJ/F15 10.9091 Tf 11.549 0 Td [(=)-278(\050)]TJ/F22 10.9091 Tf 15.758 0 Td [(p)]TJ/F23 7.9701 Tf 5.489 -1.637 Td [(ij)]TJ/F15 10.9091 Tf 7.265 1.637 Td [(\051)]TJ/F22 10.9091 Tf 4.242 0 Td [(;)-1167(p)]TJ/F23 7.9701 Tf 21.247 -1.637 Td [(ij)]TJ/F15 10.9091 Tf 10.295 1.637 Td [(=)]TJ/F28 10.9091 Tf 11.515 15.381 Td [(\032)]TJ/F15 10.9091 Tf 13.163 -9.135 Td [(1)-1913(if)]TJ/F22 10.9091 Tf 35.721 0 Td [(i)]TJ/F25 10.9091 Tf 6.788 0 Td [(2)]TJ/F22 10.9091 Tf 10.303 0 Td [(V)]TJ/F23 7.9701 Tf 8.788 5.307 Td [(j)]TJ -2.424 -8.741 Td [(C)]TJ/F15 10.9091 Tf -59.176 -10.116 Td [(0)-1913(otherwise)]TJ/F22 10.9091 Tf 79.261 7.304 Td [(:)]TJ 0 g 0 G -1 0 0 1 -492.4295 -672.7685 cm -BT -/F15 10.9091 Tf 492.4295 672.7685 Td[(\0502\051)]TJ -ET -1 0 0 1 506.3689 672.7685 cm +/F15 10.9091 Tf 103.909 0 Td [(\0502\051)]TJ 0 g 0 G -1 0 0 1 -506.3689 -672.7685 cm -BT -/F24 10.9091 Tf 93.9178 645.1545 Td[(P)]TJ/F25 7.9701 Tf 7.0038 -1.6886 Td[(C)]TJ/F15 10.9091 Tf 10.7331 1.6886 Td[(is)-334(ob)1(tain)1(e)-1(d)-333(b)29(y)-334(ap)1(pl)1(ying)-333(to)]TJ/F24 10.9091 Tf 128.8487 0 Td[(P)]TJ/F15 10.9091 Tf 12.1553 0 Td[(a)-333(s)-1(mo)-28(oth)1(e)-1(r)]TJ/F24 10.9091 Tf 56.7576 0 Td[(S)]TJ/F27 10.9091 Tf 10.3484 0 Td[(2)-277(<)]TJ/F25 7.9701 Tf 18.1818 3.9588 Td[(n)]TJ/F28 7.9701 Tf 5.1382 0 Td[(\002)]TJ/F25 7.9701 Tf 6.5865 0 Td[(n)]TJ/F15 10.9091 Tf 5.6363 -3.9588 Td[(:)]TJ/F24 10.9091 Tf -79.2239 -24.5081 Td[(P)]TJ/F25 7.9701 Tf 7.0038 -1.6887 Td[(C)]TJ/F15 10.9091 Tf 10.127 1.6887 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(S)-58(P)-28(;)]TJ -ET -1 0 0 1 492.4295 620.6464 cm +/F22 10.9091 Tf -398.511 -27.614 Td [(P)]TJ/F23 7.9701 Tf 7.004 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.733 1.689 Td [(is)-333(obtained)-334(b)28(y)-333(applying)-333(to)]TJ/F22 10.9091 Tf 128.848 0 Td [(P)]TJ/F15 10.9091 Tf 12.156 0 Td [(a)-333(smo)-28(other)]TJ/F22 10.9091 Tf 56.757 0 Td [(S)]TJ/F25 10.9091 Tf 10.349 0 Td [(2)-278(<)]TJ/F23 7.9701 Tf 18.181 3.958 Td [(n)]TJ/F26 7.9701 Tf 5.139 0 Td [(\002)]TJ/F23 7.9701 Tf 6.586 0 Td [(n)]TJ/F15 10.9091 Tf 5.636 -3.958 Td [(:)]TJ/F22 10.9091 Tf -79.223 -24.508 Td [(P)]TJ/F23 7.9701 Tf 7.003 -1.689 Td [(C)]TJ/F15 10.9091 Tf 10.127 1.689 Td [(=)]TJ/F22 10.9091 Tf 11.516 0 Td [(S)-58(P)-27(;)]TJ 0 g 0 G -1 0 0 1 -492.4295 -620.6464 cm -BT -/F15 10.9091 Tf 492.4295 620.6464 Td[(\0503\051)]TJ -ET -1 0 0 1 506.3689 620.6464 cm +/F15 10.9091 Tf 187.699 0 Td [(\0503\051)]TJ 0 g 0 G -1 0 0 1 -506.3689 -620.6464 cm -BT -/F15 10.9091 Tf 93.9178 596.1383 Td[(in)-303(or)1(der)-303(to)-303(rem)-1(o)28(v)28(e)-303(os)-1(cillator)1(y)-303(c)-1(omp)-27(onen)28(ts)-304(f)1(rom)-303(the)-303(range)-303(of)-303(th)1(e)-304(pr)1(olongat)1(or)-303(and)-303(h)1(e)-1(n)1(c)-1(e)]TJ 0 -13.5492 Td[(to)-433(impro)28(v)28(e)-434(t)1(he)-434(con)28(v)28(ergenc)-1(e)-433(pr)1(op)-28(erties)-434(of)-433(th)1(e)-434(m)28(ulti)1(-)-1(lev)28(el)-434(S)1(c)27(h)28(w)28(arz)-433(m)-1(etho)-27(d)-433([)]TJ -ET -1 0 0 1 459.8851 582.5891 cm + -398.511 -24.509 Td [(in)-303(order)-303(to)-303(remo)27(v)28(e)-303(oscillatory)-303(comp)-28(onen)28(ts)-303(from)-304(th)1(e)-304(range)-303(of)-303(the)-303(prolongator)-303(and)-303(hence)]TJ 0 -13.549 Td [(to)-433(impro)28(v)27(e)-433(the)-433(con)27(v)28(ergence)-433(prop)-28(erties)-433(of)-433(the)-434(m)28(ulti-lev)28(el)-433(Sc)27(h)28(w)28(arz)-433(me)-1(th)1(o)-28(d)-434([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -459.8851 -582.5891 cm -BT -/F15 10.9091 Tf 459.8851 582.5891 Td[(1)]TJ -ET -1 0 0 1 465.3397 582.5891 cm + [1(1)]TJ 0 g 0 G -1 0 0 1 -465.3397 -582.5891 cm -BT -/F15 10.9091 Tf 465.3397 582.5891 Td[(,)]TJ -ET -1 0 0 1 473.097 582.5891 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -473.097 -582.5891 cm -BT -/F15 10.9091 Tf 473.097 582.5891 Td[(17)]TJ -ET -1 0 0 1 484.0061 582.5891 cm + [-434(17)]TJ 0 g 0 G -1 0 0 1 -484.0061 -582.5891 cm -BT -/F15 10.9091 Tf 484.0061 582.5891 Td[(].)-744(A)]TJ -390.0883 -13.5492 Td[(sim)-1(p)1(le)-334(c)28(hoice)-334(f)1(or)]TJ/F24 10.9091 Tf 83.1213 0 Td[(S)]TJ/F15 10.9091 Tf 10.9545 0 Td[(is)-334(t)1(he)-334(d)1(am)-1(p)-27(ed)-333(Jac)-1(ob)1(i)-333(s)-1(mo)-28(oth)1(e)-1(r)1(:)]TJ/F24 10.9091 Tf 71.2927 -24.5081 Td[(S)]TJ/F15 10.9091 Tf 10.3484 0 Td[(=)]TJ/F24 10.9091 Tf 11.5152 0 Td[(I)]TJ/F27 10.9091 Tf 8.0757 0 Td[(\000)]TJ/F24 10.9091 Tf 10.909 0 Td[(!)-36(D)]TJ/F28 7.9701 Tf 16.5167 4.5043 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -4.5043 Td[(A;)]TJ -ET -1 0 0 1 492.4295 544.5318 cm + [(].)-744(A)]TJ 0 -13.549 Td [(simple)-333(c)27(hoice)-333(for)]TJ/F22 10.9091 Tf 83.121 0 Td [(S)]TJ/F15 10.9091 Tf 10.955 0 Td [(is)-333(the)-334(damp)-27(ed)-334(Jacobi)-333(smo)-28(other:)]TJ/F22 10.9091 Tf 71.292 -24.508 Td [(S)]TJ/F15 10.9091 Tf 10.349 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(I)]TJ/F25 10.9091 Tf 8.076 0 Td [(\000)]TJ/F22 10.9091 Tf 10.909 0 Td [(!)-36(D)]TJ/F26 7.9701 Tf 16.516 4.504 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -4.504 Td [(A;)]TJ 0 g 0 G -1 0 0 1 -492.4295 -544.5318 cm -BT -/F15 10.9091 Tf 492.4295 544.5318 Td[(\0504\051)]TJ -ET -1 0 0 1 506.3689 544.5318 cm +/F15 10.9091 Tf 164.459 0 Td [(\0504\051)]TJ 0 g 0 G -1 0 0 1 -506.3689 -544.5318 cm -BT -/F15 10.9091 Tf 93.9178 520.0237 Td[(where)-305(the)-305(v)55(al)1(ue)-305(of)]TJ/F24 10.9091 Tf 89.7069 0 Td[(!)]TJ/F15 10.9091 Tf 10.5101 0 Td[(can)-305(b)-27(e)-306(c)27(h)1(os)-1(en)-305(u)1(s)-1(i)1(ng)-305(s)-1(ome)-305(e)-1(stimate)-306(of)-304(the)-305(s)-1(p)-27(e)-1(ctral)-304(radi)1(us)-306(of)]TJ/F24 10.9091 Tf 283.3986 0 Td[(D)]TJ/F28 7.9701 Tf 9.3349 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf -404.2693 -13.5492 Td[([)]TJ -ET -1 0 0 1 96.9481 506.4745 cm + -398.511 -24.508 Td [(where)-305(the)-305(v)55(alue)-305(of)]TJ/F22 10.9091 Tf 89.707 0 Td [(!)]TJ/F15 10.9091 Tf 10.51 0 Td [(can)-305(b)-28(e)-305(c)28(hosen)-305(using)-305(some)-306(estimate)-305(of)-305(the)-305(sp)-28(ectral)-305(radius)-305(of)]TJ/F22 10.9091 Tf 283.398 0 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf -404.269 -13.549 Td [([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -96.9481 -506.4745 cm -BT -/F15 10.9091 Tf 96.9481 506.4745 Td[(1)]TJ -ET -1 0 0 1 102.4027 506.4745 cm + [(1)]TJ 0 g 0 G -1 0 0 1 -102.4027 -506.4745 cm -BT -/F15 10.9091 Tf 102.4027 506.4745 Td[(].)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [(].)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -334 0 obj << +302 0 obj << /Type /Page -/Contents 335 0 R -/Resources 333 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 311 0 R -/Annots [ 337 0 R 340 0 R 341 0 R 343 0 R ] +/Contents 303 0 R +/Resources 301 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 281 0 R +/Annots [ 300 0 R 297 0 R 298 0 R 299 0 R ] >> endobj -337 0 obj << +300 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -340 0 obj << +297 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [458.8888 581.5929 466.3359 590.6157] +/Rect [458.889 581.593 466.336 590.616] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -341 0 obj << +298 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [472.1007 581.5929 485.0023 590.6157] +/Rect [472.101 581.593 485.002 590.616] /Subtype /Link /A << /S /GoTo /D (cite.StubenGMD69_99) >> >> endobj -343 0 obj << +299 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [95.9519 505.4783 103.3989 514.5011] +/Rect [95.952 505.478 103.399 514.501] /Subtype /Link /A << /S /GoTo /D (cite.BREZINA_VANEK) >> >> endobj -336 0 obj << -/D [334 0 R /XYZ 93.9178 740.0018 null] +304 0 obj << +/D [302 0 R /XYZ 93.918 740.002 null] >> endobj -338 0 obj << -/D [334 0 R /XYZ 208.7363 686.3177 null] +305 0 obj << +/D [302 0 R /XYZ 208.736 686.318 null] >> endobj -339 0 obj << -/D [334 0 R /XYZ 276.0837 634.1956 null] +306 0 obj << +/D [302 0 R /XYZ 276.084 634.196 null] >> endobj -342 0 obj << -/D [334 0 R /XYZ 259.2863 558.081 null] +307 0 obj << +/D [302 0 R /XYZ 259.286 558.081 null] >> endobj -333 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F24 176 0 R /F25 267 0 R /F20 171 0 R /F27 179 0 R /F28 270 0 R /F26 276 0 R /F30 279 0 R /F22 273 0 R >> +301 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F22 165 0 R /F23 248 0 R /F18 163 0 R /F25 166 0 R /F26 249 0 R /F24 251 0 R /F28 252 0 R /F20 250 0 R >> /ProcSet [ /PDF /Text ] >> endobj -346 0 obj << -/Length 13082 +322 0 obj << +/Length 8798 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(16)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(16)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F19 14.3462 Tf 141.7385 704.1363 Td[(6)-1125(G)-1(et)-1(ti)-1(ng)-375(St)-1(a)1(r)-1(te)-1(d)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(W)84(e)-442(des)-1(crib)-27(e)-442(th)1(e)-442(basics)-442(for)-441(b)1(uil)1(din)1(g)-442(an)1(d)-441(app)1(lyin)1(g)-442(M)1(LD2P4)-441(one-le)-1(v)28(el)-441(and)-441(m)28(ult)1(i-)-1(l)1(e)-1(v)28(el)]TJ 0 -13.5492 Td[(Sc)28(h)28(w)28(arz)-314(p)1(rec)-1(on)1(diti)1(oners)-314(with)-312(the)-313(Kry)1(lo)28(v)-313(s)-1(olv)28(ers)-313(inclu)1(ded)-313(in)-313(P)1(SBLAS)-313([)]TJ -ET -1 0 0 1 478.7257 666.2349 cm +/F17 14.3462 Tf -203.265 -35.866 Td [(6)-1125(Getting)-375(Started)]TJ/F15 10.9091 Tf 0 -24.352 Td [(W)83(e)-441(describ)-28(e)-441(the)-442(basics)-441(for)-441(building)-442(and)-441(applying)-441(MLD2P4)-441(one-lev)27(el)-441(and)-441(m)27(ulti-lev)28(el)]TJ 0 -13.549 Td [(Sc)28(h)28(w)27(arz)-313(preconditioners)-313(with)-313(the)-313(Krylo)28(v)-313(solv)27(ers)-313(included)-313(in)-313(PSBLAS)-313([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -478.7257 -666.2349 cm -BT -/F15 10.9091 Tf 478.7257 666.2349 Td[(11)]TJ -ET -1 0 0 1 489.6348 666.2349 cm + [(11)]TJ 0 g 0 G -1 0 0 1 -489.6348 -666.2349 cm -BT -/F15 10.9091 Tf 489.6348 666.2349 Td[(].)-437(The)-314(f)1(ollo)28(w-)]TJ -347.8963 -13.5492 Td[(in)1(g)-334(steps)-334(ar)1(e)-334(requi)1(re)-1(d)1(:)]TJ -ET -1 0 0 1 141.7385 631.6256 cm + [(].)-438(The)-313(follo)28(w-)]TJ 0 -13.549 Td [(ing)-333(steps)-334(are)-333(required:)]TJ 0 g 0 G -1 0 0 1 -141.7385 -631.6256 cm -BT -/F15 10.9091 Tf 155.0719 631.6256 Td[(1.)]TJ -ET -1 0 0 1 163.5567 631.6256 cm + 13.334 -21.06 Td [(1.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -631.6256 cm -BT -/F20 10.9091 Tf 169.0113 631.6256 Td[(De)51(cl)1(a)-1(r)52(e)-256(the)-256(pr)52(e)51(c)51(onditioner)-255(d)-1(ata)-256(s)1(t)-1(r)1(uctur)52(e)]TJ/F15 10.9091 Tf 190.4228 0 Td[(.)-407(It)-222(is)-223(a)-222(deriv)28(ed)-222(d)1(ata)-222(t)27(y)1(p)-28(e,)]TJ/F48 10.9091 Tf 122.9597 0 Td[(mld_)]TJ/F20 10.9091 Tf 22.9089 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type)]TJ/F15 10.9091 Tf 51.5449 0 Td[(,)]TJ -394.2105 -13.5492 Td[(where)]TJ/F20 10.9091 Tf 31.0466 0 Td[(x)]TJ/F15 10.9091 Tf 9.5117 0 Td[(ma)27(y)-287(b)-27(e)]TJ/F48 10.9091 Tf 37.4871 0 Td[(s)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F48 10.9091 Tf 6.2675 0 Td[(d)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F48 10.9091 Tf 6.2676 0 Td[(c)]TJ/F15 10.9091 Tf 8.8646 0 Td[(or)]TJ/F48 10.9091 Tf 12.8648 0 Td[(z)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-297(accordi)1(ng)-288(t)1(o)-288(the)-288(b)1(as)-1(i)1(c)-288(data)-287(t)27(y)1(p)-28(e)-288(of)-287(th)1(e)-288(s)-1(p)1(arse)-289(matr)1(ix)]TJ -129.4915 -13.5492 Td[(\050)]TJ/F48 10.9091 Tf 4.2424 0 Td[(s)]TJ/F15 10.9091 Tf 8.861 0 Td[(=)-287(real)-287(s)-1(i)1(ngle)-287(prec)-1(i)1(s)-1(ion)1(;)]TJ/F48 10.9091 Tf 110.4605 0 Td[(d)]TJ/F15 10.9091 Tf 8.861 0 Td[(=)-287(real)-287(dou)1(ble)-287(precis)-1(i)1(on;)]TJ/F48 10.9091 Tf 115.2483 0 Td[(c)]TJ/F15 10.9091 Tf 8.8611 0 Td[(=)-287(com)-1(p)1(le)-1(x)-287(sin)1(gle)-288(p)1(re)-1(cision;)]TJ/F48 10.9091 Tf -256.5343 -13.5492 Td[(z)]TJ/F15 10.9091 Tf 9.6138 0 Td[(=)-356(com)-1(p)1(le)-1(x)-356(d)1(oub)1(le)-357(p)1(re)-1(cision\051)1(.)-513(T)-1(h)1(is)-357(d)1(ata)-356(s)-1(tr)1(ucture)-356(is)-357(acc)-1(es)-1(sed)-356(b)28(y)-356(the)-356(use)-1(r)-356(on)1(ly)]TJ -9.6138 -13.5492 Td[(th)1(rough)-333(t)1(he)-334(M)1(LD2P4)-333(rou)1(tines)-1(,)-333(f)1(ollo)28(wing)-333(an)-333(ob)-55(j)1(e)-1(ct-)-1(or)1(ien)28(te)-1(d)-332(appr)1(oac)27(h)1(.)]TJ -ET -1 0 0 1 141.7385 555.4954 cm +/F18 10.9091 Tf 13.939 0 Td [(De)51(clar)51(e)-255(the)-256(pr)51(e)51(c)52(ond)-1(i)1(tioner)-256(data)-256(structur)52(e)]TJ/F15 10.9091 Tf 190.423 0 Td [(.)-407(It)-223(is)-222(a)-222(deriv)28(ed)-222(data)-223(t)28(yp)-28(e,)]TJ/F46 10.9091 Tf 122.96 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type)]TJ/F15 10.9091 Tf 51.545 0 Td [(,)]TJ -394.211 -13.55 Td [(where)]TJ/F18 10.9091 Tf 31.047 0 Td [(x)]TJ/F15 10.9091 Tf 9.512 0 Td [(ma)28(y)-288(b)-28(e)]TJ/F46 10.9091 Tf 37.487 0 Td [(s)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F46 10.9091 Tf 6.267 0 Td [(d)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)]TJ/F46 10.9091 Tf 6.267 0 Td [(c)]TJ/F15 10.9091 Tf 8.865 0 Td [(or)]TJ/F46 10.9091 Tf 12.865 0 Td [(z)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-297(according)-287(to)-288(the)-287(basic)-288(data)-288(t)28(yp)-28(e)-287(of)-288(the)-287(sparse)-288(matrix)]TJ -129.492 -13.549 Td [(\050)]TJ/F46 10.9091 Tf 4.243 0 Td [(s)]TJ/F15 10.9091 Tf 8.861 0 Td [(=)-287(real)-287(s)-1(in)1(gle)-288(precision;)]TJ/F46 10.9091 Tf 110.46 0 Td [(d)]TJ/F15 10.9091 Tf 8.861 0 Td [(=)-287(real)-288(d)1(ouble)-288(precision;)]TJ/F46 10.9091 Tf 115.249 0 Td [(c)]TJ/F15 10.9091 Tf 8.861 0 Td [(=)-287(complex)-288(sin)1(gle)-288(precision;)]TJ/F46 10.9091 Tf -256.535 -13.549 Td [(z)]TJ/F15 10.9091 Tf 9.614 0 Td [(=)-356(complex)-357(dou)1(ble)-357(precision\051.)-513(This)-356(data)-356(structure)-357(is)-356(accessed)-356(b)27(y)-356(the)-356(user)-356(only)]TJ -9.614 -13.549 Td [(through)-333(the)-334(M)1(LD2P4)-334(routines,)-333(follo)28(wing)-333(an)-334(ob)-55(ject-orien)28(te)-1(d)-333(approac)28(h.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -555.4954 cm -BT -/F15 10.9091 Tf 155.0719 555.4954 Td[(2.)]TJ -ET -1 0 0 1 163.5567 555.4954 cm + -13.939 -21.934 Td [(2.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -555.4954 cm -BT -/F20 10.9091 Tf 169.0113 555.4954 Td[(A)25(l)-50(lo)51(c)51(ate)-364(an)-1(d)-364(ini)1(t)-1(i)1(aliz)1(e)-365(the)-364(pr)51(e)51(c)52(o)-1(nditi)1(o)-1(ner)-364(data)-364(structur)52(e,)-365(a)-1(c)52(c)51(or)51(ding)-364(to)-364(a)-365(pr)52(e)51(c)51(ond)-1(i)1(-)]TJ 0 -13.5492 Td[(tioner)-376(typ)51(e)-375(cho)-1(s)1(en)-377(by)-375(the)-376(user)]TJ/F15 10.9091 Tf 144.0045 0 Td[(.)-503(This)-353(is)-353(p)-28(erfor)1(m)-1(ed)-353(b)29(y)-353(the)-353(rou)1(tin)1(e)]TJ/F48 10.9091 Tf 169.417 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)]TJ -382.148 -13.5492 Td[(whic)28(h)-406(al)1(s)-1(o)-405(s)-1(ets)-406(defaul)1(ts)-406(for)-405(e)-1(ac)28(h)-406(p)1(rec)-1(on)1(diti)1(oner)-406(t)28(yp)-27(e)-406(s)-1(elec)-1(ted)-405(b)28(y)-406(th)1(e)-406(use)-1(r)1(.)-662(The)]TJ 0 -13.5492 Td[(defau)1(lts)-404(ass)-1(o)-28(ciated)-404(to)-403(e)-1(ac)28(h)-404(p)1(re)-1(cond)1(ition)1(e)-1(r)-403(t)28(yp)-27(e)-405(ar)1(e)-404(giv)28(e)-1(n)-403(in)-403(T)83(abl)1(e)]TJ -ET -1 0 0 1 493.6411 514.8478 cm +/F18 10.9091 Tf 13.939 0 Td [(A)26(l)-52(lo)52(c)51(ate)-364(and)-365(initi)1(a)-1(l)1(ize)-365(the)-364(pr)51(e)52(c)51(onditioner)-364(data)-365(str)1(uctur)51(e,)-366(ac)51(c)51(or)51(ding)-364(to)-364(a)-364(pr)51(e)51(c)51(ondi-)]TJ 0 -13.549 Td [(tioner)-376(typ)51(e)-376(chosen)-376(by)-375(the)-376(user)]TJ/F15 10.9091 Tf 144.005 0 Td [(.)-503(This)-353(is)-353(p)-28(erformed)-353(b)28(y)-353(the)-353(routine)]TJ/F46 10.9091 Tf 169.417 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)]TJ -382.148 -13.549 Td [(whic)28(h)-406(also)-406(sets)-406(d)1(e)-1(f)1(aults)-406(for)-406(eac)28(h)-406(preconditioner)-405(t)27(yp)-27(e)-406(selected)-406(b)28(y)-406(the)-406(user.)-661(The)]TJ 0 -13.549 Td [(defaults)-404(asso)-28(ciated)-403(to)-404(eac)27(h)-403(preconditioner)-404(t)28(yp)-28(e)-404(are)-404(giv)28(en)-404(in)-403(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -493.6411 -514.8478 cm -BT -/F15 10.9091 Tf 493.6411 514.8478 Td[(1)]TJ -ET -1 0 0 1 499.0956 514.8478 cm + [-404(1)]TJ 0 g 0 G -1 0 0 1 -499.0956 -514.8478 cm -BT -/F15 10.9091 Tf 499.0956 514.8478 Td[(,)-421(where)-404(the)]TJ -330.0843 -13.5492 Td[(strin)1(gs)-306(use)-1(d)-304(b)28(y)]TJ/F48 10.9091 Tf 74.4455 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 72.0568 0 Td[(to)-305(iden)28(ti)1(fy)-305(th)1(e)-306(pr)1(e)-1(cond)1(ition)1(e)-1(r)-305(t)28(yp)-27(es)-306(are)-306(al)1(s)-1(o)-305(giv)28(en.)]TJ -146.5023 -13.5492 Td[(Note)-353(th)1(at)-352(thes)-1(e)-352(s)-1(tr)1(ings)-353(ar)1(e)-353(v)56(alid)-352(al)1(s)-1(o)-352(if)-352(u)1(pp)-27(e)-1(r)1(c)-1(ase)-353(letters)-353(are)-352(s)-1(u)1(bstitu)1(te)-1(d)-352(b)29(y)-353(cor-)]TJ 0 -13.5492 Td[(res)-1(p)-27(on)1(din)1(g)-334(l)1(o)27(w)28(e)-1(r)1(c)-1(ase)-334(on)1(e)-1(s.)]TJ -ET -1 0 0 1 141.7385 452.2668 cm + [(,)-421(where)-404(the)]TJ 0 -13.549 Td [(strings)-305(used)-306(b)28(y)]TJ/F46 10.9091 Tf 74.446 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 72.057 0 Td [(to)-305(iden)28(tify)-306(the)-305(preconditioner)-305(t)28(yp)-28(es)-305(are)-306(also)-305(giv)28(en.)]TJ -146.503 -13.55 Td [(Note)-352(that)-353(these)-352(strings)-352(are)-353(v)56(alid)-352(also)-353(if)-352(upp)-28(ercase)-352(letters)-352(are)-353(substituted)-352(b)28(y)-353(cor-)]TJ 0 -13.549 Td [(resp)-28(onding)-333(lo)28(w)28(ercas)-1(e)-333(ones.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -452.2668 cm -BT -/F15 10.9091 Tf 155.0719 452.2668 Td[(3.)]TJ -ET -1 0 0 1 163.5567 452.2668 cm + -13.939 -21.933 Td [(3.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -452.2668 cm -BT -/F20 10.9091 Tf 169.0113 452.2668 Td[(Mo)51(di)1(fy)-340(the)-341(sel)1(e)51(cte)51(d)-341(pr)51(e)52(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-340(typ)51(e,)-343(by)-340(pr)51(op)51(erl)1(y)-340(setting)-341(pr)52(e)51(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-340(p)51(ar)52(am-)]TJ 0 -13.5492 Td[(eters.)]TJ/F15 10.9091 Tf 30.6684 0 Td[(This)-266(i)1(s)-266(p)-28(erf)1(orme)-1(d)-265(b)28(y)-265(th)1(e)-266(routi)1(ne)]TJ/F48 10.9091 Tf 155.1694 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)-422(Th)1(is)-266(rou)1(tine)-266(m)28(ust)-266(b)-27(e)-266(called)]TJ -248.8371 -13.5492 Td[(onl)1(y)-365(i)1(f)-364(the)-365(u)1(s)-1(er)-364(w)27(an)28(ts)-365(t)1(o)-365(mo)-28(di)1(fy)-364(the)-365(d)1(e)-1(f)1(aul)1(t)-365(v)56(alu)1(e)-1(s)-365(of)-364(th)1(e)-365(paramete)-1(r)1(s)-365(as)-1(so)-28(ciated)]TJ 0 -13.5492 Td[(to)-468(t)1(he)-468(se)-1(lec)-1(t)1(e)-1(d)-467(pr)1(e)-1(cond)1(ition)1(e)-1(r)-467(t)28(yp)-27(e)-1(,)-501(to)-467(obtai)1(n)-468(a)-467(v)56(arian)28(t)-467(of)-467(the)-468(p)1(re)-1(cond)1(ition)1(e)-1(r)1(.)]TJ 0 -13.5492 Td[(Ex)1(am)-1(p)1(les)-396(of)-394(u)1(s)-1(e)-395(of)]TJ/F48 10.9091 Tf 95.9773 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 67.3042 0 Td[(are)-395(giv)28(en)-394(in)-394(Sec)-1(t)1(ion)]TJ -ET -1 0 0 1 432.5731 398.07 cm +/F18 10.9091 Tf 13.939 0 Td [(Mo)51(dify)-340(the)-341(sele)51(cte)52(d)-341(pr)51(e)51(c)51(onditioner)-340(typ)51(e,)-344(by)-340(pr)51(op)51(erly)-340(setting)-341(pr)51(e)51(c)52(onditioner)-341(p)51(ar)51(am-)]TJ 0 -13.549 Td [(eters.)]TJ/F15 10.9091 Tf 30.669 0 Td [(This)-266(is)-265(p)-28(erformed)-265(b)27(y)-265(the)-266(routi)1(ne)]TJ/F46 10.9091 Tf 155.169 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)-422(This)-265(routine)-266(m)28(ust)-266(b)-27(e)-266(called)]TJ -248.837 -13.55 Td [(only)-364(if)-365(the)-364(user)-365(w)28(an)28(ts)-365(to)-364(mo)-28(dify)-365(th)1(e)-365(default)-364(v)55(alues)-364(of)-365(the)-364(parameters)-365(asso)-28(ciated)]TJ 0 -13.549 Td [(to)-468(the)-467(selected)-468(preconditioner)-467(t)27(yp)-27(e,)-502(to)-467(obtain)-468(a)-467(v)55(arian)28(t)-468(of)-467(the)-468(preconditioner.)]TJ 0 -13.549 Td [(Examples)-395(of)-394(use)-395(of)]TJ/F46 10.9091 Tf 95.978 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 67.304 0 Td [(are)-395(giv)28(en)-394(in)-395(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -432.5731 -398.07 cm -BT -/F15 10.9091 Tf 432.5731 398.07 Td[(6.1)]TJ -ET -1 0 0 1 446.5125 398.07 cm + [-395(6.1)]TJ 0 g 0 G -1 0 0 1 -446.5125 -398.07 cm -BT -/F15 10.9091 Tf 446.5125 398.07 Td[(;)-425(a)-395(complete)-395(list)-395(of)-394(all)]TJ -277.5012 -13.5492 Td[(th)1(e)-304(p)1(rec)-1(on)1(diti)1(oner)-303(p)1(arame)-1(ters)-303(an)1(d)-303(th)1(e)-1(i)1(r)-303(all)1(o)27(w)28(e)-1(d)-302(an)1(d)-303(d)1(e)-1(f)1(ault)-302(v)56(alues)-303(is)-303(pro)28(vi)1(ded)-303(i)1(n)]TJ 0 -13.5492 Td[(Section)]TJ -ET -1 0 0 1 207.1931 370.9716 cm + [(;)-425(a)-394(complete)-395(list)-395(of)-394(all)]TJ -163.282 -13.549 Td [(the)-303(preconditioner)-302(parameters)-303(and)-303(their)-302(allo)27(w)28(ed)-303(and)-302(default)-303(v)56(alues)-303(is)-303(pro)28(vided)-303(in)]TJ 0 -13.549 Td [(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -207.1931 -370.9716 cm -BT -/F15 10.9091 Tf 207.1931 370.9716 Td[(7)]TJ -ET -1 0 0 1 212.6477 370.9716 cm + [-333(7)]TJ 0 g 0 G -1 0 0 1 -212.6477 -370.9716 cm -BT -/F15 10.9091 Tf 212.6477 370.9716 Td[(,)-333(T)83(abl)1(e)-1(s)]TJ -ET -1 0 0 1 253.6174 370.9716 cm + [(,)-334(T)84(ables)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -253.6174 -370.9716 cm -BT -/F15 10.9091 Tf 253.6174 370.9716 Td[(2)]TJ -ET -1 0 0 1 259.0719 370.9716 cm + [-334(2)]TJ 0 g 0 G -1 0 0 1 -259.0719 -370.9716 cm -BT -/F15 10.9091 Tf 259.0719 370.9716 Td[(-)]TJ -ET -1 0 0 1 262.7083 370.9716 cm + [(-)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -262.7083 -370.9716 cm -BT -/F15 10.9091 Tf 262.7083 370.9716 Td[(5)]TJ -ET -1 0 0 1 268.1628 370.9716 cm + [(5)]TJ 0 g 0 G -1 0 0 1 -268.1628 -370.9716 cm -BT -/F15 10.9091 Tf 268.1628 370.9716 Td[(.)]TJ -ET -1 0 0 1 141.7385 349.0382 cm + [(.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -349.0382 cm -BT -/F15 10.9091 Tf 155.0719 349.0382 Td[(4.)]TJ -ET -1 0 0 1 163.5567 349.0382 cm + -13.939 -21.934 Td [(4.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -349.0382 cm -BT -/F20 10.9091 Tf 169.0113 349.0382 Td[(Bui)1(ld)-457(the)-457(pr)51(e)51(c)51(onditioner)-457(f)1(or)-457(a)-457(given)-457(matrix.)]TJ/F15 10.9091 Tf 223.3234 0 Td[(This)-441(is)-442(p)-27(erfor)1(m)-1(ed)-441(b)28(y)-441(th)1(e)-442(r)1(outin)1(e)]TJ/F48 10.9091 Tf -223.3234 -13.5492 Td[(mld_precbld)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)]TJ -ET -1 0 0 1 141.7385 313.5556 cm +/F18 10.9091 Tf 13.939 0 Td [(Build)-457(the)-457(pr)51(e)51(c)51(onditioner)-457(for)-457(a)-457(given)-457(matrix.)]TJ/F15 10.9091 Tf 223.324 0 Td [(This)-441(is)-441(p)-28(erformed)-441(b)27(y)-441(the)-441(routine)]TJ/F46 10.9091 Tf -223.324 -13.549 Td [(mld_precbld)]TJ/F15 10.9091 Tf 63 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -313.5556 cm -BT -/F15 10.9091 Tf 155.0719 313.5556 Td[(5.)]TJ -ET -1 0 0 1 163.5567 313.5556 cm + -76.939 -21.933 Td [(5.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -313.5556 cm -BT -/F20 10.9091 Tf 169.0113 313.5556 Td[(App)-1(l)1(y)-281(th)-1(e)-281(pr)51(e)51(c)51(onditioner)-281(at)-282(e)51(ach)-282(iter)52(at)-1(i)1(on)-282(of)-282(a)-281(Kryl)1(ov)-282(sol)1(ver.)]TJ/F15 10.9091 Tf 288.3113 0 Td[(This)-251(i)1(s)-251(p)-28(erf)1(orme)-1(d)-250(b)28(y)]TJ -288.3113 -13.5492 Td[(th)1(e)-341(rou)1(tine)]TJ/F48 10.9091 Tf 56.5445 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 68.7265 0 Td[(.)-465(Wh)1(e)-1(n)-339(using)-340(th)1(e)-341(PS)1(B)-1(LAS)-339(Kryl)1(o)27(v)-340(solv)28(ers,)-342(thi)1(s)-341(s)-1(t)1(e)-1(p)-340(i)1(s)]TJ -125.271 -13.5492 Td[(com)-1(p)1(le)-1(t)1(e)-1(ly)-301(tran)1(s)-1(p)1(aren)28(t)-302(to)-301(the)-302(u)1(s)-1(er,)-308(sin)1(c)-1(e)]TJ/F48 10.9091 Tf 196.4514 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 72.0175 0 Td[(is)-302(called)-302(b)29(y)-302(th)1(e)-302(PS)1(B)-1(LAS)]TJ -268.4689 -13.5492 Td[(rou)1(tin)1(e)-334(impleme)-1(n)28(ti)1(ng)-333(the)-333(Kryl)1(o)27(v)-333(solv)28(er)-333(\050)]TJ/F48 10.9091 Tf 195.9093 0 Td[(psb_krylov)]TJ/F15 10.9091 Tf 57.2721 0 Td[(\051.)]TJ -ET -1 0 0 1 141.7385 250.9746 cm +/F18 10.9091 Tf 13.939 0 Td [(Apply)-282(the)-281(pr)51(e)51(c)51(onditioner)-281(at)-282(e)51(ach)-282(iter)52(at)-1(i)1(on)-282(of)-282(a)-281(Krylov)-282(solver.)]TJ/F15 10.9091 Tf 288.312 0 Td [(This)-251(is)-250(p)-28(erformed)-250(b)27(y)]TJ -288.312 -13.55 Td [(the)-340(routine)]TJ/F46 10.9091 Tf 56.545 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 68.726 0 Td [(.)-465(When)-340(using)-340(the)-341(PSBLAS)-340(Krylo)28(v)-340(solv)28(ers,)-342(this)-341(step)-340(is)]TJ -125.271 -13.549 Td [(completely)-302(transparen)28(t)-302(to)-301(the)-302(user,)-308(since)]TJ/F46 10.9091 Tf 196.452 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 72.017 0 Td [(is)-302(called)-301(b)27(y)-301(the)-302(PSBLAS)]TJ -268.469 -13.549 Td [(routine)-333(implemen)28(ting)-334(the)-333(Krylo)28(v)-334(solv)28(er)-333(\050)]TJ/F46 10.9091 Tf 195.91 0 Td [(psb_krylov)]TJ/F15 10.9091 Tf 57.272 0 Td [(\051.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -250.9746 cm -BT -/F15 10.9091 Tf 155.0719 250.9746 Td[(6.)]TJ -ET -1 0 0 1 163.5567 250.9746 cm + -267.121 -21.933 Td [(6.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -250.9746 cm -BT -/F20 10.9091 Tf 169.0113 250.9746 Td[(F)77(r)51(e)51(e)-255(the)-256(pr)51(e)51(c)52(o)-1(ndi)1(t)-1(i)1(on)-1(er)-255(data)-256(stru)1(ct)-1(u)1(r)51(e)]TJ/F15 10.9091 Tf 175.0895 0 Td[(.)-407(This)-222(is)-223(p)-27(e)-1(r)1(formed)-222(b)28(y)-222(th)1(e)-223(rou)1(tin)1(e)]TJ/F48 10.9091 Tf 159.8083 0 Td[(mld_precfree)]TJ/F15 10.9091 Tf 68.7265 0 Td[(.)]TJ -403.6243 -13.5492 Td[(This)-326(s)-1(tep)-326(is)-326(c)-1(ompl)1(e)-1(me)-1(n)29(tary)-326(to)-326(s)-1(tep)-326(1)-326(and)-325(s)-1(h)1(ould)-326(b)-27(e)-327(p)-27(erfor)1(m)-1(ed)-326(when)-326(th)1(e)-327(pr)1(e)-1(con-)]TJ 0 -13.5492 Td[(di)1(tioner)-333(is)-334(n)1(o)-333(m)-1(or)1(e)-334(use)-1(d)1(.)]TJ -27.2728 -21.0602 Td[(A)-384(detail)1(e)-1(d)-384(d)1(e)-1(scrip)1(tion)-384(of)-383(the)-384(ab)-28(o)28(v)28(e)-384(rout)1(ines)-385(i)1(s)-385(giv)28(en)-384(in)-383(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 451.0974 202.8161 cm +/F18 10.9091 Tf 13.939 0 Td [(F)77(r)51(e)51(e)-256(the)-255(pr)51(e)51(c)51(onditioner)-255(data)-256(structur)51(e)]TJ/F15 10.9091 Tf 175.09 0 Td [(.)-407(This)-223(is)-222(p)-28(erformed)-222(b)28(y)-222(the)-222(routine)]TJ/F46 10.9091 Tf 159.808 0 Td [(mld_precfree)]TJ/F15 10.9091 Tf 68.727 0 Td [(.)]TJ -403.625 -13.55 Td [(This)-326(step)-327(is)-326(complemen)28(tary)-326(to)-327(step)-326(1)-326(and)-326(should)-326(b)-28(e)-326(p)-28(erformed)-326(when)-327(the)-326(precon-)]TJ 0 -13.549 Td [(ditioner)-333(is)-334(no)-333(more)-333(used.)]TJ -27.273 -21.06 Td [(A)-384(detailed)-384(description)-384(of)-384(the)-384(ab)-28(o)28(v)28(e)-384(routines)-384(is)-384(giv)27(en)-384(in)-384(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -451.0974 -202.8161 cm -BT -/F15 10.9091 Tf 451.0974 202.8161 Td[(7)]TJ -ET -1 0 0 1 456.552 202.8161 cm + [-384(7)]TJ 0 g 0 G -1 0 0 1 -456.552 -202.8161 cm -BT -/F15 10.9091 Tf 456.552 202.8161 Td[(.)-596(Exampl)1(e)-1(s)-384(s)-1(h)1(o)27(win)1(g)]TJ -314.8135 -13.5492 Td[(th)1(e)-334(basic)-334(u)1(s)-1(e)-334(of)-332(MLD2P4)-333(are)-333(rep)-28(or)1(te)-1(d)-333(i)1(n)-333(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 379.3751 189.2669 cm + [(.)-596(Examples)-384(sho)27(win)1(g)]TJ 0 -13.549 Td [(the)-333(basic)-334(use)-333(of)-333(MLD2P4)-334(are)-333(rep)-28(orted)-333(in)-333(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -379.3751 -189.2669 cm -BT -/F15 10.9091 Tf 379.3751 189.2669 Td[(6.1)]TJ -ET -1 0 0 1 393.3145 189.2669 cm + [-334(6.1)]TJ 0 g 0 G -1 0 0 1 -393.3145 -189.2669 cm -BT -/F15 10.9091 Tf 393.3145 189.2669 Td[(.)]TJ -234.6395 -13.5492 Td[(Note)-422(th)1(at)-422(th)1(e)-422(F)84(ortran)-421(95)-421(m)-1(o)-27(du)1(le)]TJ/F48 10.9091 Tf 167.194 0 Td[(mld_prec_mod)]TJ/F15 10.9091 Tf 68.7266 0 Td[(,)-443(c)-1(on)28(t)1(ainin)1(g)-422(t)1(he)-422(d)1(e)-1(\014)1(niti)1(on)-422(of)-421(t)1(he)]TJ -252.8571 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-350(data)-351(t)28(yp)-27(e)-351(and)-350(the)-351(in)28(terf)1(ac)-1(es)-351(to)-351(the)-351(rou)1(tin)1(e)-1(s)-351(of)-351(M)1(LD2P4,)-355(m)27(u)1(s)-1(t)-350(b)-28(e)-351(used)]TJ 0 -13.5492 Td[(in)-245(an)29(y)-245(progr)1(am)-246(callin)1(g)-245(s)-1(u)1(c)27(h)-245(rou)1(tin)1(e)-1(s.)-415(The)-246(mo)-28(d)1(ules)]TJ/F48 10.9091 Tf 240.4978 0 Td[(psb_base_mod)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)-263(f)1(or)-245(the)-245(s)-1(p)1(arse)-246(matrix)]TJ -309.2243 -13.5492 Td[(and)-405(comm)27(un)1(ication)-405(des)-1(cri)1(ptor)-405(dat)1(a)-406(t)28(yp)-27(e)-1(s,)-423(and)]TJ/F48 10.9091 Tf 231.165 0 Td[(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.1809 0 Td[(,)-423(for)-405(in)28(terf)1(ac)-1(i)1(ng)-406(wit)1(h)]TJ -311.3459 -13.5492 Td[(th)1(e)-334(Kry)1(lo)28(v)-334(solv)28(ers,)-333(m)27(ust)-333(b)-28(e)-333(als)-1(o)-333(u)1(s)-1(ed)-333(\050s)-1(ee)-334(S)1(e)-1(ction)]TJ -ET -1 0 0 1 383.6781 121.5209 cm + [(.)]TJ 16.937 -13.549 Td [(Note)-422(t)1(hat)-422(the)-421(F)83(ortran)-421(95)-422(mo)-28(dule)]TJ/F46 10.9091 Tf 167.194 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)-443(con)27(taining)-421(the)-421(de\014nition)-422(of)-421(the)]TJ -252.858 -13.549 Td [(preconditioner)-351(data)-351(t)28(yp)-28(e)-351(and)-350(the)-351(in)28(terfaces)-351(to)-351(the)-351(routines)-351(of)-351(MLD2P4,)-355(m)28(ust)-351(b)-28(e)-351(used)]TJ 0 -13.55 Td [(in)-245(an)28(y)-246(progr)1(am)-246(calling)-245(suc)28(h)-245(routines.)-415(The)-246(mo)-27(dules)]TJ/F46 10.9091 Tf 240.498 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)-263(for)-245(the)-245(sparse)-245(m)-1(atr)1(ix)]TJ -309.225 -13.549 Td [(and)-405(c)-1(omm)28(unication)-405(descriptor)-406(data)-405(t)28(yp)-28(es,)-424(and)]TJ/F46 10.9091 Tf 231.165 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)-424(for)-405(in)28(terfacing)-406(with)]TJ -311.346 -13.549 Td [(the)-333(Krylo)28(v)-334(solv)28(ers,)-333(m)27(ust)-333(b)-28(e)-333(also)-333(used)-334(\050see)-333(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -383.6781 -121.5209 cm -BT -/F15 10.9091 Tf 383.6781 121.5209 Td[(6.1)]TJ -ET -1 0 0 1 397.6175 121.5209 cm + [-334(6.1)]TJ 0 g 0 G -1 0 0 1 -397.6175 -121.5209 cm -BT -/F15 10.9091 Tf 397.6175 121.5209 Td[(\051.)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [(\051.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -345 0 obj << +321 0 obj << /Type /Page -/Contents 346 0 R -/Resources 344 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 311 0 R -/Annots [ 348 0 R 351 0 R 353 0 R 354 0 R 355 0 R 356 0 R 360 0 R 361 0 R 362 0 R ] +/Contents 322 0 R +/Resources 320 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 281 0 R +/Annots [ 308 0 R 309 0 R 310 0 R 311 0 R 312 0 R 313 0 R 314 0 R 315 0 R 316 0 R ] >> endobj -348 0 obj << +308 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [477.7294 665.2387 490.6311 674.2615] +/Rect [477.729 665.239 490.631 674.261] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -351 0 obj << +309 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [492.6448 511.7303 500.0919 523.4198] +/Rect [492.645 511.73 500.092 523.42] /Subtype /Link /A << /S /GoTo /D (table.1) >> >> endobj -353 0 obj << +310 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [431.5768 394.6495 447.5088 406.642] +/Rect [431.577 394.65 447.509 406.642] /Subtype /Link /A << /S /GoTo /D (subsection.6.1) >> >> endobj -354 0 obj << +311 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [206.1969 367.8541 213.6439 379.5436] +/Rect [206.197 367.854 213.644 379.544] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -355 0 obj << +312 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [252.6211 367.8541 260.0682 379.5436] +/Rect [252.621 367.854 260.068 379.544] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -356 0 obj << +313 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [261.712 367.8541 269.1591 379.5436] +/Rect [261.712 367.854 269.159 379.544] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -360 0 obj << +314 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [450.1012 199.6986 457.5483 211.3881] +/Rect [450.101 199.699 457.548 211.388] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -361 0 obj << +315 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [378.3788 186.1494 394.3107 197.8389] +/Rect [378.379 186.149 394.311 197.839] /Subtype /Link /A << /S /GoTo /D (subsection.6.1) >> >> endobj -362 0 obj << +316 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [382.6818 117.7973 398.6138 130.699] +/Rect [382.682 117.797 398.614 130.699] /Subtype /Link /A << /S /GoTo /D (subsection.6.1) >> >> endobj -347 0 obj << -/D [345 0 R /XYZ 141.7385 740.0018 null] +323 0 obj << +/D [321 0 R /XYZ 141.738 740.002 null] >> endobj 54 0 obj << -/D [345 0 R /XYZ 141.7385 715.0952 null] +/D [321 0 R /XYZ 141.738 715.095 null] >> endobj -349 0 obj << -/D [345 0 R /XYZ 141.7385 647.2457 null] +324 0 obj << +/D [321 0 R /XYZ 141.738 647.246 null] >> endobj -350 0 obj << -/D [345 0 R /XYZ 141.7385 571.1155 null] +325 0 obj << +/D [321 0 R /XYZ 141.738 571.115 null] >> endobj -352 0 obj << -/D [345 0 R /XYZ 141.7385 467.8869 null] +326 0 obj << +/D [321 0 R /XYZ 141.738 467.887 null] >> endobj -357 0 obj << -/D [345 0 R /XYZ 141.7385 364.6583 null] +327 0 obj << +/D [321 0 R /XYZ 141.738 364.658 null] >> endobj -358 0 obj << -/D [345 0 R /XYZ 141.7385 328.8727 null] +328 0 obj << +/D [321 0 R /XYZ 141.738 328.873 null] >> endobj -359 0 obj << -/D [345 0 R /XYZ 141.7385 265.9886 null] +329 0 obj << +/D [321 0 R /XYZ 141.738 265.989 null] >> endobj -344 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F19 105 0 R /F20 171 0 R /F48 214 0 R >> +320 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F17 103 0 R /F18 163 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -368 0 obj << -/Length 11008 +338 0 obj << +/Length 7971 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(6)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(6)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Getti)-1(ng)-378(St)67(a)-1(r)67(ted)]TJ/F15 10.9091 Tf 391.3906 0 Td[(17)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(17)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F41 10.9091 Tf 93.9178 690.5871 Td[(Re)-1(mark)-395(1.)]TJ/F15 10.9091 Tf 62.779 0 Td[(The)-344(c)-1(oarses)-1(t-lev)28(e)-1(l)-344(solv)28(er)-344(use)-1(d)-343(b)28(y)-344(the)-344(defau)1(lt)-344(t)28(w)27(o-lev)28(e)-1(l)-344(p)1(rec)-1(on)1(diti)1(oner)-344(has)]TJ -62.779 -13.5492 Td[(b)-27(e)-1(en)-432(c)28(hose)-1(n)-431(b)28(y)-431(takin)1(g)-432(in)28(to)-431(ac)-1(coun)28(t)-431(that,)-456(on)-431(par)1(allel)-432(mac)27(h)1(ines)-1(,)-456(it)-431(often)-431(le)-1(ad)1(s)-432(to)-432(the)]TJ 0 -13.5492 Td[(sm)-1(all)1(e)-1(st)-422(exec)-1(u)1(tion)-421(time)-422(w)-1(h)1(e)-1(n)-421(ap)1(pli)1(e)-1(d)-421(to)-422(l)1(inear)-421(s)-1(ystem)-1(s)-422(com)-1(i)1(ng)-422(f)1(rom)-422(\014)1(nite-di\013ere)-1(n)1(c)-1(e)]TJ 0 -13.5492 Td[(di)1(s)-1(cretizations)-376(of)-376(b)1(as)-1(ic)-376(ellip)1(tic)-376(PDE)-375(prob)1(lem)-1(s,)-387(consid)1(e)-1(red)-376(as)-376(s)-1(t)1(andar)1(d)-376(tes)-1(t)1(s)-377(f)1(or)-376(m)27(u)1(lti-)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)-223(S)1(c)27(h)28(w)28(arz)-224(p)1(rec)-1(on)1(diti)1(oners)-224([)]TJ -ET -1 0 0 1 236.8345 636.3903 cm +/F39 10.9091 Tf -401.542 -49.415 Td [(Remark)-396(1.)]TJ/F15 10.9091 Tf 62.779 0 Td [(The)-344(coarsest-lev)27(el)-344(solv)28(er)-344(used)-344(b)27(y)-344(the)-344(default)-344(t)28(w)28(o-)-1(l)1(e)-1(v)28(el)-344(preconditioner)-344(has)]TJ -62.779 -13.549 Td [(b)-28(een)-432(c)28(hosen)-432(b)28(y)-432(tak)1(ing)-432(in)28(to)-432(accoun)28(t)-432(that,)-456(on)-432(parallel)-432(mac)28(hines,)-456(it)-432(often)-432(leads)-432(to)-432(th)1(e)]TJ 0 -13.549 Td [(smallest)-422(execution)-421(time)-422(when)-422(applied)-421(to)-422(linear)-421(systems)-422(coming)-422(from)-421(\014nite-di\013erence)]TJ 0 -13.549 Td [(discretizations)-376(of)-376(basic)-376(elliptic)-376(PDE)-376(problems,)-387(considered)-376(as)-376(standard)-376(tests)-376(for)-376(m)28(ulti-)]TJ 0 -13.55 Td [(lev)28(el)-224(Sc)28(h)28(w)28(arz)-224(precondition)1(e)-1(r)1(s)-224([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -236.8345 -636.3903 cm -BT -/F15 10.9091 Tf 236.8345 636.3903 Td[(3)]TJ -ET -1 0 0 1 242.289 636.3903 cm + [(3)]TJ 0 g 0 G -1 0 0 1 -242.289 -636.3903 cm -BT -/F15 10.9091 Tf 242.289 636.3903 Td[(,)]TJ -ET -1 0 0 1 247.7561 636.3903 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -247.7561 -636.3903 cm -BT -/F15 10.9091 Tf 247.7561 636.3903 Td[(4)]TJ -ET -1 0 0 1 253.2107 636.3903 cm + [-223(4)]TJ 0 g 0 G -1 0 0 1 -253.2107 -636.3903 cm -BT -/F15 10.9091 Tf 253.2107 636.3903 Td[(].)-407(Ho)27(w)28(ev)28(e)-1(r,)-245(th)1(is)-224(solv)28(er)-223(do)-28(es)-224(not)-223(n)1(e)-1(ce)-1(ss)-1(ar)1(ily)-223(c)-1(or)1(res)-1(p)-27(ond)]TJ -159.2929 -13.5492 Td[(to)-446(the)-447(smalles)-1(t)-446(n)28(um)28(b)-27(e)-1(r)-446(of)-446(iteration)1(s)-447(of)-446(th)1(e)-447(precondi)1(tioned)-446(Kr)1(ylo)28(v)-446(m)-1(etho)-28(d)1(,)-475(wh)1(ic)27(h)-446(is)]TJ 0 -13.5492 Td[(usual)1(ly)-334(obt)1(ained)-334(b)28(y)-334(ap)1(ply)1(ing)-334(a)-334(di)1(rec)-1(t)-334(solv)28(e)-1(r)-333(to)-334(the)-334(c)-1(oarses)-1(t-lev)28(e)-1(l)-334(syste)-1(m,)-334(e)-1(.)1(g.)-334(base)-1(d)-333(on)]TJ 0 -13.5492 Td[(th)1(e)-313(LU)-311(factorization)-311(\050s)-1(ee)-312(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 253.5905 595.7428 cm + [(].)-408(Ho)28(w)28(ev)27(er,)-245(this)-223(solv)27(er)-223(do)-28(es)-223(not)-224(n)1(e)-1(cessarily)-223(corresp)-28(ond)]TJ 0 -13.549 Td [(to)-446(the)-447(smallest)-446(n)27(um)28(b)-28(er)-446(of)-446(iterations)-447(of)-446(the)-447(preconditioned)-446(Krylo)28(v)-447(metho)-27(d,)-475(whic)28(h)-447(is)]TJ 0 -13.549 Td [(usually)-334(obtained)-334(b)28(y)-334(applying)-334(a)-334(direct)-335(solv)28(er)-334(to)-334(the)-334(coarsest-lev)27(el)-334(system,)-334(e.g.)-334(based)-335(on)]TJ 0 -13.549 Td [(the)-312(LU)-312(f)1(ac)-1(tor)1(ization)-312(\050see)-312(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -253.5905 -595.7428 cm -BT -/F15 10.9091 Tf 253.5905 595.7428 Td[(7)]TJ -ET -1 0 0 1 259.045 595.7428 cm + [-312(7)]TJ 0 g 0 G -1 0 0 1 -259.045 -595.7428 cm -BT -/F15 10.9091 Tf 262.4462 595.7428 Td[(for)-311(th)1(e)-313(coarse)-1(st-le)-1(v)28(el)-312(solv)28(ers)-312(a)28(v)55(ai)1(labl)1(e)-313(i)1(n)-312(M)1(LD2P4\051.)]TJ/F41 10.9091 Tf -168.5284 -32.0642 Td[(Re)-1(mark)-403(2.)]TJ/F15 10.9091 Tf 63.0959 0 Td[(The)-351(includ)1(e)-352(p)1(ath)-351(f)1(or)-351(MLD2P)1(4)-352(m)28(ust)-351(o)28(v)28(e)-1(rr)1(ide)-351(those)-352(f)1(or)-351(PS)1(B)-1(LAS)1(,)-351(e)-1(.)1(g.)-351(the)]TJ -63.0959 -13.5492 Td[(latter)-344(m)27(u)1(s)-1(t)-344(c)-1(ome)-345(\014r)1(s)-1(t)-344(in)-344(the)-345(se)-1(q)1(uence)-346(p)1(as)-1(sed)-345(to)-344(the)-345(compiler,)-347(as)-345(th)1(e)-345(MLD2P4)-344(v)28(e)-1(r)1(s)-1(i)1(on)]TJ 0 -13.5492 Td[(of)-483(the)-483(Kryl)1(o)27(v)-483(solv)28(e)-1(r)-483(in)29(te)-1(r)1(face)-1(s)-484(m)28(ust)-484(o)28(v)28(errid)1(e)-484(that)-483(of)-483(PS)1(B)-1(LAS)1(.)-483(T)-1(h)1(is)-484(will)-483(c)27(h)1(ange)-484(i)1(n)]TJ 0 -13.5492 Td[(th)1(e)-384(fut)1(ure)-384(wh)1(e)-1(n)-383(th)1(e)-384(s)-1(u)1(pp)-27(ort)-383(for)-383(the)]TJ/F48 10.9091 Tf 178.2279 0 Td[(class)]TJ/F15 10.9091 Tf 32.8201 0 Td[(state)-1(men)28(t)-384(b)-27(ec)-1(ome)-1(s)-384(wid)1(e)-1(spr)1(e)-1(ad)-383(in)-383(F)84(ortr)1(an)]TJ -211.048 -13.5492 Td[(com)-1(p)1(ilers.)]TJ -ET -1 0 0 1 93.9178 485.4738 cm + [-312(for)-311(the)-312(coarsest-lev)28(e)-1(l)-311(solv)27(ers)-311(a)27(v)56(ailable)-312(in)-311(MLD2P4\051.)]TJ/F39 10.9091 Tf 0 -32.064 Td [(Remark)-404(2.)]TJ/F15 10.9091 Tf 63.096 0 Td [(The)-351(include)-351(path)-351(for)-351(MLD2P4)-352(m)28(ust)-351(o)28(v)28(e)-1(r)1(ride)-352(those)-351(for)-351(PSBLAS,)-351(e.g.)-351(the)]TJ -63.096 -13.55 Td [(latter)-345(m)28(ust)-344(com)-1(e)-344(\014rst)-345(in)-344(the)-345(sequence)-345(passed)-344(to)-345(the)-345(compiler,)-347(as)-345(the)-344(MLD2P4)-345(v)28(ersion)]TJ 0 -13.549 Td [(of)-483(the)-484(Krylo)28(v)-484(solv)28(er)-483(in)27(terf)1(ac)-1(es)-483(m)28(ust)-484(o)28(v)28(erride)-484(that)-483(of)-484(PSBLAS.)-483(This)-484(will)-483(c)28(hange)-484(in)]TJ 0 -13.549 Td [(the)-384(f)1(uture)-384(when)-383(the)-384(supp)-28(ort)-383(for)-384(the)]TJ/F46 10.9091 Tf 178.228 0 Td [(class)]TJ/F15 10.9091 Tf 32.82 0 Td [(statemen)28(t)-384(b)-28(ecomes)-383(widespread)-384(in)-383(F)83(ortran)]TJ -211.048 -13.549 Td [(compilers.)]TJ 0 g 0 G -1 0 0 1 26.3117 -159.9377 cm 0 g 0 G 0 g 0 G -1 0 0 1 5.4546 159.5392 cm +ET q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 485.275 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -0.1993 -13.5492 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 125.684 471.526 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -125.4848 -471.5261 cm BT -/F42 10.9091 Tf 131.6616 475.5909 Td[(type)]TJ +/F40 10.9091 Tf 131.662 475.591 Td [(type)]TJ ET -1 0 0 1 223.2583 471.5261 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 223.458 471.526 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -223.2583 -471.5261 cm BT -/F42 10.9091 Tf 229.4351 475.5909 Td[(strin)-1(g)]TJ +/F40 10.9091 Tf 229.435 475.591 Td [(string)]TJ ET -1 0 0 1 281.0311 471.5261 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 281.23 471.526 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -281.0311 -471.5261 cm BT -/F42 10.9091 Tf 287.208 475.5909 Td[(def)89(a)22(ul)66(t)-378(preco)1(n)-1(diti)-1(o)1(n)-1(e)1(r)]TJ +/F40 10.9091 Tf 287.208 475.591 Td [(def)89(a)22(ul)67(t)-378(preconditioner)]TJ ET -1 0 0 1 474.4035 471.5261 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 474.603 471.526 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -348.7194 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 471.327 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -0.1993 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 125.684 444.029 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -125.4848 -444.0292 cm BT -/F15 10.9091 Tf 131.6616 461.6432 Td[(No)-333(precondi)1(tioner)]TJ +/F15 10.9091 Tf 131.662 461.643 Td [(No)-333(preconditioner)]TJ ET -1 0 0 1 223.2583 444.0292 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 223.458 444.029 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -223.2583 -444.0292 cm BT -/F48 10.9091 Tf 229.4351 461.6432 Td[('NOPREC')]TJ +/F46 10.9091 Tf 229.435 461.643 Td [('NOPREC')]TJ ET -1 0 0 1 281.0311 444.0292 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 281.23 444.029 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -281.0311 -444.0292 cm BT -/F15 10.9091 Tf 287.208 461.6432 Td[(Considered)-476(on)1(ly)-476(to)-476(u)1(s)-1(e)-476(th)1(e)-477(P)1(SBLAS)]TJ 0 -13.5492 Td[(Kr)1(ylo)28(v)-298(solv)28(ers)-298(w)-1(i)1(th)-297(no)-298(p)1(rec)-1(on)1(diti)1(oner.)]TJ +/F15 10.9091 Tf 287.208 461.643 Td [(Considered)-476(only)-476(to)-476(use)-476(the)-476(PSBLAS)]TJ 0 -13.549 Td [(Krylo)28(v)-298(solv)28(ers)-298(with)-298(no)-297(preconditioner.)]TJ ET -1 0 0 1 474.4035 444.0292 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 474.603 444.029 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -348.7194 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 443.83 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -0.1993 -13.5492 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 125.684 430.082 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -125.4848 -430.0815 cm BT -/F15 10.9091 Tf 131.6616 434.1463 Td[(Diagon)1(al)]TJ +/F15 10.9091 Tf 131.662 434.146 Td [(Diagonal)]TJ ET -1 0 0 1 223.2583 430.0816 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 223.458 430.082 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -223.2583 -430.0816 cm BT -/F48 10.9091 Tf 229.4351 434.1463 Td[('DIAG')]TJ +/F46 10.9091 Tf 229.435 434.146 Td [('DIAG')]TJ ET -1 0 0 1 281.0311 430.0816 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 281.23 430.082 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -281.0311 -430.0816 cm BT -/F15 10.9091 Tf 287.208 434.1463 Td[(|)]TJ +/F15 10.9091 Tf 287.208 434.146 Td [(|)]TJ ET -1 0 0 1 474.4035 430.0816 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 474.603 430.082 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -348.7194 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 429.882 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -0.1993 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 125.684 402.585 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -125.4848 -402.5847 cm BT -/F15 10.9091 Tf 131.6616 420.1987 Td[(Blo)-28(c)27(k)-333(Jacobi)]TJ +/F15 10.9091 Tf 131.662 420.199 Td [(Blo)-28(c)28(k)-333(Jacobi)]TJ ET -1 0 0 1 223.2583 402.5847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 223.458 402.585 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -223.2583 -402.5847 cm BT -/F48 10.9091 Tf 229.4351 420.1987 Td[('BJAC')]TJ +/F46 10.9091 Tf 229.435 420.199 Td [('BJAC')]TJ ET -1 0 0 1 281.0311 402.5847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 281.23 402.585 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -281.0311 -402.5847 cm BT -/F15 10.9091 Tf 287.208 420.1987 Td[(Blo)-28(c)27(k)-324(Jac)-1(ob)1(i)-325(with)-324(ILU\0500\051)-325(on)-324(the)-325(lo)-28(cal)]TJ 0 -13.5492 Td[(bl)1(o)-28(c)27(ks.)]TJ +/F15 10.9091 Tf 287.208 420.199 Td [(Blo)-28(c)28(k)-325(Jacobi)-325(with)-325(ILU\0500\051)-324(on)-325(the)-325(lo)-28(cal)]TJ 0 -13.55 Td [(blo)-28(c)28(ks.)]TJ ET -1 0 0 1 474.4035 402.5847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 474.603 402.585 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -348.7194 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 402.385 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -0.1993 -40.6476 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 125.684 361.539 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -125.4848 -361.5386 cm BT -/F15 10.9091 Tf 131.6616 392.7018 Td[(Add)1(itiv)28(e)-333(Sc)27(h)29(w)27(ar)1(z)]TJ +/F15 10.9091 Tf 131.662 392.702 Td [(Additiv)28(e)-333(Sc)27(h)28(w)28(arz)]TJ ET -1 0 0 1 223.2583 361.5386 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 223.458 361.539 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -223.2583 -361.5386 cm BT -/F48 10.9091 Tf 229.4351 392.7018 Td[('AS')]TJ +/F46 10.9091 Tf 229.435 392.702 Td [('AS')]TJ ET -1 0 0 1 281.0311 361.5386 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 281.23 361.539 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -281.0311 -361.5386 cm BT -/F15 10.9091 Tf 287.208 392.7018 Td[(Re)-1(stri)1(c)-1(ted)-595(Ad)1(diti)1(v)28(e)-596(Sc)28(h)28(w)28(arz)-596(\050RAS)1(\051,)]TJ 0 -13.5492 Td[(with)-278(o)28(v)28(erlap)-277(1)-278(and)-278(ILU\0500\051)-278(on)-277(the)-278(lo)-28(cal)]TJ 0 -13.5492 Td[(bl)1(o)-28(c)27(ks.)]TJ +/F15 10.9091 Tf 287.208 392.702 Td [(Restricted)-595(Additiv)28(e)-595(Sc)27(h)28(w)28(arz)-595(\050RAS\051,)]TJ 0 -13.549 Td [(with)-278(o)28(v)28(erlap)-278(1)-279(and)-278(ILU\0500\051)-278(on)-278(the)-278(lo)-27(c)-1(al)]TJ 0 -13.55 Td [(blo)-28(c)28(ks.)]TJ ET -1 0 0 1 474.4035 361.5386 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 474.603 361.539 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -348.7194 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 361.339 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -0.1993 -189.6887 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 189.6887 l -S +1 0 0 1 125.684 171.451 cm +[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S Q -1 0 0 1 -125.4848 -171.4514 cm BT -/F15 10.9091 Tf 131.6616 351.6557 Td[(Mu)1(ltil)1(e)-1(v)28(el)]TJ +/F15 10.9091 Tf 131.662 351.656 Td [(Multilev)28(el)]TJ ET -1 0 0 1 223.2583 171.4514 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 189.6887 l -S +1 0 0 1 223.458 171.451 cm +[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S Q -1 0 0 1 -223.2583 -171.4514 cm BT -/F48 10.9091 Tf 229.4351 351.6557 Td[('ML')]TJ +/F46 10.9091 Tf 229.435 351.656 Td [('ML')]TJ ET -1 0 0 1 281.0311 171.4514 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 189.6887 l -S +1 0 0 1 281.23 171.451 cm +[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S Q -1 0 0 1 -281.0311 -171.4514 cm BT -/F15 10.9091 Tf 287.208 351.6557 Td[(Mu)1(lti-lev)28(e)-1(l)-346(h)29(ybr)1(id)-346(p)1(rec)-1(on)1(diti)1(oner)-346(\050ad-)]TJ 0 -13.5492 Td[(di)1(tiv)28(e)-674(on)-673(th)1(e)-674(s)-1(ame)-674(lev)28(e)-1(l)-673(and)-673(m)28(ul-)]TJ 0 -13.5492 Td[(tip)1(licativ)28(e)-611(th)1(rou)1(gh)-610(the)-610(le)-1(v)28(els\051,)-679(w)-1(i)1(th)]TJ 0 -13.5492 Td[(p)-27(os)-1(t-sm)-1(o)-28(ot)1(hin)1(g)-413(only)84(.)-683(Nu)1(m)27(b)-27(e)-1(r)-412(of)-413(l)1(e)-1(v-)]TJ 0 -13.5492 Td[(els)-1(:)-999(2.)-1278(P)28(ost-s)-1(mo)-28(oth)1(e)-1(r)1(:)-1000(RAS)-610(w)-1(i)1(th)]TJ 0 -13.5492 Td[(o)28(v)28(e)-1(r)1(lap)-648(1)-649(an)1(d)-648(ILU\0500\051)-649(on)-648(th)1(e)-649(lo)-28(cal)]TJ 0 -13.5492 Td[(bl)1(o)-28(c)27(ks.)-440(Aggr)1(e)-1(gati)1(on:)-437(s)-1(mo)-28(oth)1(e)-1(d)-318(aggre)-1(-)]TJ 0 -13.5492 Td[(gation)-344(w)-1(i)1(th)-345(th)1(re)-1(shol)1(d)]TJ/F24 10.9091 Tf 106.5389 0 Td[(\022)]TJ/F15 10.9091 Tf 8.6697 0 Td[(=)-297(0.)-480(Coarse)-1(st)]TJ -115.2086 -13.5492 Td[(matrix)1(:)-421(d)1(is)-1(t)1(rib)1(uted)-285(am)-1(on)1(g)-286(th)1(e)-286(pr)1(o)-28(c)-1(es)-1(-)]TJ 0 -13.5492 Td[(sors)-1(.)-422(Coarse)-1(st-le)-1(v)28(el)-268(solv)28(er:)-412(4)-268(sw)27(eeps)-268(of)]TJ 0 -13.5492 Td[(th)1(e)-421(b)1(lo)-28(c)27(k)1(-)-1(Jacobi)-419(s)-1(olv)28(er,)-441(with)-420(LU)-420(f)1(ac)-1(-)]TJ 0 -13.5492 Td[(tori)1(z)-1(ati)1(on)-496(of)-495(th)1(e)-496(blo)-28(c)28(ks)-496(\050UMF)1(P)83(A)28(CK)]TJ 0 -13.5492 Td[(for)-448(th)1(e)-450(d)1(oub)1(le)-449(pr)1(e)-1(cis)-1(i)1(on)-449(v)28(ersions)-449(an)1(d)]TJ 0 -13.5492 Td[(Su)1(p)-27(e)-1(rLU)-312(for)-312(the)-313(sin)1(gle)-313(pr)1(e)-1(cis)-1(i)1(on)-313(on)1(e)-1(s\051)]TJ +/F15 10.9091 Tf 287.208 351.656 Td [(Multi-lev)28(el)-346(h)28(ybrid)-346(preconditioner)-346(\050ad-)]TJ 0 -13.549 Td [(ditiv)28(e)-674(on)-673(the)-674(same)-673(lev)28(el)-674(and)-673(m)27(ul-)]TJ 0 -13.55 Td [(tiplicativ)28(e)-610(through)-611(the)-610(lev)28(els\051,)-680(with)]TJ 0 -13.549 Td [(p)-28(ost-smo)-28(othing)-412(only)83(.)-683(Num)28(b)-28(er)-413(of)-413(lev-)]TJ 0 -13.549 Td [(els:)-1000(2.)-1278(P)28(ost-smo)-28(other:)-1000(RAS)-610(with)]TJ 0 -13.549 Td [(o)28(v)28(erlap)-649(1)-648(and)-649(ILU\0500\051)-648(on)-649(the)-648(lo)-28(cal)]TJ 0 -13.549 Td [(blo)-28(c)28(ks.)-440(Aggregation:)-437(smo)-28(othed)-319(aggre-)]TJ 0 -13.55 Td [(gation)-345(with)-345(threshold)]TJ/F22 10.9091 Tf 106.539 0 Td [(\022)]TJ/F15 10.9091 Tf 8.67 0 Td [(=)-297(0.)-480(Coarsest)]TJ -115.209 -13.549 Td [(matrix:)-420(distributed)-286(among)-285(the)-286(pro)-28(ces-)]TJ 0 -13.549 Td [(sors.)-423(Coarsest-lev)28(el)-268(solv)28(er:)-412(4)-268(sw)28(eeps)-268(of)]TJ 0 -13.549 Td [(the)-420(blo)-28(c)28(k-Jacobi)-420(solv)28(er,)-442(with)-420(LU)-420(fac-)]TJ 0 -13.549 Td [(torization)-496(of)-495(the)-496(blo)-28(c)28(ks)-496(\050UM)1(FP)83(A)28(CK)]TJ 0 -13.55 Td [(for)-449(the)-448(double)-449(precision)-449(v)28(ersions)-449(and)]TJ 0 -13.549 Td [(Sup)-28(erLU)-312(for)-313(the)-313(sin)1(gle)-313(precision)-313(ones\051)]TJ ET -1 0 0 1 474.4035 171.4514 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 189.6887 l -S +1 0 0 1 474.603 171.451 cm +[]0 d 0 J 0.398 w 0 0 m 0 189.689 l S Q -1 0 0 1 -348.7194 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -348.9187 0.1992 l -S +1 0 0 1 125.684 171.252 cm +[]0 d 0 J 0.398 w 0 0 m 348.919 0 l S Q -1 0 0 1 -2.056 -30.4898 cm 0 g 0 G -1 0 0 1 -123.6281 -140.5631 cm BT -/F15 10.9091 Tf 123.6281 140.5631 Td[(T)83(ab)1(le)-334(1:)-444(Pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(t)28(yp)-27(e)-1(s,)-333(c)-1(or)1(res)-1(p)-27(ond)1(ing)-333(strin)1(gs)-334(and)-332(defaul)1(t)-334(c)28(hoices)-1(.)]TJ -ET -1 0 0 1 476.6587 140.5631 cm +/F15 10.9091 Tf 123.628 140.563 Td [(T)83(able)-333(1:)-444(Preconditioner)-334(t)28(yp)-28(es,)-333(corresp)-28(onding)-333(strings)-333(and)-333(default)-334(c)28(hoices.)]TJ 0 g 0 G -1 0 0 1 -382.7409 -2.1212 cm 0 g 0 G -1 0 0 1 0 -46.8089 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -367 0 obj << +337 0 obj << /Type /Page -/Contents 368 0 R -/Resources 366 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 311 0 R -/Annots [ 370 0 R 371 0 R 372 0 R 373 0 R ] +/Contents 338 0 R +/Resources 336 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 281 0 R +/Annots [ 335 0 R 317 0 R 318 0 R 319 0 R ] >> endobj -370 0 obj << +335 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -371 0 obj << +317 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [235.8382 635.3941 243.2853 644.4169] +/Rect [235.838 635.394 243.285 644.417] /Subtype /Link /A << /S /GoTo /D (cite.aaecc_07) >> >> endobj -372 0 obj << +318 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [246.7599 635.3941 254.207 644.4169] +/Rect [246.76 635.394 254.207 644.417] /Subtype /Link /A << /S /GoTo /D (cite.apnum_07) >> >> endobj -373 0 obj << +319 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [252.5942 592.0192 260.0413 604.9208] +/Rect [252.594 592.019 260.041 604.921] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -369 0 obj << -/D [367 0 R /XYZ 93.9178 740.0018 null] +339 0 obj << +/D [337 0 R /XYZ 93.918 740.002 null] >> endobj -363 0 obj << -/D [367 0 R /XYZ 166.9614 154.1122 null] +330 0 obj << +/D [337 0 R /XYZ 166.961 154.112 null] >> endobj -366 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F41 126 0 R /F48 214 0 R /F24 176 0 R >> +336 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F39 116 0 R /F46 195 0 R /F22 165 0 R >> /ProcSet [ /PDF /Text ] >> endobj -376 0 obj << -/Length 13316 +353 0 obj << +/Length 8940 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(18)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(18)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F19 11.9552 Tf 141.7385 704.1363 Td[(6.)-1(1)-1125(E)-1(xampl)-1(es)]TJ/F15 10.9091 Tf 0 -22.0076 Td[(The)-340(c)-1(o)-27(de)-340(re)-1(p)-27(ort)1(e)-1(d)-339(in)-340(F)1(igur)1(e)]TJ -ET -1 0 0 1 280.8283 682.1287 cm +/F17 11.9552 Tf -203.265 -35.866 Td [(6.1)-1125(Examples)]TJ/F15 10.9091 Tf 0 -22.007 Td [(The)-340(co)-28(de)-340(rep)-28(orted)-340(in)-339(Figure)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -280.8283 -682.1287 cm -BT -/F15 10.9091 Tf 280.8283 682.1287 Td[(2)]TJ -ET -1 0 0 1 286.2828 682.1287 cm + [-340(2)]TJ 0 g 0 G -1 0 0 1 -286.2828 -682.1287 cm -BT -/F15 10.9091 Tf 289.9916 682.1287 Td[(sho)28(ws)-341(h)1(o)27(w)-340(to)-340(se)-1(t)-339(and)-340(ap)1(pl)1(y)-340(the)-340(defau)1(lt)-340(m)28(ulti)1(-)-1(lev)28(el)-340(pr)1(e)-1(-)]TJ -148.2531 -13.5492 Td[(condi)1(tioner)-257(a)27(v)56(ail)1(able)-258(i)1(n)-258(th)1(e)-258(real)-258(d)1(oub)1(le)-258(pr)1(e)-1(cis)-1(i)1(on)-258(v)28(ersion)-257(of)-257(MLD2P)1(4)-258(\050se)-1(e)-258(T)83(ab)1(le)]TJ -ET -1 0 0 1 515.6164 668.5795 cm + [-340(sho)27(ws)-340(ho)28(w)-340(to)-340(set)-340(and)-340(apply)-340(th)1(e)-340(default)-340(m)27(ulti-lev)28(el)-340(pre-)]TJ 0 -13.549 Td [(conditioner)-258(a)28(v)56(ailable)-258(in)-257(the)-258(real)-258(dou)1(ble)-258(precision)-258(v)28(ersion)-258(of)-257(MLD2P4)-258(\050see)-257(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -515.6164 -668.5795 cm -BT -/F15 10.9091 Tf 515.6164 668.5795 Td[(1)]TJ -ET -1 0 0 1 521.0709 668.5795 cm + [-258(1)]TJ 0 g 0 G -1 0 0 1 -521.0709 -668.5795 cm -BT -/F15 10.9091 Tf 521.0709 668.5795 Td[(\051.)-419(Thi)1(s)]TJ -379.3324 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-237(is)-238(c)27(hosen)-238(b)28(y)-237(s)-1(i)1(m)-1(p)1(ly)-238(sp)-28(ecifyi)1(ng)]TJ/F48 10.9091 Tf 212.5392 0 Td[('ML')]TJ/F15 10.9091 Tf 25.5027 0 Td[(as)-238(s)-1(ec)-1(on)1(d)-238(ar)1(gume)-1(n)29(t)-238(of)]TJ/F48 10.9091 Tf 105.6827 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf -343.7246 -13.5492 Td[(\050a)-359(c)-1(all)-359(to)]TJ/F48 10.9091 Tf 47.52 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 66.9201 0 Td[(is)-360(n)1(ot)-359(nee)-1(d)1(e)-1(d)1(\051)-360(an)1(d)-359(is)-360(ap)1(plied)-359(with)-359(th)1(e)-360(BiCGST)83(AB)-359(s)-1(olv)28(er)-359(pr)1(o-)]TJ -114.4401 -13.5492 Td[(vid)1(e)-1(d)-300(b)28(y)-301(P)1(SBLAS.)-300(As)-302(p)1(re)-1(v)1(iously)-301(ob)1(s)-1(erv)28(ed,)-307(the)-301(mo)-28(du)1(les)]TJ/F48 10.9091 Tf 268.6135 0 Td[(psb_base_mod)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)]TJ/F48 10.9091 Tf 6.3846 0 Td[(mld_prec_mod)]TJ/F15 10.9091 Tf -343.7246 -13.5492 Td[(and)]TJ/F48 10.9091 Tf 21.2121 0 Td[(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.8173 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(u)1(s)-1(ed)-333(b)28(y)-333(the)-333(e)-1(xamp)1(le)-334(pr)1(ogram.)]TJ -88.0929 -14.2764 Td[(The)-395(part)-394(of)-395(the)-395(c)-1(o)-27(de)-395(c)-1(on)1(c)-1(erni)1(ng)-395(th)1(e)-396(readi)1(ng)-395(and)-394(as)-1(se)-1(m)28(bl)1(ing)-395(of)-394(the)-395(s)-1(p)1(ars)-1(e)-395(matrix)]TJ -16.9365 -13.5492 Td[(and)-456(th)1(e)-458(r)1(igh)28(t-han)1(d)-456(s)-1(id)1(e)-457(v)28(e)-1(ctor,)-487(p)-28(erf)1(orme)-1(d)-456(thr)1(ough)-456(the)-457(P)1(SBLAS)-456(rout)1(ines)-457(for)-456(s)-1(p)1(ars)-1(e)]TJ 0 -13.5492 Td[(matrix)-385(an)1(d)-385(v)28(ec)-1(tor)-384(m)-1(an)1(age)-1(me)-1(n)29(t,)-398(is)-386(n)1(ot)-385(rep)-28(or)1(te)-1(d)-384(here)-386(f)1(or)-385(br)1(e)-1(v)1(it)28(y;)-411(th)1(e)-386(state)-1(men)28(ts)-386(con-)]TJ 0 -13.5492 Td[(ce)-1(rn)1(in)1(g)-265(the)-265(d)1(e)-1(al)1(lo)-28(cation)-264(of)-265(th)1(e)-265(PS)1(B)-1(LAS)-264(d)1(ata)-265(stru)1(c)-1(tu)1(re)-265(are)-265(neglec)-1(ted)-264(to)-28(o.)-421(The)-265(c)-1(omp)1(le)-1(te)]TJ 0 -13.5492 Td[(co)-28(de)-307(can)-306(b)-28(e)-306(foun)1(d)-306(in)-306(th)1(e)-307(e)-1(xamp)1(le)-307(pr)1(ogram)-307(\014)1(le)]TJ/F48 10.9091 Tf 223.4846 0 Td[(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td[(,)-312(i)1(n)-306(the)-307(d)1(irec)-1(tor)1(y)]TJ/F48 10.9091 Tf -332.3016 -13.5492 Td[(examples/fileread)]TJ/F15 10.9091 Tf 100.9306 0 Td[(of)-327(th)1(e)-328(M)1(LD2P4)-327(tr)1(e)-1(e)-327(\050s)-1(ee)-328(S)1(e)-1(ction)]TJ -ET -1 0 0 1 402.5013 532.3603 cm + [(\051.)-419(This)]TJ 0 -13.55 Td [(preconditioner)-238(is)-238(c)28(hosen)-238(b)28(y)-238(simply)-238(sp)-27(ec)-1(i)1(fying)]TJ/F46 10.9091 Tf 212.54 0 Td [('ML')]TJ/F15 10.9091 Tf 25.502 0 Td [(as)-238(second)-238(argumen)28(t)-238(of)]TJ/F46 10.9091 Tf 105.683 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf -343.725 -13.549 Td [(\050a)-359(call)-360(to)]TJ/F46 10.9091 Tf 47.52 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 66.921 0 Td [(is)-359(not)-360(needed\051)-359(and)-359(is)-360(applied)-359(with)-360(th)1(e)-360(BiCGST)83(AB)-359(solv)28(er)-360(pro-)]TJ -114.441 -13.549 Td [(vided)-301(b)28(y)-301(PSBLAS.)-301(As)-301(previously)-301(observ)28(ed,)-308(the)-301(mo)-27(dules)]TJ/F46 10.9091 Tf 268.614 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf 68.726 0 Td [(,)]TJ/F46 10.9091 Tf 6.385 0 Td [(mld_prec_mod)]TJ/F15 10.9091 Tf -343.725 -13.549 Td [(and)]TJ/F46 10.9091 Tf 21.213 0 Td [(psb_krylov_mod)]TJ/F15 10.9091 Tf 83.817 0 Td [(m)28(ust)-334(b)-27(e)-334(used)-333(b)28(y)-334(t)1(he)-334(example)-333(program.)]TJ -88.093 -14.277 Td [(The)-395(part)-395(of)-395(the)-395(co)-28(de)-395(concerning)-395(the)-395(reading)-395(and)-395(assem)27(bl)1(ing)-396(of)-395(th)1(e)-396(sparse)-395(matrix)]TJ -16.937 -13.549 Td [(and)-457(the)-456(righ)27(t-hand)-456(side)-457(v)28(ector,)-488(p)-28(erformed)-456(through)-457(the)-457(PSBLAS)-456(routines)-457(for)-457(sparse)]TJ 0 -13.549 Td [(matrix)-385(and)-385(v)28(ec)-1(t)1(or)-386(managemen)28(t,)-398(is)-385(not)-385(rep)-28(orted)-385(here)-385(for)-385(brevit)27(y;)-411(the)-385(statemen)28(ts)-385(con-)]TJ 0 -13.549 Td [(cerning)-265(the)-264(deallo)-28(cation)-265(of)-264(the)-265(PSBLAS)-265(dat)1(a)-265(structure)-265(are)-265(n)1(e)-1(gl)1(e)-1(cted)-264(to)-28(o.)-422(The)-264(complete)]TJ 0 -13.549 Td [(co)-28(de)-306(can)-307(b)-28(e)-306(found)-306(in)-307(the)-306(example)-307(program)-306(\014le)]TJ/F46 10.9091 Tf 223.485 0 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 108.817 0 Td [(,)-312(in)-306(the)-307(directory)]TJ/F46 10.9091 Tf -332.302 -13.55 Td [(examples/fileread)]TJ/F15 10.9091 Tf 100.931 0 Td [(of)-327(the)-327(MLD2P4)-327(tree)-327(\050see)-327(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -402.5013 -532.3603 cm -BT -/F15 10.9091 Tf 402.5013 532.3603 Td[(4)]TJ -ET -1 0 0 1 407.9559 532.3603 cm + [-327(4)]TJ 0 g 0 G -1 0 0 1 -407.9559 -532.3603 cm -BT -/F15 10.9091 Tf 407.9559 532.3603 Td[(\051.)-442(F)84(or)-327(details)-327(on)-327(th)1(e)-328(u)1(s)-1(e)-327(of)-327(th)1(e)]TJ -266.2174 -13.5492 Td[(PS)1(BLAS)-333(rout)1(ines)-1(,)-333(se)-1(e)-333(the)-334(P)1(SBLAS)-333(Use)-1(r')1(s)-334(Gu)1(ide)-334([)]TJ -ET -1 0 0 1 382.7236 518.8111 cm + [(\051.)-443(F)84(or)-327(details)-327(on)-327(the)-328(u)1(s)-1(e)-327(of)-327(the)]TJ -100.931 -13.549 Td [(PSBLAS)-333(routines,)-334(see)-333(the)-333(PSBLAS)-334(User's)-333(Guide)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -382.7236 -518.8111 cm -BT -/F15 10.9091 Tf 382.7236 518.8111 Td[(11)]TJ -ET -1 0 0 1 393.6327 518.8111 cm + [(11)]TJ 0 g 0 G -1 0 0 1 -393.6327 -518.8111 cm -BT -/F15 10.9091 Tf 393.6327 518.8111 Td[(].)]TJ -234.9577 -14.2764 Td[(The)-461(se)-1(tu)1(p)-460(and)-460(app)1(lication)-460(of)-460(the)-461(d)1(e)-1(f)1(ault)-460(m)27(u)1(lti-lev)28(e)-1(l)-460(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-461(for)-460(the)-461(r)1(e)-1(al)]TJ -16.9365 -13.5492 Td[(single)-450(prec)-1(i)1(s)-1(ion)-450(an)1(d)-450(the)-450(c)-1(omplex,)-479(s)-1(in)1(gle)-451(an)1(d)-450(dou)1(ble)-451(p)1(rec)-1(ision)1(,)-480(v)28(ersions)-451(ar)1(e)-451(obtai)1(ned)]TJ 0 -13.5492 Td[(with)-352(straigh)28(t)1(forw)28(ard)-352(mo)-28(d)1(i\014cation)1(s)-353(of)-352(the)-353(p)1(revious)-353(exampl)1(e)-353(\050s)-1(ee)-353(Sec)-1(t)1(ion)]TJ -ET -1 0 0 1 489.7412 477.4363 cm + [(].)]TJ 16.937 -14.276 Td [(The)-461(setup)-460(and)-461(application)-460(of)-461(the)-460(default)-461(m)28(ulti-lev)28(el)-461(preconditioners)-460(for)-461(the)-460(real)]TJ -16.937 -13.549 Td [(single)-450(prec)-1(i)1(s)-1(ion)-450(and)-450(the)-451(complex,)-479(s)-1(in)1(gle)-451(and)-450(double)-451(precision,)-479(v)27(ersions)-450(are)-450(obtained)]TJ 0 -13.55 Td [(with)-352(s)-1(tr)1(aigh)27(tforw)28(ard)-352(mo)-28(di\014cations)-352(of)-353(the)-352(previous)-353(example)-352(\050see)-353(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -489.7412 -477.4363 cm -BT -/F15 10.9091 Tf 489.7412 477.4363 Td[(7)]TJ -ET -1 0 0 1 495.1958 477.4363 cm + [-352(7)]TJ 0 g 0 G -1 0 0 1 -495.1958 -477.4363 cm -BT -/F15 10.9091 Tf 499.0411 477.4363 Td[(for)-352(d)1(e)-1(tai)1(ls)-1(\051.)]TJ -357.3026 -13.5492 Td[(If)-502(thes)-1(e)-503(v)28(ersions)-503(are)-503(i)1(nstalled,)-545(th)1(e)-503(c)-1(or)1(re)-1(sp)-27(ond)1(ing)-502(F)83(ort)1(ran)-502(95)-503(co)-28(des)-503(are)-503(a)28(v)55(ai)1(lable)-503(i)1(n)]TJ/F48 10.9091 Tf 0 -13.5492 Td[(examples/fileread/)]TJ/F15 10.9091 Tf 103.0898 0 Td[(.)]TJ -86.1533 -14.2764 Td[(Di\013ere)-1(n)29(t)-270(v)28(ersions)-269(of)-269(m)27(ul)1(ti-le)-1(v)28(el)-269(pr)1(e)-1(cond)1(ition)1(e)-1(rs)-269(c)-1(an)-269(b)-27(e)-270(obtai)1(ned)-269(b)28(y)-269(c)27(han)1(gin)1(g)-270(th)1(e)-270(de-)]TJ -16.9365 -13.5492 Td[(fau)1(lt)-273(v)56(alu)1(e)-1(s)-273(of)-272(th)1(e)-274(p)1(rec)-1(on)1(dit)1(ioner)-273(p)1(arame)-1(ters.)-424(The)-273(co)-28(de)-273(rep)-27(orted)-273(i)1(n)-273(Fi)1(gure)]TJ -ET -1 0 0 1 495.9969 422.5122 cm + [-353(for)-352(details\051.)]TJ 0 -13.549 Td [(If)-503(these)-502(v)27(ersions)-502(are)-503(installed,)-545(the)-503(corresp)-28(on)1(ding)-503(F)83(ortran)-502(95)-503(co)-28(des)-503(are)-502(a)28(v)55(ailable)-503(in)]TJ/F46 10.9091 Tf 0 -13.549 Td [(examples/fileread/)]TJ/F15 10.9091 Tf 103.09 0 Td [(.)]TJ -86.153 -14.276 Td [(Di\013eren)28(t)-270(v)28(ersions)-269(of)-270(m)28(ulti-lev)28(el)-270(precondit)1(ioners)-270(can)-269(b)-28(e)-270(obtain)1(e)-1(d)-269(b)28(y)-269(c)27(hanging)-269(the)-269(de-)]TJ -16.937 -13.55 Td [(fault)-273(v)56(alues)-273(of)-272(the)-273(preconditioner)-273(parameters.)-424(The)-273(co)-28(de)-272(rep)-28(orted)-273(in)-272(Figure)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -495.9969 -422.5122 cm -BT -/F15 10.9091 Tf 495.9969 422.5122 Td[(3)]TJ -ET -1 0 0 1 501.4515 422.5122 cm + [-273(3)]TJ 0 g 0 G -1 0 0 1 -501.4515 -422.5122 cm -BT -/F15 10.9091 Tf 504.4266 422.5122 Td[(sho)28(ws)-274(h)1(o)28(w)]TJ -362.6881 -13.5492 Td[(to)-281(s)-1(et)-282(a)-281(thr)1(e)-1(e-)-1(l)1(e)-1(v)28(el)-282(h)29(ybr)1(id)-281(Sc)28(h)28(w)27(ar)1(z)-282(pr)1(e)-1(cond)1(ition)1(e)-1(r,)-291(whic)28(h)-282(u)1(s)-1(es)-282(b)1(lo)-28(c)27(k)-281(Jacobi)-281(with)-281(ILU\0500\051)]TJ 0 -13.5492 Td[(on)-265(t)1(he)-265(lo)-28(cal)-265(bl)1(o)-28(c)27(ks)-265(as)-265(p)-28(ost-s)-1(mo)-28(oth)1(e)-1(r,)-278(h)1(as)-266(a)-265(coarse)-1(st)-265(matrix)-264(re)-1(p)1(licate)-1(d)-264(on)-265(t)1(he)-265(pro)-27(c)-1(es)-1(sors,)]TJ 0 -13.5492 Td[(and)-249(s)-1(olv)28(es)-251(th)1(e)-251(coarse)-1(st-le)-1(v)28(el)-250(s)-1(y)1(s)-1(tem)-251(with)-249(the)-250(LU)-251(f)1(ac)-1(tor)1(ization)-250(f)1(rom)-251(UM)1(FP)84(A)27(CK)-250([)]TJ -ET -1 0 0 1 519.3403 381.8646 cm + [-273(sho)28(ws)-273(ho)28(w)]TJ 0 -13.549 Td [(to)-282(set)-281(a)-282(three-lev)28(el)-281(h)27(ybrid)-281(Sc)28(h)28(w)27(arz)-281(preconditioner,)-292(whic)28(h)-282(uses)-281(blo)-28(c)28(k)-282(Jacobi)-281(with)-282(ILU\0500\051)]TJ 0 -13.549 Td [(on)-265(the)-265(lo)-28(cal)-265(blo)-27(c)27(ks)-265(as)-265(p)-27(ost-smo)-28(other,)-279(has)-265(a)-265(coarsest)-265(matrix)-265(replicated)-265(on)-264(the)-265(pro)-28(cessors,)]TJ 0 -13.549 Td [(and)-250(solv)28(es)-251(the)-250(coarsest-lev)28(el)-251(system)-250(with)-250(the)-250(LU)-250(factorization)-251(fr)1(om)-251(UMFP)84(A)27(CK)-250([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -519.3403 -381.8646 cm -BT -/F15 10.9091 Tf 519.3403 381.8646 Td[(8)]TJ -ET -1 0 0 1 524.7948 381.8646 cm + [(8)]TJ 0 g 0 G -1 0 0 1 -524.7948 -381.8646 cm -BT -/F15 10.9091 Tf 524.7948 381.8646 Td[(].)-416(T)-1(h)1(e)]TJ -383.0563 -13.5492 Td[(n)28(u)1(m)27(b)-27(e)-1(r)-362(of)-361(le)-1(v)28(els)-363(i)1(s)-363(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)-361(b)28(y)-362(using)]TJ/F48 10.9091 Tf 182.1814 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(;)-377(t)1(he)-363(oth)1(e)-1(r)-362(p)1(rec)-1(on)1(dit)1(ioner)-362(par)1(am)-1(-)]TJ -250.9079 -13.5492 Td[(ete)-1(r)1(s)-352(ar)1(e)-351(s)-1(et)-351(b)28(y)-350(c)-1(al)1(ling)]TJ/F48 10.9091 Tf 112.0394 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)-496(Note)-351(that)-351(t)1(he)-351(t)28(yp)-27(e)-352(of)-350(m)28(ulti)1(le)-1(v)28(el)-351(f)1(rame)-1(w)28(ork)-350(\050i.e.)]TJ -175.0387 -13.5492 Td[(m)27(u)1(ltip)1(licativ)28(e)-279(am)-1(on)1(g)-280(th)1(e)-280(lev)28(els)-280(with)-279(p)-27(ost-)-1(smo)-28(othi)1(ng)-279(only)1(\051)-279(is)-280(n)1(ot)-280(sp)-27(e)-1(ci\014ed)-279(since)-280(it)-279(i)1(s)-280(the)]TJ 0 -13.5492 Td[(defau)1(lt)-333(s)-1(et)-333(b)28(y)]TJ/F48 10.9091 Tf 68.8485 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(.)]TJ -120.6386 -14.2764 Td[(Figu)1(re)]TJ -ET -1 0 0 1 192.7448 313.3914 cm + [(].)-416(The)]TJ 0 -13.549 Td [(n)28(um)28(b)-28(er)-362(of)-363(lev)28(els)-362(is)-363(sp)-27(eci\014ed)-363(b)28(y)-362(using)]TJ/F46 10.9091 Tf 182.182 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.726 0 Td [(;)-377(the)-362(other)-362(preconditioner)-362(param-)]TJ -250.908 -13.55 Td [(eters)-351(are)-351(set)-350(b)27(y)-350(calling)]TJ/F46 10.9091 Tf 112.04 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)-497(Note)-350(that)-351(the)-351(t)28(yp)-28(e)-350(of)-351(m)28(ultilev)28(e)-1(l)-350(framew)28(ork)-351(\050i.e.)]TJ -175.039 -13.549 Td [(m)28(ultiplicativ)28(e)-280(among)-279(the)-279(lev)28(els)-280(with)-279(p)-28(ost-smo)-27(othing)-280(only\051)-279(is)-279(not)-279(sp)-28(eci\014ed)-279(since)-280(it)-279(is)-279(the)]TJ 0 -13.549 Td [(default)-333(set)-334(b)28(y)]TJ/F46 10.9091 Tf 68.849 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.726 0 Td [(.)]TJ -120.638 -14.276 Td [(Figure)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -192.7448 -313.3914 cm -BT -/F15 10.9091 Tf 192.7448 313.3914 Td[(4)]TJ -ET -1 0 0 1 198.1993 313.3914 cm + [-301(4)]TJ 0 g 0 G -1 0 0 1 -198.1993 -313.3914 cm -BT -/F15 10.9091 Tf 201.4812 313.3914 Td[(sho)28(ws)-302(h)1(o)27(w)-301(t)1(o)-301(s)-1(et)-301(a)-301(th)1(ree)-1(-lev)28(e)-1(l)-300(addi)1(tiv)28(e)-301(Sc)28(h)28(w)27(ar)1(z)-302(p)1(rec)-1(on)1(diti)1(oner,)-307(whic)28(h)-301(u)1(s)-1(es)]TJ -59.7427 -13.5492 Td[(RAS,)-432(w)-1(i)1(th)-433(o)28(v)28(erlap)-432(1)-433(and)-432(ILU\0500\051)-433(on)-433(t)1(he)-433(blo)-28(c)28(ks,)-458(as)-433(pre-)-433(and)-432(p)-28(ost-s)-1(mo)-28(oth)1(e)-1(r)1(,)-458(and)-432(ap-)]TJ 0 -13.5492 Td[(pl)1(ie)-1(s)-340(\014v)28(e)-340(bl)1(o)-28(c)27(k-Jacobi)-339(s)-1(w)28(e)-1(eps,)-342(with)-339(the)-340(UMF)1(P)83(A)28(CK)-340(LU)-340(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-340(on)-339(the)-340(blo)-27(c)27(ks,)-342(as)]TJ 0 -13.5492 Td[(di)1(s)-1(tr)1(ibu)1(te)-1(d)-402(coarse)-1(st-lev)28(e)-1(l)-402(s)-1(ol)1(v)28(e)-1(r.)-651(Again)1(,)]TJ/F48 10.9091 Tf 196.8656 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 67.3899 0 Td[(is)-403(u)1(s)-1(ed)-402(only)-402(to)-402(s)-1(et)-402(non)1(-)-1(d)1(e)-1(f)1(ault)]TJ -264.2555 -13.5492 Td[(v)56(alues)-271(of)-270(the)-271(par)1(am)-1(eters)-271(\050se)-1(e)-271(T)83(abl)1(e)-1(s)]TJ -ET -1 0 0 1 314.0027 259.1946 cm + [-301(sho)28(ws)-301(ho)28(w)-301(to)-301(set)-301(a)-300(three-lev)27(el)-300(additiv)27(e)-300(Sc)27(h)28(w)28(arz)-301(preconditioner,)-307(whic)28(h)-301(uses)]TJ -16.937 -13.55 Td [(RAS,)-433(with)-433(o)28(v)28(erlap)-433(1)-433(and)-433(ILU\0500\051)-433(on)-433(the)-433(bl)1(o)-28(c)27(ks,)-457(as)-433(pre-)-433(and)-433(p)-28(ost-smo)-28(other,)-458(an)1(d)-433(ap-)]TJ 0 -13.549 Td [(plies)-340(\014v)28(e)-340(blo)-28(c)28(k-Jacobi)-340(sw)28(eeps,)-342(with)-340(the)-340(UMFP)83(A)28(CK)-340(LU)-340(factorization)-340(on)-340(th)1(e)-340(blo)-28(c)28(ks)-1(,)-341(as)]TJ 0 -13.549 Td [(distributed)-402(coarsest-le)-1(v)28(el)-402(solv)28(er.)-652(Again,)]TJ/F46 10.9091 Tf 196.866 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 67.39 0 Td [(is)-402(use)-1(d)-402(only)-402(to)-403(set)-402(non-default)]TJ -264.256 -13.549 Td [(v)56(alues)-271(of)-271(the)-271(p)1(arame)-1(ters)-270(\050see)-271(T)83(ables)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -314.0027 -259.1946 cm -BT -/F15 10.9091 Tf 314.0027 259.1946 Td[(2)]TJ -ET -1 0 0 1 319.4572 259.1946 cm + [-271(2)]TJ 0 g 0 G -1 0 0 1 -319.4572 -259.1946 cm -BT -/F15 10.9091 Tf 319.4572 259.1946 Td[(-)]TJ -ET -1 0 0 1 323.0936 259.1946 cm + [(-)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -323.0936 -259.1946 cm -BT -/F15 10.9091 Tf 323.0936 259.1946 Td[(5)]TJ -ET -1 0 0 1 328.5482 259.1946 cm + [(5)]TJ 0 g 0 G -1 0 0 1 -328.5482 -259.1946 cm -BT -/F15 10.9091 Tf 328.5482 259.1946 Td[(\051.)-423(In)-271(b)-27(oth)-270(c)-1(ases)-1(,)-283(th)1(e)-271(c)-1(on)1(s)-1(tr)1(uction)-270(and)-270(the)-271(ap)1(pli)1(-)]TJ -186.8097 -13.5492 Td[(cation)-268(of)-269(th)1(e)-269(precondi)1(tioner)-268(are)-269(c)-1(ar)1(ried)-268(out)-269(as)-269(f)1(or)-269(th)1(e)-269(defau)1(lt)-269(m)28(ulti)1(-)-1(lev)28(el)-269(p)1(re)-1(cond)1(ition)1(e)-1(r)1(.)]TJ 0 -13.5492 Td[(The)-368(c)-1(o)-27(de)-369(f)1(ragme)-1(n)29(ts)-369(sho)28(wn)-368(i)1(n)-368(in)-367(Figur)1(e)-1(s)]TJ -ET -1 0 0 1 339.6307 232.0962 cm + [(\051.)-423(In)-271(b)-27(oth)-271(cases,)-284(th)1(e)-271(construction)-271(and)-270(the)-271(appli-)]TJ 0 -13.549 Td [(cation)-269(of)-268(the)-269(preconditioner)-269(are)-268(carried)-269(out)-269(as)-269(f)1(or)-269(the)-269(default)-268(m)27(ulti-lev)28(el)-269(precondition)1(e)-1(r)1(.)]TJ 0 -13.55 Td [(The)-368(co)-28(de)-368(fragmen)28(ts)-368(sho)28(wn)-368(in)-368(in)-368(Figures)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -339.6307 -232.0962 cm -BT -/F15 10.9091 Tf 339.6307 232.0962 Td[(3)]TJ -ET -1 0 0 1 345.0852 232.0962 cm + [-368(3)]TJ 0 g 0 G -1 0 0 1 -345.0852 -232.0962 cm -BT -/F15 10.9091 Tf 345.0852 232.0962 Td[(-)]TJ -ET -1 0 0 1 348.7216 232.0962 cm + [(-)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -348.7216 -232.0962 cm -BT -/F15 10.9091 Tf 348.7216 232.0962 Td[(4)]TJ -ET -1 0 0 1 354.1761 232.0962 cm + [(4)]TJ 0 g 0 G -1 0 0 1 -354.1761 -232.0962 cm -BT -/F15 10.9091 Tf 358.191 232.0962 Td[(are)-368(in)1(c)-1(lu)1(ded)-368(in)-367(the)-368(e)-1(x)1(am)-1(p)1(le)-369(p)1(rogr)1(am)-369(\014)1(le)]TJ/F48 10.9091 Tf -216.4525 -13.5492 Td[(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 112.4533 0 Td[(to)-28(o.)]TJ -95.5168 -14.2764 Td[(Fin)1(ally)84(,)-295(Figu)1(re)]TJ -ET -1 0 0 1 231.4106 204.2706 cm + [-368(are)-368(included)-368(in)-368(the)-368(example)-368(program)-368(\014le)]TJ/F46 10.9091 Tf 0 -13.549 Td [(mld_dexample_ml.f90)]TJ/F15 10.9091 Tf 112.454 0 Td [(to)-28(o.)]TJ -95.517 -14.276 Td [(Finally)83(,)-295(Figure)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -231.4106 -204.2706 cm -BT -/F15 10.9091 Tf 231.4106 204.2706 Td[(5)]TJ -ET -1 0 0 1 236.8651 204.2706 cm + [-286(5)]TJ 0 g 0 G -1 0 0 1 -236.8651 -204.2706 cm -BT -/F15 10.9091 Tf 239.9842 204.2706 Td[(sho)28(ws)-287(th)1(e)-287(setup)-285(of)-286(a)-286(on)1(e)-1(-lev)28(e)-1(l)-285(addi)1(tiv)28(e)-286(Sc)27(h)29(w)27(arz)-286(p)1(re)-1(cond)1(ition)1(e)-1(r)1(,)-295(i.e.)]TJ -98.2457 -13.5492 Td[(RAS)-222(with)-221(o)27(v)28(erlap)-221(2.)-408(Th)1(e)-223(corres)-1(p)-27(ond)1(in)1(g)-223(example)-222(pr)1(ogram)-223(i)1(s)-223(a)28(v)55(ai)1(labl)1(e)-223(in)]TJ/F48 10.9091 Tf 336.9891 0 Td[(mld_dexample_1lev.f90)]TJ/F15 10.9091 Tf 120.2714 0 Td[(.)]TJ -440.324 -14.2765 Td[(F)84(or)-452(all)-452(th)1(e)-453(p)1(reviou)1(s)-453(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-1(,)-481(e)-1(x)1(am)-1(p)1(le)-453(p)1(rogr)1(am)-1(s)-452(where)-453(t)1(he)-452(s)-1(p)1(ars)-1(e)-452(matrix)]TJ -16.9365 -13.5492 Td[(and)-370(th)1(e)-371(righ)29(t-)-1(h)1(and)-370(side)-371(ar)1(e)-371(ge)-1(n)1(e)-1(r)1(ate)-1(d)-370(b)28(y)-370(di)1(s)-1(cretiz)-1(i)1(ng)-370(a)-371(PD)1(E)-371(wit)1(h)-371(D)1(iric)28(hlet)-371(b)-27(ou)1(ndar)1(y)]TJ 0 -13.5492 Td[(condi)1(tions)-333(are)-334(also)-333(a)27(v)56(ail)1(able)-333(in)-333(the)-333(dir)1(e)-1(ctory)]TJ/F48 10.9091 Tf 215.0608 0 Td[(examples/pdegen)]TJ/F15 10.9091 Tf 85.9082 0 Td[(.)]TJ/F41 10.9091 Tf -300.969 -27.8256 Td[(Re)-1(mark)-318(3.)]TJ/F15 10.9091 Tf 61.3782 0 Td[(An)28(y)-277(P)1(SBLAS-based)-277(pr)1(ogram)-278(u)1(s)-1(i)1(ng)-277(th)1(e)-278(basic)-277(prec)-1(on)1(di)1(tioners)-277(implem)-1(en)28(ted)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [-286(sho)28(ws)-286(the)-286(setup)-286(of)-286(a)-285(one-lev)27(el)-286(additi)1(v)27(e)-286(Sc)28(h)28(w)28(arz)-286(preconditioner,)-295(i.e.)]TJ -16.937 -13.549 Td [(RAS)-222(with)-222(o)27(v)28(erlap)-222(2.)-407(The)-223(corr)1(e)-1(sp)-27(onding)-222(example)-223(program)-222(is)-222(a)28(v)55(ailable)-222(in)]TJ/F46 10.9091 Tf 336.989 0 Td [(mld_dexample_1lev.f90)]TJ/F15 10.9091 Tf 120.272 0 Td [(.)]TJ -440.324 -14.277 Td [(F)83(or)-452(all)-452(the)-452(previous)-452(precondi)1(tioners,)-482(example)-452(programs)-452(where)-452(the)-452(sparse)-452(matrix)]TJ -16.937 -13.549 Td [(and)-371(th)1(e)-371(righ)28(t-hand)-371(side)-370(are)-371(generated)-370(b)27(y)-370(discretizing)-371(a)-370(PDE)-371(with)-370(Diric)28(hlet)-371(b)-28(oundary)]TJ 0 -13.549 Td [(conditions)-333(are)-334(also)-333(a)28(v)55(ailable)-333(in)-333(the)-333(directory)]TJ/F46 10.9091 Tf 215.061 0 Td [(examples/pdegen)]TJ/F15 10.9091 Tf 85.908 0 Td [(.)]TJ/F39 10.9091 Tf -300.969 -27.826 Td [(Remark)-319(3.)]TJ/F15 10.9091 Tf 61.379 0 Td [(An)28(y)-277(PSBLAS-based)-277(program)-277(using)-277(the)-278(basic)-277(preconditioners)-277(implemen)28(ted)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -375 0 obj << +352 0 obj << /Type /Page -/Contents 376 0 R -/Resources 374 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 311 0 R -/Annots [ 378 0 R 379 0 R 380 0 R 381 0 R 382 0 R 383 0 R 384 0 R 385 0 R 386 0 R 387 0 R 388 0 R 389 0 R 390 0 R ] +/Contents 353 0 R +/Resources 351 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 281 0 R +/Annots [ 333 0 R 334 0 R 340 0 R 341 0 R 342 0 R 343 0 R 344 0 R 345 0 R 346 0 R 347 0 R 348 0 R 349 0 R 350 0 R ] >> endobj -378 0 obj << +333 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [279.832 679.0112 287.2791 690.7007] +/Rect [279.832 679.011 287.279 690.701] /Subtype /Link /A << /S /GoTo /D (figure.2) >> >> endobj -379 0 obj << +334 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [514.6201 664.856 522.0672 677.7576] +/Rect [514.62 664.856 522.067 677.758] /Subtype /Link /A << /S /GoTo /D (table.1) >> >> endobj -380 0 obj << +340 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [401.5051 528.6368 408.9522 541.5384] +/Rect [401.505 528.637 408.952 541.538] /Subtype /Link /A << /S /GoTo /D (section.4) >> >> endobj -381 0 obj << +341 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [381.7273 517.8148 394.629 526.8377] +/Rect [381.727 517.815 394.629 526.838] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -382 0 obj << +342 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [488.7449 473.7127 496.192 486.6143] +/Rect [488.745 473.713 496.192 486.614] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -383 0 obj << +343 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [495.0007 419.3948 502.4477 431.0842] +/Rect [495.001 419.395 502.448 431.084] /Subtype /Link /A << /S /GoTo /D (figure.3) >> >> endobj -384 0 obj << +344 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [518.344 380.8684 525.7911 389.8912] +/Rect [518.344 380.868 525.791 389.891] /Subtype /Link /A << /S /GoTo /D (cite.UMFPACK) >> >> endobj -385 0 obj << +345 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [191.7485 310.2739 199.1956 321.9634] +/Rect [191.749 310.274 199.196 321.963] /Subtype /Link /A << /S /GoTo /D (figure.4) >> >> endobj -386 0 obj << +346 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [313.0064 255.4711 320.4535 268.3727] +/Rect [313.006 255.471 320.453 268.373] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -387 0 obj << +347 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [322.0973 255.4711 329.5444 268.3727] +/Rect [322.097 255.471 329.544 268.373] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -388 0 obj << +348 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [338.6344 228.9787 346.0815 240.6682] +/Rect [338.634 228.979 346.081 240.668] /Subtype /Link /A << /S /GoTo /D (figure.3) >> >> endobj -389 0 obj << +349 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [347.7253 228.9787 355.1724 240.6682] +/Rect [347.725 228.979 355.172 240.668] /Subtype /Link /A << /S /GoTo /D (figure.4) >> >> endobj -390 0 obj << +350 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [230.4143 201.1531 237.8614 212.8426] +/Rect [230.414 201.153 237.861 212.843] /Subtype /Link /A << /S /GoTo /D (figure.5) >> >> endobj -377 0 obj << -/D [375 0 R /XYZ 141.7385 740.0018 null] +354 0 obj << +/D [352 0 R /XYZ 141.738 740.002 null] >> endobj 58 0 obj << -/D [375 0 R /XYZ 141.7385 715.0952 null] +/D [352 0 R /XYZ 141.738 715.095 null] >> endobj -374 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F19 105 0 R /F48 214 0 R /F41 126 0 R >> +351 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F17 103 0 R /F46 195 0 R /F39 116 0 R >> /ProcSet [ /PDF /Text ] >> endobj -398 0 obj << -/Length 3980 +363 0 obj << +/Length 3396 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(6)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(6)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Getti)-1(ng)-378(St)67(a)-1(r)67(ted)]TJ/F15 10.9091 Tf 391.3906 0 Td[(19)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Getting)-378(St)67(ar)67(ted)]TJ/F15 10.9091 Tf 401.542 0 Td [(19)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 15.1693 -293.8024 cm 0 g 0 G 0 g 0 G -1 0 0 1 0 287.7141 cm 0 g 0 G 0 g 0 G -1 0 0 1 -109.0871 -709.0069 cm -BT -/F48 9.9626 Tf 125.0023 709.0069 Td[(use)-525(psb_base_mod)]TJ 0 -11.9552 Td[(use)-525(mld_prec_mod)]TJ 0 -11.9551 Td[(use)-525(psb_krylov_mod)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)]TJ 0 -11.9551 Td[(!)-525(sparse)-525(matrix)]TJ 10.4607 -11.9552 Td[(type\050psb_dspmat_type\051)-525(::)-525(A)]TJ -10.4607 -11.9552 Td[(!)-525(sparse)-525(matrix)-525(descriptor)]TJ 10.4607 -11.9551 Td[(type\050psb_desc_type\051)-1575(::)-525(desc_A)]TJ -10.4607 -11.9552 Td[(!)-525(preconditioner)]TJ 10.4607 -11.9552 Td[(type\050mld_dprec_type\051)-1050(::)-525(P)]TJ -10.4607 -11.9551 Td[(!)-525(right-hand)-525(side)-525(and)-525(solution)-525(vectors)]TJ 10.4607 -11.9552 Td[(real\050kind\0501.d0\051\051)-3150(::)-525(b\050:\051,)-525(x\050:\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ 0 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(initialize)-525(the)-525(parallel)-525(environment)]TJ 10.4607 -11.9552 Td[(call)-525(psb_init\050ictxt\051)]TJ 0 -11.9551 Td[(call)-525(psb_info\050ictxt,iam,np\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)]TJ 0 -11.9551 Td[(!)-525(read)-525(and)-525(assemble)-525(the)-525(matrix)-525(A)-525(and)-525(the)-525(right-hand)-525(side)-525(b)]TJ 0 -11.9552 Td[(!)-525(using)-525(PSBLAS)-525(routines)-525(for)-525(sparse)-525(matrix)-525(/)-525(vector)-525(management)]TJ 0 -11.9552 Td[(...)-525(...)]TJ 0 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(initialize)-525(the)-525(default)-525(multi-level)-525(preconditioner,)-525(i.e.)-525(hybrid)]TJ 0 -11.9552 Td[(!)-525(Schwarz,)-525(using)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)]TJ 0 -11.9551 Td[(!)-525(as)-525(post-smoother)-525(and)-525(4)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.9552 Td[(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarse-level)-525(solver)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'ML',info\051)]TJ -10.4607 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(build)-525(the)-525(preconditioner)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precbld\050A,desc_A,P,info\051)]TJ -10.4607 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(set)-525(the)-525(solver)-525(parameters)-525(and)-525(the)-525(initial)-525(guess)]TJ 10.4607 -11.9552 Td[(...)-525(...)]TJ -10.4607 -11.9551 Td[(!)]TJ 0 -11.9552 Td[(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.4607 -11.9552 Td[(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ 0 -11.9551 Td[(...)-525(...)]TJ -10.4607 -11.9552 Td[(!)]TJ 0 -11.9552 Td[(!)-525(deallocate)-525(the)-525(preconditioner)]TJ 10.4607 -11.9551 Td[(call)-525(mld_precfree\050P,info\051)]TJ -10.4607 -11.9552 Td[(!)]TJ 0 -11.9552 Td[(!)-525(deallocate)-525(other)-525(data)-525(structures)]TJ 10.4607 -11.9551 Td[(...)-525(...)]TJ -10.4607 -11.9552 Td[(!)]TJ 0 -11.9552 Td[(!)-525(exit)-525(the)-525(parallel)-525(environment)]TJ 10.4607 -11.9551 Td[(call)-525(psb_exit\050ictxt\051)]TJ 0 -11.9552 Td[(stop)]TJ -ET -1 0 0 1 101.9765 114.4103 cm +/F46 9.9626 Tf -370.458 -30.995 Td [(use)-525(psb_base_mod)]TJ 0 -11.955 Td [(use)-525(mld_prec_mod)]TJ 0 -11.955 Td [(use)-525(psb_krylov_mod)]TJ -10.46 -11.956 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(sparse)-525(matrix)]TJ 10.46 -11.955 Td [(type\050psb_dspmat_type\051)-525(::)-525(A)]TJ -10.46 -11.955 Td [(!)-525(sparse)-525(matrix)-525(descriptor)]TJ 10.46 -11.955 Td [(type\050psb_desc_type\051)-1575(::)-525(desc_A)]TJ -10.46 -11.956 Td [(!)-525(preconditioner)]TJ 10.46 -11.955 Td [(type\050mld_dprec_type\051)-1050(::)-525(P)]TJ -10.46 -11.955 Td [(!)-525(right-hand)-525(side)-525(and)-525(solution)-525(vectors)]TJ 10.46 -11.955 Td [(real\050kind\0501.d0\051\051)-3150(::)-525(b\050:\051,)-525(x\050:\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.956 Td [(!)-525(initialize)-525(the)-525(parallel)-525(environment)]TJ 10.46 -11.955 Td [(call)-525(psb_init\050ictxt\051)]TJ 0 -11.955 Td [(call)-525(psb_info\050ictxt,iam,np\051)]TJ -10.46 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(read)-525(and)-525(assemble)-525(the)-525(matrix)-525(A)-525(and)-525(the)-525(right-hand)-525(side)-525(b)]TJ 0 -11.956 Td [(!)-525(using)-525(PSBLAS)-525(routines)-525(for)-525(sparse)-525(matrix)-525(/)-525(vector)-525(management)]TJ 0 -11.955 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(initialize)-525(the)-525(default)-525(multi-level)-525(preconditioner,)-525(i.e.)-525(hybrid)]TJ 0 -11.955 Td [(!)-525(Schwarz,)-525(using)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)]TJ 0 -11.956 Td [(!)-525(as)-525(post-smoother)-525(and)-525(4)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.955 Td [(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarse-level)-525(solver)]TJ 10.46 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info\051)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(build)-525(the)-525(preconditioner)]TJ 10.46 -11.955 Td [(call)-525(mld_precbld\050A,desc_A,P,info\051)]TJ -10.46 -11.956 Td [(!)]TJ 0 -11.955 Td [(!)-525(set)-525(the)-525(solver)-525(parameters)-525(and)-525(the)-525(initial)-525(guess)]TJ 10.46 -11.955 Td [(...)-525(...)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(solve)-525(Ax=b)-525(with)-525(preconditioned)-525(BiCGSTAB)]TJ 10.46 -11.955 Td [(call)-525(psb_krylov\050'BICGSTAB',A,P,b,x,tol,desc_A,info\051)]TJ 0 -11.956 Td [(...)-525(...)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(the)-525(preconditioner)]TJ 10.46 -11.955 Td [(call)-525(mld_precfree\050P,info\051)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(deallocate)-525(other)-525(data)-525(structures)]TJ 10.46 -11.956 Td [(...)-525(...)]TJ -10.46 -11.955 Td [(!)]TJ 0 -11.955 Td [(!)-525(exit)-525(the)-525(parallel)-525(environment)]TJ 10.46 -11.955 Td [(call)-525(psb_exit\050ictxt\051)]TJ 0 -11.955 Td [(stop)]TJ 0 g 0 G -1 0 0 1 -101.9765 -114.4103 cm -BT -/F15 10.9091 Tf 101.9765 114.4103 Td[(Figu)1(re)-334(2:)-444(S)1(e)-1(tu)1(p)-333(and)-333(ap)1(pl)1(ic)-1(ati)1(on)-333(of)-333(the)-333(defau)1(lt)-333(m)27(ul)1(ti-le)-1(v)28(el)-333(Sc)28(h)28(w)27(ar)1(z)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ -ET -1 0 0 1 498.3102 114.4103 cm +/F15 10.9091 Tf -23.025 -20.749 Td [(Figure)-333(2:)-445(Setup)-333(and)-333(application)-333(of)-334(the)-333(default)-333(m)28(ulti-lev)27(el)-333(Sc)28(h)28(w)27(arz)-333(preconditioner.)]TJ 0 g 0 G -1 0 0 1 -404.3924 -14.0764 cm 0 g 0 G -1 0 0 1 0 -8.701 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -397 0 obj << +362 0 obj << /Type /Page -/Contents 398 0 R -/Resources 396 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 401 0 R -/Annots [ 400 0 R ] +/Contents 363 0 R +/Resources 361 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 365 0 R +/Annots [ 360 0 R ] >> endobj -400 0 obj << +360 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.6) >> >> endobj -399 0 obj << -/D [397 0 R /XYZ 93.9178 740.0018 null] +364 0 obj << +/D [362 0 R /XYZ 93.918 740.002 null] >> endobj -391 0 obj << -/D [397 0 R /XYZ 149.7341 127.9595 null] +355 0 obj << +/D [362 0 R /XYZ 149.734 127.96 null] >> endobj -396 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F48 214 0 R >> +361 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -404 0 obj << -/Length 4744 +368 0 obj << +/Length 3556 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(20)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(20)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 15.1693 -57.1482 cm 0 g 0 G 0 g 0 G -1 0 0 1 0 55.9029 cm 0 g 0 G 0 g 0 G -1 0 0 1 -156.9078 -713.8499 cm -BT -/F48 9.9626 Tf 162.3623 713.8499 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)-525(set)-525(a)-525(three-level)-525(hybrid)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.9551 Td[(!)-525(block)-525(Jacobi)-525(\050with)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(post-smoother,)]TJ 0 -11.9552 Td[(!)-525(a)-525(coarsest)-525(matrix)-525(replicated)-525(on)-525(the)-525(processors,)-525(and)-525(the)]TJ 0 -11.9552 Td[(!)-525(LU)-525(factorization)-525(from)-525(UMFPACK)-525(as)-525(coarse-level)-525(solver)]TJ 10.4607 -11.9551 Td[(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.9552 Td[(call_mld_precset\050P,mld_smoother_type_,'BJAC',info\051)]TJ 0 -11.9552 Td[(call)-525(mld_precset\050P,mld_coarse_mat_,'REPL',info\051)]TJ 0 -11.9551 Td[(call)-525(mld_precset\050P,mld_coarse_solve_,'UMF',info\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ -ET -1 0 0 1 197.3427 587.7187 cm +/F46 9.9626 Tf -182.641 -26.152 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(a)-525(three-level)-525(hybrid)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.955 Td [(!)-525(block)-525(Jacobi)-525(\050with)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(post-smoother,)]TJ 0 -11.956 Td [(!)-525(a)-525(coarsest)-525(matrix)-525(replicated)-525(on)-525(the)-525(processors,)-525(and)-525(the)]TJ 0 -11.955 Td [(!)-525(LU)-525(factorization)-525(from)-525(UMFPACK)-525(as)-525(coarse-level)-525(solver)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.955 Td [(call_mld_precset\050P,mld_smoother_type_,'BJAC',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_coarse_mat_,'REPL',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_coarse_solve_,'UMF',info\051)]TJ -10.461 -11.956 Td [(...)-525(...)]TJ 0 g 0 G -1 0 0 1 -197.3427 -587.7187 cm -BT -/F15 10.9091 Tf 197.3427 587.7187 Td[(Figu)1(re)-334(3:)-444(S)1(e)-1(tu)1(p)-333(of)-333(a)-333(h)28(yb)1(rid)-333(th)1(ree)-1(-lev)28(e)-1(l)-333(S)1(c)27(h)28(w)28(arz)-334(p)1(rec)-1(on)1(diti)1(oner.)]TJ -ET -1 0 0 1 498.5854 587.7187 cm +/F15 10.9091 Tf 34.981 -18.534 Td [(Figure)-333(3:)-445(Setup)-333(of)-333(a)-334(h)28(ybrid)-333(three-lev)28(el)-333(Sc)27(h)28(w)28(arz)-333(preconditioner.)]TJ 0 g 0 G -1 0 0 1 -356.8469 -14.0764 cm 0 g 0 G -1 0 0 1 0 -11.9551 cm 0 g 0 G -1 0 0 1 15.1693 -57.1482 cm 0 g 0 G 0 g 0 G -1 0 0 1 0 55.9029 cm 0 g 0 G 0 g 0 G -1 0 0 1 -156.9078 -560.4419 cm -BT -/F48 9.9626 Tf 162.3623 560.4419 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)-525(set)-525(a)-525(three-level)-525(additive)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.9552 Td[(!)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(pre-)-525(and)]TJ 0 -11.9551 Td[(!)-525(post-smoother,)-525(and)-525(5)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.9552 Td[(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarsest-level)-525(solver)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.9551 Td[(call)-525(mld_precset\050P,mld_ml_type_,'ADD',info\051)]TJ 0 -11.9552 Td[(call_mld_precset\050P,mld_smoother_pos_,'TWOSIDE',info\051)]TJ 0 -11.9552 Td[(call)-525(mld_precset\050P,mld_coarse_sweeps_,5,info\051)]TJ -10.4607 -11.9551 Td[(...)-525(...)]TJ -ET -1 0 0 1 190.6912 434.3107 cm +/F46 9.9626 Tf -34.981 -27.277 Td [(...)-525(...)]TJ 0 -11.955 Td [(!)-525(set)-525(a)-525(three-level)-525(additive)-525(Schwarz)-525(preconditioner,)-525(which)-525(uses)]TJ 0 -11.955 Td [(!)-525(RAS)-525(\050with)-525(overlap)-525(1)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(blocks\051)-525(as)-525(pre-)-525(and)]TJ 0 -11.956 Td [(!)-525(post-smoother,)-525(and)-525(5)-525(block-Jacobi)-525(sweeps)-525(\050with)-525(UMFPACK)-525(LU)]TJ 0 -11.955 Td [(!)-525(on)-525(the)-525(blocks\051)-525(as)-525(distributed)-525(coarsest-level)-525(solver)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'ML',info,nlev=3\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_ml_type_,'ADD',info\051)]TJ 0 -11.955 Td [(call_mld_precset\050P,mld_smoother_pos_,'TWOSIDE',info\051)]TJ 0 -11.956 Td [(call)-525(mld_precset\050P,mld_coarse_sweeps_,5,info\051)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ 0 g 0 G -1 0 0 1 -190.6912 -434.3107 cm -BT -/F15 10.9091 Tf 190.6912 434.3107 Td[(Figu)1(re)-334(4:)-444(S)1(e)-1(tu)1(p)-333(of)-333(an)-333(ad)1(diti)1(v)28(e)-334(thr)1(e)-1(e-)-1(l)1(e)-1(v)28(el)-333(Sc)27(h)29(w)27(ar)1(z)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r.)]TJ -ET -1 0 0 1 505.2369 434.3107 cm +/F15 10.9091 Tf 28.329 -18.534 Td [(Figure)-333(4:)-445(Setup)-333(of)-333(an)-334(ad)1(ditiv)27(e)-333(three-lev)28(el)-334(Sc)28(h)28(w)28(arz)-334(pr)1(e)-1(cond)1(itioner.)]TJ 0 g 0 G -1 0 0 1 -363.4984 -14.0764 cm 0 g 0 G -1 0 0 1 -141.7385 -420.2343 cm -BT -/F15 10.9091 Tf 141.7385 389.3501 Td[(in)-269(P)1(SBLAS)-269(2.0,)-282(i.)1(e)-1(.)-269(th)1(e)-270(diagon)1(al)-269(and)-269(b)1(lo)-28(c)27(k)1(-)-1(Jacobi)-269(on)1(e)-1(s,)-282(c)-1(an)-268(use)-270(the)-270(d)1(iagon)1(al)-270(an)1(d)-269(bl)1(o)-28(c)27(k-)]TJ 0 -13.5492 Td[(Jacobi)-337(p)1(rec)-1(on)1(diti)1(oners)-337(implem)-1(en)28(ted)-337(i)1(n)-337(MLD)1(2P4)-337(with)1(out)-337(an)28(y)-336(c)27(han)1(ge)-337(in)-337(th)1(e)-338(co)-28(d)1(e)-1(.)-455(The)]TJ 0 -13.5492 Td[(PS)1(BLAS-base)-1(d)-333(p)1(rogram)-333(m)27(u)1(s)-1(t)-333(b)-27(e)-334(onl)1(y)-334(r)1(e)-1(compiled)-333(an)1(d)-333(lin)1(k)28(e)-1(d)-333(to)-333(th)1(e)-334(MLD2P)1(4)-334(l)1(ibr)1(ary)83(.)]TJ -ET -1 0 0 1 141.7385 203.1979 cm + -48.953 -44.961 Td [(in)-269(PSBLAS)-270(2.0,)-282(i.e.)-269(the)-269(diagonal)-270(and)-269(blo)-28(c)28(k-Jacobi)-269(ones,)-283(can)-269(use)-269(the)-270(diagonal)-269(and)-269(blo)-28(c)28(k-)]TJ 0 -13.549 Td [(Jacobi)-337(preconditioners)-337(implemen)28(ted)-337(in)-337(MLD2P4)-337(without)-337(an)28(y)-337(c)28(hange)-337(in)-337(the)-337(co)-27(de.)-456(The)]TJ 0 -13.549 Td [(PSBLAS-based)-333(program)-334(m)28(ust)-333(b)-28(e)-333(only)-334(r)1(e)-1(compiled)-333(and)-333(link)28(ed)-334(to)-333(the)-333(MLD2P4)-333(library)83(.)]TJ 0 g 0 G -1 0 0 1 15.1693 -27.2603 cm 0 g 0 G 0 g 0 G -1 0 0 1 0 26.015 cm 0 g 0 G 0 g 0 G -1 0 0 1 -156.9078 -201.9526 cm -BT -/F48 9.9626 Tf 162.3623 201.9526 Td[(...)-525(...)]TJ 0 -11.9552 Td[(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.4607 -11.9552 Td[(call)-525(mld_precinit\050P,'AS',info\051)]TJ 0 -11.9551 Td[(call)-525(mld_precset\050P,mld_sub_ovr_,2,info\051)]TJ -10.4607 -11.9552 Td[(...)-525(...)]TJ -ET -1 0 0 1 218.5852 135.5973 cm +/F46 9.9626 Tf 20.624 -160.299 Td [(...)-525(...)]TJ 0 -11.956 Td [(!)-525(set)-525(RAS)-525(with)-525(overlap)-525(2)-525(and)-525(ILU\0500\051)-525(on)-525(the)-525(local)-525(blocks)]TJ 10.461 -11.955 Td [(call)-525(mld_precinit\050P,'AS',info\051)]TJ 0 -11.955 Td [(call)-525(mld_precset\050P,mld_sub_ovr_,2,info\051)]TJ -10.461 -11.955 Td [(...)-525(...)]TJ 0 g 0 G -1 0 0 1 -218.5852 -135.5973 cm -BT -/F15 10.9091 Tf 218.5852 135.5973 Td[(Figu)1(re)-334(5:)-444(S)1(e)-1(tu)1(p)-333(of)-333(a)-333(one-)-1(l)1(e)-1(v)28(el)-333(Sc)27(h)29(w)27(arz)-333(precondi)1(tioner.)]TJ -ET -1 0 0 1 477.3429 135.5973 cm +/F15 10.9091 Tf 56.223 -18.535 Td [(Figure)-333(5:)-445(Setup)-333(of)-333(a)-334(one-lev)28(el)-333(Sc)28(h)27(w)28(arz)-333(preconditioner.)]TJ 0 g 0 G -1 0 0 1 -335.6044 -14.0764 cm 0 g 0 G -1 0 0 1 0 -29.8879 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -403 0 obj << +367 0 obj << /Type /Page -/Contents 404 0 R -/Resources 402 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 401 0 R +/Contents 368 0 R +/Resources 366 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 365 0 R >> endobj -405 0 obj << -/D [403 0 R /XYZ 141.7385 740.0018 null] +369 0 obj << +/D [367 0 R /XYZ 141.738 740.002 null] >> endobj -392 0 obj << -/D [403 0 R /XYZ 245.1003 601.2679 null] +356 0 obj << +/D [367 0 R /XYZ 245.1 601.268 null] >> endobj -394 0 obj << -/D [403 0 R /XYZ 238.4488 447.8599 null] +358 0 obj << +/D [367 0 R /XYZ 238.449 447.86 null] >> endobj -395 0 obj << -/D [403 0 R /XYZ 266.3428 149.1465 null] +359 0 obj << +/D [367 0 R /XYZ 266.343 149.146 null] >> endobj -402 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F48 214 0 R >> +366 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -408 0 obj << -/Length 9602 +376 0 obj << +/Length 7573 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(7)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(7)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(21)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(21)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(7)-1125(User)-376(In)32(t)-1(er)-1(f)1(ace)]TJ/F15 10.9091 Tf 0 -30.694 Td[(The)-222(basic)-223(u)1(s)-1(er)-222(in)28(terf)1(ac)-1(e)-222(of)-222(MLD2P)1(4)-223(consists)-223(of)-222(six)-222(r)1(outin)1(e)-1(s.)-407(T)-1(h)1(e)-223(f)1(our)-222(r)1(outin)1(e)-1(s)]TJ/F48 10.9091 Tf 364.3237 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)]TJ/F48 10.9091 Tf -433.0502 -13.5492 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(,)]TJ/F48 10.9091 Tf 7.5847 0 Td[(mld_precbld)]TJ/F15 10.9091 Tf 67.3701 0 Td[(and)]TJ/F48 10.9091 Tf 21.9466 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 73.0973 0 Td[(encapsulate)-401(all)-400(th)1(e)-402(f)1(un)1(c)-1(ti)1(onali)1(tie)-1(s)-401(f)1(or)]TJ -232.998 -13.5492 Td[(th)1(e)-447(s)-1(etu)1(p)-446(and)-445(the)-447(ap)1(pl)1(ic)-1(ati)1(on)-446(of)-446(an)28(y)-446(on)1(e)-1(-lev)28(e)-1(l)-445(and)-446(m)28(ulti)1(-)-1(l)1(e)-1(v)28(el)-446(precondi)1(tioner)-446(imp)1(le)-1(-)]TJ 0 -13.5492 Td[(me)-1(n)28(t)1(e)-1(d)-308(in)-309(t)1(he)-309(pac)27(k)56(age.)-436(T)-1(h)1(e)-309(routi)1(ne)]TJ/F48 10.9091 Tf 173.4573 0 Td[(mld_precfree)]TJ/F15 10.9091 Tf 72.0963 0 Td[(deallo)-27(c)-1(ates)-309(the)-309(pr)1(e)-1(cond)1(ition)1(e)-1(r)-308(data)]TJ -245.5536 -13.5492 Td[(structu)1(re)-1(,)-312(whil)1(e)]TJ/F48 10.9091 Tf 77.7976 0 Td[(mld_precdescr)]TJ/F15 10.9091 Tf 77.8092 0 Td[(pr)1(in)28(ts)-308(a)-307(des)-1(crip)1(tion)-307(of)-307(the)-308(p)1(rec)-1(on)1(diti)1(oner)-308(setup)-307(b)28(y)-307(the)]TJ -155.6068 -13.5492 Td[(user.)]TJ 16.9365 -16.8133 Td[(F)84(or)-222(e)-1(ac)28(h)-222(rou)1(tine,)-244(the)-222(s)-1(ame)-223(u)1(s)-1(er)-222(in)28(terf)1(ac)-1(e)-222(is)-223(o)28(v)28(e)-1(r)1(loaded)-222(with)-221(re)-1(sp)-27(e)-1(ct)-222(to)-222(the)-223(r)1(e)-1(al)1(/c)-1(omplex)]TJ -16.9365 -13.5492 Td[(cas)-1(e)-371(and)-370(th)1(e)-372(sin)1(gle)-1(/d)1(oub)1(le)-371(pr)1(e)-1(cis)-1(i)1(on;)-389(argu)1(m)-1(en)28(ts)-371(with)-370(app)1(rop)1(riate)-371(dat)1(a)-371(t)28(yp)-27(e)-1(s)-371(m)27(u)1(s)-1(t)-370(b)-28(e)]TJ 0 -13.5492 Td[(passe)-1(d)-333(to)-333(th)1(e)-334(rou)1(tine,)-333(i.e.)]TJ -ET -1 0 0 1 93.9178 526.2127 cm +/F17 14.3462 Tf -401.542 -35.866 Td [(7)-1125(User)-375(In)31(terface)]TJ/F15 10.9091 Tf 0 -30.694 Td [(The)-222(basic)-222(use)-1(r)-222(in)28(terface)-222(of)-222(MLD2P4)-222(c)-1(on)1(s)-1(i)1(s)-1(ts)-222(of)-222(six)-222(routines.)-408(Th)1(e)-223(four)-222(routines)]TJ/F46 10.9091 Tf 364.323 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 68.727 0 Td [(,)]TJ/F46 10.9091 Tf -433.05 -13.549 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(,)]TJ/F46 10.9091 Tf 7.585 0 Td [(mld_precbld)]TJ/F15 10.9091 Tf 67.37 0 Td [(and)]TJ/F46 10.9091 Tf 21.947 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 73.097 0 Td [(encapsulate)-401(all)-400(the)-401(functionalities)-400(for)]TJ -232.998 -13.549 Td [(the)-446(setup)-446(and)-446(the)-447(appl)1(ic)-1(at)1(ion)-447(of)-446(an)28(y)-446(one-lev)28(el)-447(and)-446(m)28(ulti-lev)28(el)-446(preconditioner)-446(imple-)]TJ 0 -13.549 Td [(men)28(ted)-309(in)-309(the)-309(pac)28(k)55(age.)-436(The)-309(routine)]TJ/F46 10.9091 Tf 173.457 0 Td [(mld_precfree)]TJ/F15 10.9091 Tf 72.096 0 Td [(deallo)-28(cates)-309(the)-309(preconditioner)-308(data)]TJ -245.553 -13.549 Td [(structure,)-313(while)]TJ/F46 10.9091 Tf 77.797 0 Td [(mld_precdescr)]TJ/F15 10.9091 Tf 77.81 0 Td [(prin)28(ts)-308(a)-307(description)-308(of)-307(the)-308(preconditioner)-307(setup)-308(b)28(y)-308(the)]TJ -155.607 -13.55 Td [(user.)]TJ 16.936 -16.813 Td [(F)83(or)-222(eac)28(h)-222(routine,)-245(the)-222(same)-222(user)-222(in)27(terface)-222(is)-222(o)28(v)27(erloaded)-222(with)-222(resp)-28(ect)-222(to)-222(the)-222(real/com)-1(p)1(lex)]TJ -16.936 -13.549 Td [(case)-371(and)-371(th)1(e)-371(single/double)-371(precision;)-389(argumen)28(ts)-371(with)-371(appropriate)-371(d)1(ata)-371(t)28(yp)-28(es)-371(m)28(ust)-371(b)-28(e)]TJ 0 -13.549 Td [(passed)-333(to)-334(the)-333(routine,)-333(i.e.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -526.2127 cm -BT -/F27 10.9091 Tf 110.2815 526.2127 Td[(\017)]TJ -ET -1 0 0 1 115.736 526.2127 cm +/F25 10.9091 Tf 16.364 -35.572 Td [(\017)]TJ 0 g 0 G -1 0 0 1 -115.736 -526.2127 cm -BT -/F15 10.9091 Tf 121.1906 526.2127 Td[(th)1(e)-464(sparse)-464(matri)1(x)-463(data)-463(stru)1(c)-1(tu)1(re,)-496(con)28(tain)1(in)1(g)-464(t)1(he)-464(matr)1(ix)-463(to)-463(b)-27(e)-464(pr)1(e)-1(cond)1(ition)1(e)-1(d)1(,)]TJ 0 -13.5492 Td[(m)27(u)1(s)-1(t)-423(b)-28(e)-424(of)-423(t)28(yp)-28(e)]TJ/F48 10.9091 Tf 82.7978 0 Td[(mld_)]TJ/F20 10.9091 Tf 22.9088 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(spmat_type)]TJ/F15 10.9091 Tf 61.8958 0 Td[(with)]TJ/F20 10.9091 Tf 25.8358 0 Td[(x)]TJ/F15 10.9091 Tf 10.9979 0 Td[(=)]TJ/F48 10.9091 Tf 13.1085 0 Td[(s)]TJ/F15 10.9091 Tf 10.3509 0 Td[(for)-423(real)-424(singl)1(e)-425(p)1(rec)-1(ision)1(,)]TJ/F20 10.9091 Tf 121.0749 0 Td[(x)]TJ/F15 10.9091 Tf 10.9979 0 Td[(=)]TJ/F48 10.9091 Tf 13.1085 0 Td[(d)]TJ/F15 10.9091 Tf -379.4511 -13.5492 Td[(for)-370(real)-371(dou)1(ble)-371(pr)1(e)-1(cision,)]TJ/F20 10.9091 Tf 123.4131 0 Td[(x)]TJ/F15 10.9091 Tf 10.4215 0 Td[(=)]TJ/F48 10.9091 Tf 12.5322 0 Td[(c)]TJ/F15 10.9091 Tf 9.7744 0 Td[(for)-370(c)-1(ompl)1(e)-1(x)-371(sin)1(gle)-372(p)1(rec)-1(i)1(s)-1(ion)1(,)]TJ/F20 10.9091 Tf 140.1102 0 Td[(x)]TJ/F15 10.9091 Tf 10.4214 0 Td[(=)]TJ/F48 10.9091 Tf 12.5322 0 Td[(z)]TJ/F15 10.9091 Tf 9.7745 0 Td[(for)-370(c)-1(ompl)1(e)-1(x)]TJ -328.9795 -13.5492 Td[(dou)1(bl)1(e)-334(pr)1(e)-1(cis)-1(i)1(on;)]TJ -ET -1 0 0 1 93.9178 449.9932 cm +/F15 10.9091 Tf 10.909 0 Td [(the)-463(sparse)-463(matrix)-463(data)-463(structure,)-496(con)28(taining)-463(the)-463(matrix)-463(to)-463(b)-28(e)-463(preconditioned,)]TJ 0 -13.549 Td [(m)28(ust)-424(b)-28(e)-424(of)-423(t)27(yp)-27(e)]TJ/F46 10.9091 Tf 82.797 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(spmat_type)]TJ/F15 10.9091 Tf 61.896 0 Td [(with)]TJ/F18 10.9091 Tf 25.836 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F46 10.9091 Tf 13.108 0 Td [(s)]TJ/F15 10.9091 Tf 10.351 0 Td [(for)-424(real)-424(single)-423(precis)-1(i)1(on,)]TJ/F18 10.9091 Tf 121.075 0 Td [(x)]TJ/F15 10.9091 Tf 10.998 0 Td [(=)]TJ/F46 10.9091 Tf 13.109 0 Td [(d)]TJ/F15 10.9091 Tf -379.451 -13.55 Td [(for)-371(real)-371(double)-371(precision,)]TJ/F18 10.9091 Tf 123.413 0 Td [(x)]TJ/F15 10.9091 Tf 10.421 0 Td [(=)]TJ/F46 10.9091 Tf 12.532 0 Td [(c)]TJ/F15 10.9091 Tf 9.775 0 Td [(for)-371(complex)-371(single)-371(precision,)]TJ/F18 10.9091 Tf 140.11 0 Td [(x)]TJ/F15 10.9091 Tf 10.421 0 Td [(=)]TJ/F46 10.9091 Tf 12.533 0 Td [(z)]TJ/F15 10.9091 Tf 9.774 0 Td [(for)-371(complex)]TJ -328.979 -13.549 Td [(double)-333(precision;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -449.9932 cm -BT -/F27 10.9091 Tf 110.2815 449.9932 Td[(\017)]TJ -ET -1 0 0 1 115.736 449.9932 cm +/F25 10.9091 Tf -10.909 -35.572 Td [(\017)]TJ 0 g 0 G -1 0 0 1 -115.736 -449.9932 cm -BT -/F15 10.9091 Tf 121.1906 449.9932 Td[(th)1(e)-338(p)1(re)-1(cond)1(ition)1(e)-1(r)-336(data)-337(stru)1(c)-1(tu)1(re)-337(m)27(u)1(s)-1(t)-337(b)-27(e)-338(of)-336(t)28(yp)-27(e)]TJ/F48 10.9091 Tf 241.7755 0 Td[(mld_)]TJ/F20 10.9091 Tf 22.9088 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type)]TJ/F15 10.9091 Tf 51.5449 0 Td[(,)-338(with)]TJ/F20 10.9091 Tf 31.6054 0 Td[(x)]TJ/F15 10.9091 Tf 10.0507 0 Td[(=)]TJ/F48 10.9091 Tf 12.1613 0 Td[(s)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F48 10.9091 Tf -382.148 -13.5492 Td[(d)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F48 10.9091 Tf 6.6667 0 Td[(c)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F48 10.9091 Tf 6.6667 0 Td[(z)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-333(ac)-1(cord)1(ing)-333(to)-333(the)-333(s)-1(p)1(arse)-334(m)-1(at)1(rix)-333(dat)1(a)-334(stru)1(c)-1(tu)1(re;)]TJ -ET -1 0 0 1 93.9178 400.872 cm +/F15 10.9091 Tf 10.909 0 Td [(the)-337(preconditioner)-337(data)-337(structure)-337(m)28(ust)-337(b)-28(e)-337(of)-337(t)28(yp)-28(e)]TJ/F46 10.9091 Tf 241.775 0 Td [(mld_)]TJ/F18 10.9091 Tf 22.909 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type)]TJ/F15 10.9091 Tf 51.545 0 Td [(,)-338(with)]TJ/F18 10.9091 Tf 31.605 0 Td [(x)]TJ/F15 10.9091 Tf 10.051 0 Td [(=)]TJ/F46 10.9091 Tf 12.161 0 Td [(s)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)]TJ/F46 10.9091 Tf -382.148 -13.549 Td [(d)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F46 10.9091 Tf 6.667 0 Td [(c)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)]TJ/F46 10.9091 Tf 6.666 0 Td [(z)]TJ/F15 10.9091 Tf 5.728 0 Td [(,)-333(according)-334(to)-333(the)-333(sparse)-334(matrix)-333(data)-333(structure;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -400.872 cm -BT -/F27 10.9091 Tf 110.2815 400.872 Td[(\017)]TJ -ET -1 0 0 1 115.736 400.872 cm +/F25 10.9091 Tf -41.424 -35.572 Td [(\017)]TJ 0 g 0 G -1 0 0 1 -115.736 -400.872 cm -BT -/F15 10.9091 Tf 121.1906 400.872 Td[(th)1(e)-322(arr)1(a)27(y)1(s)-322(con)28(tain)1(ing)-321(th)1(e)-322(v)28(ec)-1(t)1(ors)]TJ/F24 10.9091 Tf 159.8466 0 Td[(v)]TJ/F15 10.9091 Tf 9.1819 0 Td[(and)]TJ/F24 10.9091 Tf 21.0784 0 Td[(w)]TJ/F15 10.9091 Tf 11.6062 0 Td[(in)28(v)28(ol)1(v)28(e)-1(d)-320(in)-321(th)1(e)-322(p)1(rec)-1(on)1(diti)1(oner)-321(app)1(lica-)]TJ -201.7131 -13.5492 Td[(tion)]TJ/F24 10.9091 Tf 21.3155 0 Td[(w)]TJ/F15 10.9091 Tf 11.1338 0 Td[(=)]TJ/F24 10.9091 Tf 11.5151 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(v)]TJ/F15 10.9091 Tf 8.2069 0 Td[(m)27(u)1(s)-1(t)-231(b)-27(e)-233(of)-231(t)28(yp)-27(e)]TJ/F20 10.9091 Tf 74.4135 0 Td[(typ)51(e)]TJ/F48 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ +/F15 10.9091 Tf 10.909 0 Td [(the)-321(arra)28(ys)-321(con)27(tai)1(ning)-321(the)-322(v)28(ectors)]TJ/F22 10.9091 Tf 159.846 0 Td [(v)]TJ/F15 10.9091 Tf 9.182 0 Td [(and)]TJ/F22 10.9091 Tf 21.079 0 Td [(w)]TJ/F15 10.9091 Tf 11.606 0 Td [(in)28(v)28(olv)27(ed)-321(in)-321(the)-321(preconditioner)-321(appl)1(ic)-1(a-)]TJ -201.713 -13.549 Td [(tion)]TJ/F22 10.9091 Tf 21.315 0 Td [(w)]TJ/F15 10.9091 Tf 11.134 0 Td [(=)]TJ/F22 10.9091 Tf 11.515 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.733 -3.959 Td [(v)]TJ/F15 10.9091 Tf 8.207 0 Td [(m)28(ust)-232(b)-28(e)-231(of)-232(t)28(yp)-28(e)]TJ/F18 10.9091 Tf 74.413 0 Td [(typ)51(e)]TJ/F46 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ ET -1 0 0 1 317.1129 387.3228 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 317.113 387.522 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -317.1129 -387.3228 cm BT -/F20 10.9091 Tf 320.4583 387.3228 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5679 0 Td[(\051)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-252(with)]TJ/F20 10.9091 Tf 29.5194 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 22.3047 0 Td[(=)]TJ/F48 10.9091 Tf 11.0125 0 Td[(real)]TJ/F15 10.9091 Tf 22.9088 0 Td[(,)]TJ/F48 10.9091 Tf 5.7797 0 Td[(complex)]TJ/F15 10.9091 Tf -345.0879 -13.5492 Td[(and)]TJ/F20 10.9091 Tf 21.3918 0 Td[(kind)]TJ +/F18 10.9091 Tf 320.458 387.323 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.568 0 Td [(\051)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-252(with)]TJ/F18 10.9091 Tf 29.52 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 22.304 0 Td [(=)]TJ/F46 10.9091 Tf 11.013 0 Td [(real)]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F46 10.9091 Tf 5.779 0 Td [(complex)]TJ/F15 10.9091 Tf -345.087 -13.549 Td [(and)]TJ/F18 10.9091 Tf 21.391 0 Td [(kind)]TJ ET -1 0 0 1 163.324 373.7736 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 163.324 373.973 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -163.324 -373.7736 cm BT -/F20 10.9091 Tf 166.6694 373.7736 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 52.3838 0 Td[(=)]TJ/F48 10.9091 Tf 12.3009 0 Td[(kind\0501.e0\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(,)]TJ/F48 10.9091 Tf 6.8912 0 Td[(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(,)-354(acc)-1(or)1(din)1(g)-350(to)-350(th)1(e)-350(s)-1(p)1(arse)-351(matri)1(x)]TJ -231.5989 -13.5492 Td[(and)-304(pr)1(e)-1(cond)1(ition)1(e)-1(r)-305(d)1(ata)-305(s)-1(tr)1(uctur)1(e)-1(;)-314(note)-305(th)1(at)-305(the)-305(PSBLAS)-305(mo)-28(d)1(ule)]TJ/F48 10.9091 Tf 316.4518 0 Td[(psb_base_mod)]TJ/F15 10.9091 Tf -316.4518 -13.5492 Td[(pr)1(o)28(vides)-334(th)1(e)-334(constan)28(ts)]TJ/F48 10.9091 Tf 110.2122 0 Td[(psb_spk_)]TJ/F15 10.9091 Tf 49.4541 0 Td[(=)]TJ/F48 10.9091 Tf 12.1212 0 Td[(kind\0501.e0\051)]TJ/F15 10.9091 Tf 60.9085 0 Td[(and)]TJ/F48 10.9091 Tf 21.2121 0 Td[(psb_dpk_)]TJ/F15 10.9091 Tf 49.454 0 Td[(=)]TJ/F48 10.9091 Tf 12.1213 0 Td[(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(;)]TJ -ET -1 0 0 1 93.9178 311.1033 cm +/F18 10.9091 Tf 166.669 373.774 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 52.384 0 Td [(=)]TJ/F46 10.9091 Tf 12.301 0 Td [(kind\0501.e0\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(,)]TJ/F46 10.9091 Tf 6.891 0 Td [(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(,)-354(according)-350(to)-349(the)-350(sparse)-350(matrix)]TJ -231.598 -13.55 Td [(and)-305(preconditioner)-305(data)-305(structure;)-314(note)-306(t)1(hat)-306(th)1(e)-306(PSBLAS)-305(mo)-27(dule)]TJ/F46 10.9091 Tf 316.451 0 Td [(psb_base_mod)]TJ/F15 10.9091 Tf -316.451 -13.549 Td [(pro)28(vides)-333(the)-334(constan)28(ts)]TJ/F46 10.9091 Tf 110.212 0 Td [(psb_spk_)]TJ/F15 10.9091 Tf 49.454 0 Td [(=)]TJ/F46 10.9091 Tf 12.121 0 Td [(kind\0501.e0\051)]TJ/F15 10.9091 Tf 60.909 0 Td [(and)]TJ/F46 10.9091 Tf 21.212 0 Td [(psb_dpk_)]TJ/F15 10.9091 Tf 49.454 0 Td [(=)]TJ/F46 10.9091 Tf 12.121 0 Td [(kind\0501.d0\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -311.1033 cm -BT -/F27 10.9091 Tf 110.2815 311.1033 Td[(\017)]TJ -ET -1 0 0 1 115.736 311.1033 cm +/F25 10.9091 Tf -383.665 -35.572 Td [(\017)]TJ 0 g 0 G -1 0 0 1 -115.736 -311.1033 cm -BT -/F15 10.9091 Tf 121.1906 311.1033 Td[(real)-450(p)1(arame)-1(ters)-450(de\014n)1(ing)-450(th)1(e)-451(p)1(rec)-1(on)1(dit)1(ioner)-450(m)28(ust)-450(b)-28(e)-450(declared)-450(acc)-1(or)1(din)1(g)-450(to)-450(the)]TJ 0 -13.5492 Td[(pr)1(e)-1(cision)-245(of)-245(the)-245(s)-1(p)1(arse)-246(m)-1(atr)1(ix)-245(and)-245(p)1(rec)-1(on)1(diti)1(oner)-246(d)1(ata)-245(s)-1(tr)1(uctures)-246(\050se)-1(e)-245(Sec)-1(tion)]TJ -ET -1 0 0 1 485.1568 297.5541 cm +/F15 10.9091 Tf 10.91 0 Td [(real)-450(parameters)-450(de\014ning)-450(the)-450(preconditioner)-450(m)28(ust)-450(b)-27(e)-450(dec)-1(l)1(are)-1(d)-449(acc)-1(or)1(ding)-450(to)-450(the)]TJ 0 -13.549 Td [(precision)-245(of)-246(the)-245(sparse)-246(matrix)-245(and)-245(preconditioner)-246(data)-245(structures)-245(\050see)-246(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -485.1568 -297.5541 cm -BT -/F15 10.9091 Tf 485.1568 297.5541 Td[(7.2)]TJ -ET -1 0 0 1 499.0962 297.5541 cm + [-245(7.2)]TJ 0 g 0 G -1 0 0 1 -499.0962 -297.5541 cm -BT -/F15 10.9091 Tf 499.0962 297.5541 Td[(\051.)]TJ -405.1784 -35.572 Td[(A)-333(des)-1(crip)1(tion)-333(of)-333(eac)27(h)-333(r)1(outin)1(e)-334(is)-333(giv)28(e)-1(n)-333(i)1(n)-333(the)-333(re)-1(main)1(der)-333(of)-333(thi)1(s)-334(s)-1(ection.)]TJ/F19 11.9552 Tf 0 -47.8657 Td[(7.)-1(1)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ + [(\051.)]TJ -27.273 -35.572 Td [(A)-333(description)-334(of)-333(eac)28(h)-333(routine)-334(is)-333(giv)28(en)-334(in)-333(the)-333(remainder)-333(of)-334(this)-333(section.)]TJ/F17 11.9552 Tf 0 -47.866 Td [(7.1)-1125(Subroutine)-375(mld)]TJ ET -1 0 0 1 216.9401 214.1164 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -4.0349 0.1992 l -S +1 0 0 1 216.94 214.316 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -1 0 0 1 -216.9401 -214.1164 cm BT -/F19 11.9552 Tf 220.975 214.1164 Td[(pre)-1(cini)-1(t)]TJ -ET -1 0 0 1 220.2351 187.18 cm +/F17 11.9552 Tf 220.975 214.116 Td [(precinit)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -220.2351 -187.18 cm -BT -/F48 10.9091 Tf 225.6896 187.18 Td[(mld_precinit\050p,ptype,info\051)]TJ -14.318 -13.5492 Td[(mld_precinit\050p,ptype,info,nlev\051)]TJ/F15 10.9091 Tf -117.4538 -38.5607 Td[(This)-268(rou)1(tine)-268(allo)-28(cates)-269(and)-267(init)1(ialize)-1(s)-268(the)-269(p)1(rec)-1(on)1(dit)1(ioner)-268(data)-268(stru)1(c)-1(tu)1(re,)-281(ac)-1(cord)1(ing)-268(to)-268(the)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-333(t)28(yp)-27(e)-334(c)28(hose)-1(n)-333(b)29(y)-334(t)1(he)-334(u)1(s)-1(er.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F46 10.9091 Tf 4.715 -26.936 Td [(mld_precinit\050p,ptype,info\051)]TJ -14.318 -13.549 Td [(mld_precinit\050p,ptype,info,nlev\051)]TJ/F15 10.9091 Tf -117.454 -38.561 Td [(This)-268(routine)-268(allo)-28(cates)-268(and)-269(ini)1(tializes)-269(the)-268(preconditioner)-268(data)-268(structure,)-281(acc)-1(or)1(ding)-269(to)-268(the)]TJ 0 -13.549 Td [(preconditioner)-333(t)28(yp)-28(e)-333(c)27(hosen)-333(b)28(y)-334(the)-333(user.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -407 0 obj << +375 0 obj << /Type /Page -/Contents 408 0 R -/Resources 406 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 401 0 R -/Annots [ 410 0 R 411 0 R ] +/Contents 376 0 R +/Resources 374 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 365 0 R +/Annots [ 373 0 R 370 0 R ] >> endobj -410 0 obj << +373 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -411 0 obj << +370 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [484.1605 293.8306 500.0924 306.7322] +/Rect [484.16 293.831 500.092 306.732] /Subtype /Link /A << /S /GoTo /D (subsection.7.2) >> >> endobj -409 0 obj << -/D [407 0 R /XYZ 93.9178 740.0018 null] +377 0 obj << +/D [375 0 R /XYZ 93.918 740.002 null] >> endobj 62 0 obj << -/D [407 0 R /XYZ 93.9178 715.0952 null] +/D [375 0 R /XYZ 93.918 715.095 null] >> endobj 66 0 obj << -/D [407 0 R /XYZ 93.9178 229.207 null] +/D [375 0 R /XYZ 93.918 229.207 null] >> endobj -406 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F48 214 0 R /F27 179 0 R /F20 171 0 R /F24 176 0 R /F28 270 0 R /F22 273 0 R >> +374 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F46 195 0 R /F25 166 0 R /F18 163 0 R /F22 165 0 R /F26 249 0 R /F20 250 0 R >> /ProcSet [ /PDF /Text ] >> endobj -414 0 obj << -/Length 9140 +385 0 obj << +/Length 6503 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(22)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(22)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F41 10.9091 Tf 141.7385 704.1363 Td[(Argumen)32(ts)]TJ/F48 10.9091 Tf 5.9776 -19.6473 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-267(prec)-1(on)1(di)1(tioner)-267(dat)1(a)-268(stru)1(c)-1(tu)1(re.)-422(Note)-268(th)1(at)]TJ/F20 10.9091 Tf 216.6391 0 Td[(x)]TJ/F15 10.9091 Tf 9.2894 0 Td[(m)27(u)1(s)-1(t)-267(b)-27(e)-268(c)28(hose)-1(n)]TJ -225.9285 -13.5492 Td[(acc)-1(ord)1(in)1(g)-352(to)-352(the)-352(real/c)-1(ompl)1(e)-1(x,)-356(single/dou)1(bl)1(e)-353(p)1(re)-1(cision)-352(v)28(ersion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(ptype)-1589(character\050len=*\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 206.3327 0 Td[(.)]TJ -160.3619 -13.5492 Td[(The)-331(t)27(y)1(p)-28(e)-331(of)-331(pr)1(e)-1(cond)1(ition)1(e)-1(r.)-443(Its)-332(v)56(alu)1(e)-1(s)-332(ar)1(e)-332(sp)-28(ec)-1(i)1(\014ed)-331(in)-331(T)83(ab)1(le)]TJ -ET -1 0 0 1 482.8398 616.7431 cm +/F39 10.9091 Tf -203.265 -35.866 Td [(Argumen)32(ts)]TJ/F46 10.9091 Tf 5.978 -19.647 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-267(preconditioner)-267(data)-267(s)-1(tr)1(ucture.)-423(Note)-267(that)]TJ/F18 10.9091 Tf 216.639 0 Td [(x)]TJ/F15 10.9091 Tf 9.289 0 Td [(m)28(ust)-268(b)-27(e)-268(c)28(hosen)]TJ -225.928 -13.549 Td [(according)-352(to)-352(the)-352(real/complex,)-357(single/double)-352(precision)-352(v)28(ersion)]TJ 0 -13.55 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(ptype)-1589(character\050len=*\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 206.333 0 Td [(.)]TJ -160.362 -13.549 Td [(The)-331(t)28(yp)-28(e)-332(of)-331(preconditioner.)-443(Its)-332(v)56(alues)-331(are)-332(sp)-27(eci\014ed)-332(in)-331(T)83(abl)1(e)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -482.8398 -616.7431 cm -BT -/F15 10.9091 Tf 482.8398 616.7431 Td[(1)]TJ -ET -1 0 0 1 488.2944 616.7431 cm + [-332(1)]TJ 0 g 0 G -1 0 0 1 -488.2944 -616.7431 cm -BT -/F15 10.9091 Tf 488.2944 616.7431 Td[(.)]TJ -294.6075 -13.5492 Td[(Note)-334(th)1(at)-333(the)-334(stri)1(ngs)-334(ar)1(e)-334(c)-1(ase)-334(in)1(s)-1(ensiti)1(v)28(e)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-307(c)-1(o)-28(d)1(e)-1(.)-435(If)-308(n)1(o)-308(e)-1(r)1(ror,)-313(0)-307(is)-308(re)-1(t)1(urn)1(e)-1(d)1(.)-436(See)-308(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 432.0924 576.0955 cm + [(.)]TJ 0 -13.549 Td [(Note)-333(that)-334(the)-333(strings)-333(are)-334(case)-333(insensitiv)28(e.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-308(co)-28(d)1(e)-1(.)-435(If)-308(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -432.0924 -576.0955 cm -BT -/F15 10.9091 Tf 432.0924 576.0955 Td[(8)]TJ -ET -1 0 0 1 437.547 576.0955 cm + [-307(8)]TJ 0 g 0 G -1 0 0 1 -437.547 -576.0955 cm -BT -/F15 10.9091 Tf 440.9055 576.0955 Td[(for)-307(details.)]TJ/F48 10.9091 Tf -293.1894 -13.5491 Td[(nlev)-2114(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.0599 0 Td[(.)]TJ -166.0891 -13.5492 Td[(The)-354(n)28(u)1(m)27(b)-27(e)-1(r)-353(of)-354(l)1(e)-1(v)28(els)-354(of)-354(t)1(he)-354(m)27(u)1(ltilev)28(el)-354(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)-506(If)]TJ/F48 10.9091 Tf 274.729 0 Td[(nlev)]TJ/F15 10.9091 Tf -274.729 -13.5492 Td[(is)-254(not)-253(prese)-1(n)28(t)-253(and)]TJ/F48 10.9091 Tf 86.0755 0 Td[(ptype)]TJ/F15 10.9091 Tf 28.6361 0 Td[(=)]TJ/F48 10.9091 Tf 8.4848 0 Td[('ML')]TJ/F15 10.9091 Tf 22.9089 0 Td[(,)]TJ/F48 10.9091 Tf 5.7991 0 Td[('ml')]TJ/F15 10.9091 Tf 22.9089 0 Td[(,)-269(then)]TJ/F48 10.9091 Tf 29.9536 0 Td[(nlev)]TJ/F15 10.9091 Tf 22.9089 0 Td[(=2)-254(i)1(s)-255(ass)-1(u)1(me)-1(d)1(.)]TJ -227.6758 -13.5492 Td[(Oth)1(e)-1(r)1(w)-1(i)1(s)-1(e,)]TJ/F48 10.9091 Tf 54.6364 0 Td[(nlev)]TJ/F15 10.9091 Tf 26.5452 0 Td[(is)-334(i)1(gnored.)]TJ/F19 11.9552 Tf -133.13 -28.056 Td[(7.)-1(2)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ + [-308(for)-308(details.)]TJ/F46 10.9091 Tf -45.971 -13.55 Td [(nlev)-2114(integer,)-525(optional,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(The)-354(n)28(um)28(b)-28(er)-354(of)-354(l)1(e)-1(v)28(els)-354(of)-353(the)-354(m)28(ultilev)27(el)-353(preconditioner.)-506(If)]TJ/F46 10.9091 Tf 274.729 0 Td [(nlev)]TJ/F15 10.9091 Tf -274.729 -13.549 Td [(is)-254(not)-254(presen)28(t)-254(and)]TJ/F46 10.9091 Tf 86.075 0 Td [(ptype)]TJ/F15 10.9091 Tf 28.636 0 Td [(=)]TJ/F46 10.9091 Tf 8.485 0 Td [('ML')]TJ/F15 10.9091 Tf 22.909 0 Td [(,)]TJ/F46 10.9091 Tf 5.799 0 Td [('ml')]TJ/F15 10.9091 Tf 22.909 0 Td [(,)-270(then)]TJ/F46 10.9091 Tf 29.954 0 Td [(nlev)]TJ/F15 10.9091 Tf 22.909 0 Td [(=2)-254(is)-254(assumed.)]TJ -227.676 -13.549 Td [(Otherwise,)]TJ/F46 10.9091 Tf 54.636 0 Td [(nlev)]TJ/F15 10.9091 Tf 26.545 0 Td [(is)-333(ignored.)]TJ/F17 11.9552 Tf -133.13 -28.056 Td [(7.2)-1125(Subroutine)-375(mld)]TJ ET -1 0 0 1 264.7607 493.8428 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -4.0349 0.1992 l -S +1 0 0 1 264.761 494.042 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -1 0 0 1 -264.7607 -493.8428 cm BT -/F19 11.9552 Tf 268.7956 493.8428 Td[(pre)-1(cset)]TJ -ET -1 0 0 1 262.3285 473.2482 cm +/F17 11.9552 Tf 268.796 493.843 Td [(precset)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -262.3285 -473.2482 cm -BT -/F48 10.9091 Tf 267.7831 473.2482 Td[(mld_precset\050p,what,val,info\051)]TJ/F15 10.9091 Tf -126.0446 -21.8621 Td[(This)-389(r)1(outin)1(e)-389(s)-1(ets)-389(the)-389(p)1(arame)-1(ters)-389(d)1(e)-1(\014)1(nin)1(g)-389(th)1(e)-389(precondi)1(tioner.)-610(Mor)1(e)-389(precis)-1(ely)84(,)-403(t)1(he)-389(pa-)]TJ 0 -13.5492 Td[(ramete)-1(r)-333(id)1(e)-1(n)29(ti\014ed)-333(b)28(y)]TJ/F48 10.9091 Tf 103.394 0 Td[(what)]TJ/F15 10.9091 Tf 26.5452 0 Td[(is)-334(assigned)-333(the)-333(v)55(al)1(ue)-334(con)28(tain)1(e)-1(d)-332(in)]TJ/F48 10.9091 Tf 163.2123 0 Td[(val)]TJ/F15 10.9091 Tf 17.1816 0 Td[(.)]TJ/F41 10.9091 Tf -310.3331 -28.2419 Td[(Argumen)32(ts)]TJ/F48 10.9091 Tf 5.9776 -19.6473 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-267(prec)-1(on)1(di)1(tioner)-267(dat)1(a)-268(stru)1(c)-1(tu)1(re.)-422(Note)-268(th)1(at)]TJ/F20 10.9091 Tf 216.6391 0 Td[(x)]TJ/F15 10.9091 Tf 9.2894 0 Td[(m)27(u)1(s)-1(t)-267(b)-27(e)-268(c)28(hose)-1(n)]TJ -225.9285 -13.5492 Td[(acc)-1(ord)1(in)1(g)-352(to)-352(the)-352(real/c)-1(ompl)1(e)-1(x,)-356(single/dou)1(bl)1(e)-353(p)1(re)-1(cision)-352(v)28(ersion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(what)-2114(integer,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.7878 0 Td[(.)]TJ -108.817 -13.5492 Td[(The)-338(n)28(u)1(m)27(b)-27(e)-1(r)-337(id)1(e)-1(n)29(tify)1(ing)-337(the)-338(p)1(arame)-1(ter)-338(t)1(o)-338(b)-27(e)-338(s)-1(et.)-457(A)-338(mnem)-1(on)1(ic)]TJ 0 -13.5492 Td[(constan)28(t)-378(has)-379(b)-27(ee)-1(n)-378(ass)-1(o)-27(c)-1(iated)-378(to)-378(e)-1(ac)28(h)-378(of)-378(th)1(e)-1(se)-379(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-1(,)-389(as)-379(re-)]TJ 0 -13.5492 Td[(p)-27(orted)-333(in)-333(T)83(ab)1(le)-1(s)]TJ -ET -1 0 0 1 275.596 295.1034 cm +/F46 10.9091 Tf -1.013 -20.595 Td [(mld_precset\050p,what,val,info\051)]TJ/F15 10.9091 Tf -126.045 -21.862 Td [(This)-389(routine)-388(sets)-389(the)-389(parameters)-388(de\014ning)-389(the)-389(p)1(rec)-1(on)1(ditioner.)-611(More)-388(precisely)83(,)-403(th)1(e)-389(pa-)]TJ 0 -13.549 Td [(rameter)-333(iden)27(ti\014ed)-333(b)28(y)]TJ/F46 10.9091 Tf 103.394 0 Td [(what)]TJ/F15 10.9091 Tf 26.546 0 Td [(is)-333(assigned)-334(the)-333(v)56(alue)-334(con)28(tained)-333(in)]TJ/F46 10.9091 Tf 163.212 0 Td [(val)]TJ/F15 10.9091 Tf 17.182 0 Td [(.)]TJ/F39 10.9091 Tf -310.334 -28.242 Td [(Argumen)32(ts)]TJ/F46 10.9091 Tf 5.978 -19.647 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-267(preconditioner)-267(data)-267(s)-1(tr)1(ucture.)-423(Note)-267(that)]TJ/F18 10.9091 Tf 216.639 0 Td [(x)]TJ/F15 10.9091 Tf 9.289 0 Td [(m)28(ust)-268(b)-27(e)-268(c)28(hosen)]TJ -225.928 -13.55 Td [(according)-352(to)-352(the)-352(real/complex,)-357(single/double)-352(precision)-352(v)28(ersion)]TJ 0 -13.549 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(what)-2114(integer,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.788 0 Td [(.)]TJ -108.817 -13.549 Td [(The)-338(n)28(um)28(b)-28(er)-337(iden)27(tify)1(ing)-338(the)-338(parameter)-337(to)-338(b)-28(e)-337(set.)-458(A)-337(mnemonic)]TJ 0 -13.549 Td [(constan)28(t)-379(h)1(as)-379(b)-28(een)-378(asso)-28(ciated)-378(to)-379(eac)28(h)-378(of)-378(these)-379(n)28(um)28(b)-28(ers,)-390(as)-378(re-)]TJ 0 -13.55 Td [(p)-28(orted)-333(in)-333(T)83(ables)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -275.596 -295.1034 cm -BT -/F15 10.9091 Tf 275.596 295.1034 Td[(2)]TJ -ET -1 0 0 1 281.0506 295.1034 cm + [-333(2)]TJ 0 g 0 G -1 0 0 1 -281.0506 -295.1034 cm -BT -/F15 10.9091 Tf 281.0506 295.1034 Td[(-)]TJ -ET -1 0 0 1 284.687 295.1034 cm + [(-)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -284.687 -295.1034 cm -BT -/F15 10.9091 Tf 284.687 295.1034 Td[(5)]TJ -ET -1 0 0 1 290.1415 295.1034 cm + [(5)]TJ 0 g 0 G -1 0 0 1 -290.1415 -295.1034 cm -BT -/F15 10.9091 Tf 290.1415 295.1034 Td[(.)]TJ/F48 10.9091 Tf -142.4254 -13.5492 Td[(val)-2639(integer)]TJ/F20 10.9091 Tf 96.6324 0 Td[(or)]TJ/F48 10.9091 Tf 21.921 0 Td[(character\050len=*\051)]TJ/F20 10.9091 Tf 102.2065 0 Td[(or)]TJ/F48 10.9091 Tf 21.921 0 Td[(real\050psb_spk_\051)]TJ/F20 10.9091 Tf 90.752 0 Td[(or)]TJ/F48 10.9091 Tf -287.4621 -13.5492 Td[(real\050psb_dpk_\051)]TJ/F15 10.9091 Tf 80.181 0 Td[(,)]TJ/F48 10.9091 Tf 6.6666 0 Td[(intent\050in\051)]TJ/F15 10.9091 Tf 57.2721 0 Td[(.)]TJ -144.1197 -13.5492 Td[(The)-281(v)56(alu)1(e)-281(of)-280(th)1(e)-281(paramete)-1(r)-280(to)-280(b)-27(e)-281(s)-1(et.)-427(Th)1(e)-281(list)-280(of)-280(allo)28(w)27(ed)-280(v)56(alues)]TJ 0 -13.5492 Td[(and)-300(the)-301(c)-1(orr)1(e)-1(sp)-27(ondi)1(ng)-301(data)-301(t)28(yp)-27(es)-302(is)-301(giv)28(e)-1(n)-300(in)-301(T)83(ab)1(le)-1(s)]TJ -ET -1 0 0 1 440.8354 240.9066 cm + [(.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(val)-2639(integer)]TJ/F18 10.9091 Tf 96.632 0 Td [(or)]TJ/F46 10.9091 Tf 21.921 0 Td [(character\050len=*\051)]TJ/F18 10.9091 Tf 102.207 0 Td [(or)]TJ/F46 10.9091 Tf 21.921 0 Td [(real\050psb_spk_\051)]TJ/F18 10.9091 Tf 90.752 0 Td [(or)]TJ/F46 10.9091 Tf -287.462 -13.549 Td [(real\050psb_dpk_\051)]TJ/F15 10.9091 Tf 80.181 0 Td [(,)]TJ/F46 10.9091 Tf 6.667 0 Td [(intent\050in\051)]TJ/F15 10.9091 Tf 57.272 0 Td [(.)]TJ -144.12 -13.549 Td [(The)-280(v)55(alue)-280(of)-281(the)-280(parameter)-280(to)-281(b)-28(e)-280(set.)-427(The)-280(list)-281(of)-280(allo)28(w)28(ed)-281(v)56(alues)]TJ 0 -13.549 Td [(and)-301(the)-301(corresp)-28(onding)-301(data)-301(t)27(y)1(p)-28(es)-302(i)1(s)-302(giv)28(en)-301(in)-301(T)83(ables)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -440.8354 -240.9066 cm -BT -/F15 10.9091 Tf 440.8354 240.9066 Td[(2)]TJ -ET -1 0 0 1 446.29 240.9066 cm + [-301(2)]TJ 0 g 0 G -1 0 0 1 -446.29 -240.9066 cm -BT -/F15 10.9091 Tf 446.29 240.9066 Td[(-)]TJ -ET -1 0 0 1 449.9263 240.9066 cm + [(-)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -449.9263 -240.9066 cm -BT -/F15 10.9091 Tf 449.9263 240.9066 Td[(5)]TJ -ET -1 0 0 1 455.3809 240.9066 cm + [(5)]TJ 0 g 0 G -1 0 0 1 -455.3809 -240.9066 cm -BT -/F15 10.9091 Tf 455.3809 240.9066 Td[(.)-434(W)1(hen)]TJ -261.694 -13.5492 Td[(th)1(e)-453(v)56(alue)-453(i)1(s)-453(of)-452(t)28(yp)-27(e)]TJ/F48 10.9091 Tf 101.3996 0 Td[(character\050len=*\051)]TJ/F15 10.9091 Tf 91.6353 0 Td[(,)-482(it)-452(is)-452(als)-1(o)-452(tr)1(e)-1(ated)-452(as)]TJ -193.0349 -13.5492 Td[(cas)-1(e)-334(i)1(nse)-1(n)1(s)-1(iti)1(v)28(e)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-307(c)-1(o)-28(d)1(e)-1(.)-435(If)-308(n)1(o)-308(e)-1(r)1(ror,)-313(0)-307(is)-308(re)-1(t)1(urn)1(e)-1(d)1(.)-436(See)-308(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 432.0924 186.7099 cm + [(.)-434(When)]TJ 0 -13.55 Td [(the)-452(v)55(alue)-452(is)-452(of)-453(t)28(yp)-28(e)]TJ/F46 10.9091 Tf 101.4 0 Td [(character\050len=*\051)]TJ/F15 10.9091 Tf 91.635 0 Td [(,)-482(it)-452(is)-453(also)-452(treated)-452(as)]TJ -193.035 -13.549 Td [(case)-333(insensitiv)27(e.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-308(co)-28(de.)-435(If)-308(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -432.0924 -186.7099 cm -BT -/F15 10.9091 Tf 432.0924 186.7099 Td[(8)]TJ -ET -1 0 0 1 437.547 186.7099 cm + [-307(8)]TJ 0 g 0 G -1 0 0 1 -437.547 -186.7099 cm -BT -/F15 10.9091 Tf 440.9055 186.7099 Td[(for)-307(details.)]TJ -299.167 -18.6103 Td[(A)-383(v)56(ari)1(e)-1(t)28(y)-383(of)-382(\050on)1(e)-1(-lev)28(e)-1(l)-383(an)1(d)-383(m)28(ul)1(ti-le)-1(v)28(el\051)-383(p)1(rec)-1(on)1(dit)1(ioners)-383(c)-1(an)-382(b)-27(e)-384(ob)1(tain)1(e)-1(d)-382(b)28(y)-383(a)-383(sui)1(table)]TJ 0 -13.5492 Td[(se)-1(tti)1(ng)-425(of)-425(th)1(e)-426(pr)1(e)-1(cond)1(ition)1(e)-1(r)-425(p)1(arame)-1(t)1(e)-1(rs.)-720(Thes)-1(e)-425(par)1(am)-1(ete)-1(r)1(s)-426(can)-425(b)-27(e)-426(logically)-425(d)1(ivi)1(ded)]TJ 0 -13.5492 Td[(in)28(t)1(o)-334(f)1(our)-333(grou)1(ps,)-333(i.e.)-333(paramete)-1(r)1(s)-334(de\014n)1(ing)]TJ -ET -1 0 0 1 141.7385 121.5209 cm + [-308(for)-308(details.)]TJ -51.948 -18.61 Td [(A)-383(v)56(ariet)28(y)-383(of)-383(\050one-lev)28(el)-383(and)-383(m)28(ulti-lev)28(el\051)-383(preconditioners)-383(can)-383(b)-27(e)-383(obtained)-383(b)28(y)-383(a)-383(suitable)]TJ 0 -13.55 Td [(setting)-425(of)-425(the)-426(p)1(rec)-1(on)1(ditioner)-426(par)1(am)-1(eters.)-720(These)-425(parameters)-425(can)-425(b)-28(e)-425(logically)-426(d)1(ivided)]TJ 0 -13.549 Td [(in)28(to)-333(four)-334(groups,)-333(i.e.)-333(parameters)-334(de\014ni)1(ng)]TJ 0 g 0 G -1 0 0 1 -141.7385 -121.5209 cm -BT -/F15 10.9091 Tf 155.0719 121.5209 Td[(1.)]TJ -ET -1 0 0 1 163.5567 121.5209 cm + 13.333 -19.48 Td [(1.)]TJ 0 g 0 G -1 0 0 1 -163.5567 -121.5209 cm -BT -/F15 10.9091 Tf 169.0113 121.5209 Td[(th)1(e)-334(t)28(yp)-27(e)-334(of)-333(m)27(u)1(lti-lev)28(e)-1(l)-333(p)1(rec)-1(on)1(diti)1(oner;)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [-500(the)-333(t)27(y)1(p)-28(e)-334(of)-333(m)28(ulti-lev)28(el)-334(precondition)1(e)-1(r;)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -413 0 obj << +384 0 obj << /Type /Page -/Contents 414 0 R -/Resources 412 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 401 0 R -/Annots [ 417 0 R 418 0 R 420 0 R 421 0 R 422 0 R 423 0 R 424 0 R ] +/Contents 385 0 R +/Resources 383 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 365 0 R +/Annots [ 371 0 R 372 0 R 378 0 R 379 0 R 380 0 R 381 0 R 382 0 R ] >> endobj -417 0 obj << +371 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [481.8436 611.682 489.2906 625.3151] +/Rect [481.844 611.682 489.291 625.315] /Subtype /Link /A << /S /GoTo /D (table.1) >> >> endobj -418 0 obj << +372 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [431.0961 571.0345 438.5432 584.6676] +/Rect [431.096 571.035 438.543 584.668] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -420 0 obj << +378 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [274.5998 290.0423 282.0469 303.6754] +/Rect [274.6 290.042 282.047 303.675] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -421 0 obj << +379 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [283.6907 290.0423 291.1378 303.6754] +/Rect [283.691 290.042 291.138 303.675] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -422 0 obj << +380 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [439.8392 237.7891 447.2863 249.4786] +/Rect [439.839 237.789 447.286 249.479] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -423 0 obj << +381 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [448.9301 237.7891 456.3772 249.4786] +/Rect [448.93 237.789 456.377 249.479] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -424 0 obj << +382 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [431.0961 181.6488 438.5432 195.2819] +/Rect [431.096 181.649 438.543 195.282] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -415 0 obj << -/D [413 0 R /XYZ 141.7385 740.0018 null] +386 0 obj << +/D [384 0 R /XYZ 141.738 740.002 null] >> endobj -416 0 obj << -/D [413 0 R /XYZ 141.7385 694.9697 null] +387 0 obj << +/D [384 0 R /XYZ 141.738 694.97 null] >> endobj 70 0 obj << -/D [413 0 R /XYZ 141.7385 503.1413 null] +/D [384 0 R /XYZ 141.738 503.141 null] >> endobj -419 0 obj << -/D [413 0 R /XYZ 141.7385 400.4284 null] +388 0 obj << +/D [384 0 R /XYZ 141.738 400.428 null] >> endobj -425 0 obj << -/D [413 0 R /XYZ 141.7385 136.825 null] +389 0 obj << +/D [384 0 R /XYZ 141.738 136.825 null] >> endobj -412 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F41 126 0 R /F48 214 0 R /F20 171 0 R /F19 105 0 R >> +383 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F39 116 0 R /F46 195 0 R /F18 163 0 R /F17 103 0 R >> /ProcSet [ /PDF /Text ] >> endobj -428 0 obj << -/Length 2658 +396 0 obj << +/Length 1133 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(7)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(7)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(23)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(23)]TJ 0 g 0 G -1 0 0 1 -412.4511 -35.8655 cm 0 g 0 G -1 0 0 1 -93.9178 -704.1363 cm -BT -/F15 10.9091 Tf 107.2512 704.1363 Td[(2.)]TJ -ET -1 0 0 1 115.736 704.1363 cm + -388.209 -35.866 Td [(2.)]TJ 0 g 0 G -1 0 0 1 -115.736 -704.1363 cm -BT -/F15 10.9091 Tf 121.1906 704.1363 Td[(th)1(e)-334(one-)-1(l)1(e)-1(v)28(el)-333(precondi)1(tioner)-333(used)-333(as)-334(s)-1(mo)-28(oth)1(e)-1(r)1(;)]TJ -ET -1 0 0 1 93.9178 681.6208 cm + [-500(the)-333(one-lev)27(el)-333(preconditioner)-333(used)-333(as)-334(smo)-28(other;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -681.6208 cm -BT -/F15 10.9091 Tf 107.2512 681.6208 Td[(3.)]TJ -ET -1 0 0 1 115.736 681.6208 cm + 0 -22.515 Td [(3.)]TJ 0 g 0 G -1 0 0 1 -115.736 -681.6208 cm -BT -/F15 10.9091 Tf 121.1906 681.6208 Td[(th)1(e)-334(aggregation)-333(algor)1(ithm;)]TJ -ET -1 0 0 1 93.9178 659.1052 cm + [-500(the)-333(aggregation)-334(algorith)1(m)-1(;)]TJ 0 g 0 G -1 0 0 1 -93.9178 -659.1052 cm -BT -/F15 10.9091 Tf 107.2512 659.1052 Td[(4.)]TJ -ET -1 0 0 1 115.736 659.1052 cm + 0 -22.516 Td [(4.)]TJ 0 g 0 G -1 0 0 1 -115.736 -659.1052 cm -BT -/F15 10.9091 Tf 121.1906 659.1052 Td[(th)1(e)-334(c)-1(oar)1(s)-1(e-)-1(space)-334(correction)-333(at)-333(the)-333(c)-1(oarses)-1(t)-333(lev)28(e)-1(l.)]TJ -27.2728 -22.5156 Td[(A)-313(list)-314(of)-313(t)1(he)-314(p)1(arame)-1(ters)-314(th)1(at)-313(c)-1(an)-313(b)-27(e)-314(se)-1(t,)-317(alon)1(g)-313(w)-1(i)1(th)-313(their)-313(allo)28(w)28(e)-1(d)-313(an)1(d)-313(defau)1(lt)-313(v)56(alues)-1(,)-317(is)]TJ 0 -13.5492 Td[(giv)28(en)-296(in)-295(T)83(ables)]TJ -ET -1 0 0 1 168.2139 623.0404 cm + [-500(the)-333(coarse-spac)-1(e)-333(correction)-333(at)-334(th)1(e)-334(coarsest)-333(lev)27(el.)]TJ -13.333 -22.515 Td [(A)-313(list)-314(of)-313(the)-313(parameters)-314(that)-313(can)-313(b)-28(e)-314(set,)-317(along)-313(with)-314(their)-313(allo)28(w)28(ed)-314(and)-313(default)-313(v)55(alues,)-317(is)]TJ 0 -13.55 Td [(giv)28(en)-296(in)-296(T)83(ables)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -168.2139 -623.0404 cm -BT -/F15 10.9091 Tf 168.2139 623.0404 Td[(2)]TJ -ET -1 0 0 1 173.6684 623.0404 cm + [-296(2)]TJ 0 g 0 G -1 0 0 1 -173.6684 -623.0404 cm -BT -/F15 10.9091 Tf 173.6684 623.0404 Td[(-)]TJ -ET -1 0 0 1 177.3048 623.0404 cm + [(-)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -177.3048 -623.0404 cm -BT -/F15 10.9091 Tf 177.3048 623.0404 Td[(5)]TJ -ET -1 0 0 1 182.7593 623.0404 cm + [(5)]TJ 0 g 0 G -1 0 0 1 -182.7593 -623.0404 cm -BT -/F15 10.9091 Tf 182.7593 623.0404 Td[(.)-432(F)84(or)-296(a)-296(detailed)-296(d)1(e)-1(sc)-1(r)1(ipt)1(ion)-296(of)-295(the)-296(m)-1(eanin)1(g)-296(of)-296(th)1(e)-297(p)1(arame)-1(ters,)-304(p)1(leas)-1(e)]TJ -88.8415 -13.5492 Td[(refer)-333(to)-333(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 170.6452 609.4912 cm + [(.)-432(F)83(or)-296(a)-296(detailed)-296(description)-296(of)-296(the)-296(meaning)-296(of)-296(the)-296(parameters,)-304(please)]TJ 0 -13.549 Td [(refer)-333(to)-334(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -170.6452 -609.4912 cm -BT -/F15 10.9091 Tf 170.6452 609.4912 Td[(5)]TJ -ET -1 0 0 1 176.0997 609.4912 cm + [-333(5)]TJ 0 g 0 G -1 0 0 1 -176.0997 -609.4912 cm -BT -/F15 10.9091 Tf 176.0997 609.4912 Td[(.)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [(.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -427 0 obj << +395 0 obj << /Type /Page -/Contents 428 0 R -/Resources 426 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 401 0 R -/Annots [ 430 0 R 434 0 R 435 0 R 436 0 R ] +/Contents 396 0 R +/Resources 394 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 365 0 R +/Annots [ 393 0 R 390 0 R 391 0 R 392 0 R ] >> endobj -430 0 obj << +393 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -434 0 obj << +390 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [167.2176 619.9229 174.6647 631.6124] +/Rect [167.218 619.923 174.665 631.612] /Subtype /Link /A << /S /GoTo /D (table.2) >> >> endobj -435 0 obj << +391 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [176.3085 619.9229 183.7556 631.6124] +/Rect [176.308 619.923 183.756 631.612] /Subtype /Link /A << /S /GoTo /D (table.5) >> >> endobj -436 0 obj << +392 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [169.6489 608.495 177.096 618.0632] +/Rect [169.649 608.495 177.096 618.063] /Subtype /Link /A << /S /GoTo /D (section.5) >> >> endobj -429 0 obj << -/D [427 0 R /XYZ 93.9178 740.0018 null] +397 0 obj << +/D [395 0 R /XYZ 93.918 740.002 null] >> endobj -431 0 obj << -/D [427 0 R /XYZ 93.9178 715.0952 null] +398 0 obj << +/D [395 0 R /XYZ 93.918 715.095 null] >> endobj -432 0 obj << -/D [427 0 R /XYZ 93.9178 697.5319 null] +399 0 obj << +/D [395 0 R /XYZ 93.918 697.532 null] >> endobj -433 0 obj << -/D [427 0 R /XYZ 93.9178 675.0164 null] +400 0 obj << +/D [395 0 R /XYZ 93.918 675.016 null] >> endobj -426 0 obj << -/Font << /F42 129 0 R /F15 123 0 R >> +394 0 obj << +/Font << /F40 117 0 R /F15 115 0 R >> /ProcSet [ /PDF /Text ] >> endobj -439 0 obj << -/Length 5926 +403 0 obj << +/Length 4350 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(24)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(24)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 206.2256 0 cm - q 0 -1 1 0 0 0 cm +ET +1 0 0 1 347.964 715.095 cm +q +0 -1 1 0 0 0 cm 0 g 0 G -1 0 0 1 15.408 16.3055 cm 0 g 0 G 0 g 0 G -1 0 0 1 5.4545 71.071 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -551.8492 0.1992 l -S +1 0 0 1 20.863 87.576 cm +[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S Q -1 0 0 1 -0.1992 -13.5492 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 20.863 73.828 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -368.6274 -788.9225 cm +1 0 0 1 -347.964 -715.095 cm BT -/F48 10.9091 Tf 374.8042 792.9873 Td[(what)]TJ +/F46 10.9091 Tf 374.804 792.987 Td [(what)]TJ ET -1 0 0 1 483.6724 788.9225 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 483.872 788.923 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -483.6724 -788.9225 cm BT -/F42 10.9091 Tf 489.8492 792.9873 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ +/F40 10.9091 Tf 489.849 792.987 Td [(d)22(a)67(t)66(a)-377(type)]TJ ET -1 0 0 1 587.2629 788.9225 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 587.462 788.923 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -587.2629 -788.9225 cm BT -/F48 10.9091 Tf 593.4397 792.9873 Td[(val)]TJ +/F46 10.9091 Tf 593.44 792.987 Td [(val)]TJ ET -1 0 0 1 655.911 788.9225 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 656.11 788.923 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -655.911 -788.9225 cm BT -/F42 10.9091 Tf 662.0878 792.9873 Td[(def)89(a)22(ul)66(t)]TJ +/F40 10.9091 Tf 662.088 792.987 Td [(def)89(a)22(ul)67(t)]TJ ET -1 0 0 1 710.0962 788.9225 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 710.295 788.923 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -710.0962 -788.9225 cm BT -/F42 10.9091 Tf 716.2731 792.9873 Td[(com)1(ments)]TJ +/F40 10.9091 Tf 716.273 792.987 Td [(comments)]TJ ET -1 0 0 1 920.4766 788.9225 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 920.676 788.923 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -551.65 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -551.8492 0.1992 l -S +1 0 0 1 368.827 788.723 cm +[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S Q -1 0 0 1 -0.1992 -40.6476 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 368.827 747.876 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -368.6274 -747.8764 cm BT -/F48 10.9091 Tf 374.8042 779.0396 Td[(mld_ml_type_)]TJ +/F46 10.9091 Tf 374.804 779.04 Td [(mld_ml_type_)]TJ ET -1 0 0 1 483.6723 747.8764 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 483.872 747.876 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -483.6723 -747.8764 cm BT -/F48 10.9091 Tf 489.8492 779.0396 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 489.849 779.04 Td [(character\050len=*\051)]TJ ET -1 0 0 1 587.2629 747.8764 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 587.462 747.876 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -587.2629 -747.8764 cm BT -/F48 10.9091 Tf 593.4397 779.0396 Td[('ADD')]TJ 0 -13.5492 Td[('MULT')]TJ +/F46 10.9091 Tf 593.44 779.04 Td [('ADD')]TJ 0 -13.55 Td [('MULT')]TJ ET -1 0 0 1 655.911 747.8764 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 656.11 747.876 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -655.911 -747.8764 cm BT -/F48 10.9091 Tf 662.0878 779.0396 Td[('MULT')]TJ +/F46 10.9091 Tf 662.088 779.04 Td [('MULT')]TJ ET -1 0 0 1 710.0962 747.8764 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 710.295 747.876 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -710.0962 -747.8764 cm BT -/F15 10.9091 Tf 716.2731 779.0396 Td[(Bas)-1(ic)-449(m)28(ulti)1(-)-1(lev)28(el)-449(fr)1(am)-1(ew)27(or)1(k:)-675(addi)1(tiv)28(e)-449(or)]TJ 0 -13.5492 Td[(m)27(u)1(ltip)1(licativ)28(e)-586(am)-1(on)1(g)-586(the)-586(le)-1(v)28(els)-586(\050alw)27(a)28(ys)]TJ 0 -13.5492 Td[(add)1(itiv)28(e)-333(insid)1(e)-334(a)-334(l)1(e)-1(v)28(el\051.)]TJ +/F15 10.9091 Tf 716.273 779.04 Td [(Basic)-449(m)28(ulti-lev)28(el)-449(framew)27(ork:)-675(additiv)28(e)-449(or)]TJ 0 -13.55 Td [(m)28(ultiplicativ)28(e)-586(am)-1(on)1(g)-587(the)-586(lev)28(els)-586(\050alw)28(a)27(ys)]TJ 0 -13.549 Td [(additiv)28(e)-333(inside)-334(a)-333(lev)28(el\051.)]TJ ET -1 0 0 1 920.4766 747.8764 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 920.676 747.876 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -551.65 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -551.8492 0.1992 l -S +1 0 0 1 368.827 747.677 cm +[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S Q -1 0 0 1 -0.1992 -40.6475 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 368.827 706.83 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -368.6274 -706.8304 cm BT -/F48 10.9091 Tf 374.8042 737.9936 Td[(mld_smoother_type_)]TJ +/F46 10.9091 Tf 374.804 737.994 Td [(mld_smoother_type_)]TJ ET -1 0 0 1 483.6723 706.8304 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 483.872 706.83 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -483.6723 -706.8304 cm BT -/F48 10.9091 Tf 489.8492 737.9936 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 489.849 737.994 Td [(character\050len=*\051)]TJ ET -1 0 0 1 587.2629 706.8304 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 587.462 706.83 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -587.2629 -706.8304 cm BT -/F48 10.9091 Tf 593.4397 737.9936 Td[('DIAG')]TJ 0 -13.5492 Td[('BJAC')]TJ 0 -13.5492 Td[('AS')]TJ +/F46 10.9091 Tf 593.44 737.994 Td [('DIAG')]TJ 0 -13.55 Td [('BJAC')]TJ 0 -13.549 Td [('AS')]TJ ET -1 0 0 1 655.911 706.8304 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 656.11 706.83 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -655.911 -706.8304 cm BT -/F48 10.9091 Tf 662.0878 737.9936 Td[('AS')]TJ +/F46 10.9091 Tf 662.088 737.994 Td [('AS')]TJ ET -1 0 0 1 710.0962 706.8304 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 710.295 706.83 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -710.0962 -706.8304 cm BT -/F15 10.9091 Tf 716.2731 737.9936 Td[(Bas)-1(ic)-1379(on)1(e)-1(-lev)28(e)-1(l)-1378(pr)1(e)-1(cond)1(ition)1(e)-1(r)-1378(\050i.e.)]TJ 0 -13.5492 Td[(sm)-1(o)-28(ot)1(her\051:)-444(diagon)1(al,)-333(bl)1(o)-28(c)27(k)-333(Jacobi,)-333(AS)]TJ +/F15 10.9091 Tf 716.273 737.994 Td [(Basic)-1379(one-lev)28(el)-1379(preconditioner)-1378(\050i.e.)]TJ 0 -13.55 Td [(smo)-28(other\051:)-444(diagonal,)-333(blo)-28(c)28(k)-334(Jacobi,)-333(AS)]TJ ET -1 0 0 1 920.4766 706.8304 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 920.676 706.83 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -551.65 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -551.8492 0.1992 l -S +1 0 0 1 368.827 706.631 cm +[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S Q -1 0 0 1 -0.1992 -40.6476 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 368.827 665.784 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -368.6274 -665.7843 cm BT -/F48 10.9091 Tf 374.8042 696.9475 Td[(mld_smoother_pos_)]TJ +/F46 10.9091 Tf 374.804 696.948 Td [(mld_smoother_pos_)]TJ ET -1 0 0 1 483.6723 665.7843 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 483.872 665.784 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -483.6723 -665.7843 cm BT -/F48 10.9091 Tf 489.8492 696.9475 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 489.849 696.948 Td [(character\050len=*\051)]TJ ET -1 0 0 1 587.2629 665.7843 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 587.462 665.784 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -587.2629 -665.7843 cm BT -/F48 10.9091 Tf 593.4397 696.9475 Td[('PRE')]TJ 0 -13.5492 Td[('POST')]TJ 0 -13.5492 Td[('TWOSIDE')]TJ +/F46 10.9091 Tf 593.44 696.948 Td [('PRE')]TJ 0 -13.55 Td [('POST')]TJ 0 -13.549 Td [('TWOSIDE')]TJ ET -1 0 0 1 655.911 665.7843 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 656.11 665.784 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -655.911 -665.7843 cm BT -/F48 10.9091 Tf 662.0878 696.9475 Td[('POST')]TJ +/F46 10.9091 Tf 662.088 696.948 Td [('POST')]TJ ET -1 0 0 1 710.0962 665.7843 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 710.295 665.784 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -710.0962 -665.7843 cm BT -/F15 10.9091 Tf 716.2731 696.9475 Td[(\134P)28(osition)1(")-234(of)-232(the)-234(sm)-1(o)-27(other:)-394(pr)1(e)-1(-s)-1(mo)-28(oth)1(e)-1(r)1(,)]TJ 0 -13.5492 Td[(p)-27(os)-1(t-sm)-1(o)-28(ot)1(her,)-333(pr)1(e)-1(-)-334(an)1(d)-333(p)-27(os)-1(t-sm)-1(o)-28(ot)1(her.)]TJ +/F15 10.9091 Tf 716.273 696.948 Td [(\134P)28(osition")-233(of)-234(the)-233(smo)-28(other:)-394(pre-smo)-28(other,)]TJ 0 -13.55 Td [(p)-28(ost-smo)-28(other,)-333(pre-)-333(and)-334(p)-27(ost-smo)-28(other.)]TJ ET -1 0 0 1 920.4766 665.7843 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 920.676 665.784 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -551.65 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -551.8492 0.1992 l -S +1 0 0 1 368.827 665.585 cm +[]0 d 0 J 0.398 w 0 0 m 551.849 0 l S Q -1 0 0 1 111.9699 -30.4898 cm 0 g 0 G -1 0 0 1 -480.7965 -634.896 cm BT -/F15 10.9091 Tf 480.7965 634.896 Td[(T)83(ab)1(le)-334(2:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(t)28(yp)-27(e)-334(of)-333(m)27(u)1(lti-lev)28(e)-1(l)-333(p)1(rec)-1(on)1(diti)1(oner.)]TJ -ET -1 0 0 1 808.7059 634.896 cm +/F15 10.9091 Tf 480.797 634.896 Td [(T)83(able)-333(2:)-444(P)27(arameters)-333(de\014ning)-333(the)-333(t)27(yp)-27(e)-334(of)-333(m)28(ulti-lev)27(el)-333(preconditioner.)]TJ 0 g 0 G -1 0 0 1 132.8325 80.1992 cm 0 g 0 G -1 0 0 1 -593.5744 0 cm - Q -1 0 0 1 -206.2255 -593.5743 cm +ET +1 0 0 1 347.964 715.095 cm +Q 0 g 0 G -1 0 0 1 0 -29.8879 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -438 0 obj << +402 0 obj << /Type /Page -/Contents 439 0 R -/Resources 437 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 401 0 R +/Contents 403 0 R +/Resources 401 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 365 0 R >> endobj -440 0 obj << -/D [438 0 R /XYZ 141.7385 740.0018 null] +404 0 obj << +/D [402 0 R /XYZ 141.738 740.002 null] >> endobj -364 0 obj << -/D [438 0 R /XYZ 524.1299 648.4452 null] +331 0 obj << +/D [402 0 R /XYZ -3799.383 538.929 null] >> endobj -437 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F48 214 0 R >> +401 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -443 0 obj << -/Length 12790 +408 0 obj << +/Length 9772 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(7)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(7)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(25)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(25)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 206.2256 0 cm - q 0 -1 1 0 0 0 cm +ET +1 0 0 1 300.143 121.521 cm +q +0 1 -1 0 0 0 cm 0 g 0 G -1 0 0 1 291.3326 170.3653 cm 0 g 0 G 0 g 0 G -1 0 0 1 -291.3326 -1.3948 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 0 169.17 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -13.5492 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 0 155.421 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -299.9441 -870.5165 cm +1 0 0 1 -300.143 -121.521 cm BT -/F48 10.9091 Tf 306.121 874.5813 Td[(what)]TJ +/F46 10.9091 Tf 306.121 281.007 Td [(what)]TJ ET -1 0 0 1 403.5347 870.5165 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 403.734 276.942 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -403.5347 -870.5165 cm BT -/F42 10.9091 Tf 409.7115 874.5813 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ +/F40 10.9091 Tf 409.712 281.007 Td [(d)22(a)67(t)67(a)-378(type)]TJ ET -1 0 0 1 522.508 870.5165 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 522.707 276.942 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -522.508 -870.5165 cm BT -/F48 10.9091 Tf 528.6849 874.5813 Td[(val)]TJ +/F46 10.9091 Tf 528.685 281.007 Td [(val)]TJ ET -1 0 0 1 625.1718 870.5165 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 625.371 276.942 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -625.1718 -870.5165 cm BT -/F42 10.9091 Tf 631.3486 874.5813 Td[(def)89(a)22(ul)66(t)]TJ +/F40 10.9091 Tf 631.349 281.007 Td [(def)89(a)22(ul)67(t)]TJ ET -1 0 0 1 708.4295 870.5165 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 708.629 276.942 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -708.4295 -870.5165 cm BT -/F42 10.9091 Tf 714.6063 874.5813 Td[(com)1(ments)]TJ +/F40 10.9091 Tf 714.606 281.007 Td [(comments)]TJ ET -1 0 0 1 918.8099 870.5165 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 919.009 276.942 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 276.743 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -27.0983 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 249.445 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -843.0197 cm BT -/F48 10.9091 Tf 306.121 860.6336 Td[(mld_sub_ovr_)]TJ +/F46 10.9091 Tf 306.121 267.059 Td [(mld_sub_ovr_)]TJ ET -1 0 0 1 403.5347 843.0197 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 403.734 249.445 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -403.5347 -843.0197 cm BT -/F48 10.9091 Tf 409.7115 860.6337 Td[(integer)]TJ +/F46 10.9091 Tf 409.712 267.059 Td [(integer)]TJ ET -1 0 0 1 522.508 843.0197 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 522.707 249.445 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -522.508 -843.0197 cm BT -/F15 10.9091 Tf 528.6849 860.6337 Td[(an)28(y)-238(i)1(n)28(tege)-1(r)-238(n)29(um)27(b)-27(er)]TJ/F27 10.9091 Tf 0 -13.5492 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ +/F15 10.9091 Tf 528.685 267.059 Td [(an)28(y)-238(in)28(teger)-238(n)27(um)28(b)-28(er)]TJ/F25 10.9091 Tf 0 -13.549 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET -1 0 0 1 625.1718 843.0197 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 625.371 249.445 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -625.1718 -843.0197 cm BT -/F15 10.9091 Tf 631.3486 860.6337 Td[(1)]TJ +/F15 10.9091 Tf 631.349 267.059 Td [(1)]TJ ET -1 0 0 1 708.4295 843.0197 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 708.629 249.445 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -708.4295 -843.0197 cm BT -/F15 10.9091 Tf 714.6063 860.6337 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(o)28(v)28(erlap)-333(la)28(y)28(ers.)]TJ +/F15 10.9091 Tf 714.606 267.059 Td [(Num)28(b)-28(er)-333(of)-334(o)28(v)28(erlap)-333(la)27(y)28(ers.)]TJ ET -1 0 0 1 918.8099 843.0197 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 919.009 249.445 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 249.246 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -40.6476 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 300.143 208.399 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -299.9441 -801.9736 cm BT -/F48 10.9091 Tf 306.121 833.1368 Td[(mld_sub_restr_)]TJ +/F46 10.9091 Tf 306.121 239.562 Td [(mld_sub_restr_)]TJ ET -1 0 0 1 403.5347 801.9736 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 403.734 208.399 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -403.5347 -801.9736 cm BT -/F48 10.9091 Tf 409.7115 833.1368 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 409.712 239.562 Td [(character\050len=*\051)]TJ ET -1 0 0 1 522.508 801.9736 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 522.707 208.399 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -522.508 -801.9736 cm BT -/F48 10.9091 Tf 528.6849 833.1368 Td[('HALO')]TJ 0 -13.5492 Td[('NONE')]TJ +/F46 10.9091 Tf 528.685 239.562 Td [('HALO')]TJ 0 -13.549 Td [('NONE')]TJ ET -1 0 0 1 625.1718 801.9736 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 625.371 208.399 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -625.1718 -801.9736 cm BT -/F48 10.9091 Tf 631.3486 833.1368 Td[('HALO')]TJ +/F46 10.9091 Tf 631.349 239.562 Td [('HALO')]TJ ET -1 0 0 1 708.4295 801.9736 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 708.629 208.399 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -708.4295 -801.9736 cm BT -/F15 10.9091 Tf 714.6063 833.1368 Td[(T)28(yp)-28(e)-429(of)-429(res)-1(t)1(riction)-429(op)-27(e)-1(r)1(ator:)]TJ/F48 10.9091 Tf 146.3202 0 Td[('HALO')]TJ/F15 10.9091 Tf 39.0444 0 Td[(for)]TJ -185.3646 -13.5492 Td[(taki)1(ng)-478(in)29(to)-478(acc)-1(ou)1(n)28(t)-478(th)1(e)-479(o)28(v)28(erlap)1(,)]TJ/F48 10.9091 Tf 164.062 0 Td[('NONE')]TJ/F15 10.9091 Tf -164.062 -13.5492 Td[(for)-333(n)1(e)-1(gl)1(e)-1(ctin)1(g)-334(it)1(.)]TJ +/F15 10.9091 Tf 714.606 239.562 Td [(T)28(yp)-28(e)-429(of)-429(restriction)-430(op)-27(erator:)]TJ/F46 10.9091 Tf 146.32 0 Td [('HALO')]TJ/F15 10.9091 Tf 39.045 0 Td [(for)]TJ -185.365 -13.549 Td [(taking)-478(in)28(to)-478(accoun)28(t)-478(the)-477(o)27(v)28(erlap,)]TJ/F46 10.9091 Tf 164.062 0 Td [('NONE')]TJ/F15 10.9091 Tf -164.062 -13.549 Td [(for)-333(neglecting)-334(it.)]TJ ET -1 0 0 1 918.8099 801.9736 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 919.009 208.399 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 208.2 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -40.6476 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 300.143 167.353 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -299.9441 -760.9275 cm BT -/F48 10.9091 Tf 306.121 792.0907 Td[(mld_sub_prol_)]TJ +/F46 10.9091 Tf 306.121 198.516 Td [(mld_sub_prol_)]TJ ET -1 0 0 1 403.5347 760.9275 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 403.734 167.353 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -403.5347 -760.9275 cm BT -/F48 10.9091 Tf 409.7115 792.0907 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 409.712 198.516 Td [(character\050len=*\051)]TJ ET -1 0 0 1 522.508 760.9275 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 522.707 167.353 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -522.508 -760.9275 cm BT -/F48 10.9091 Tf 528.6849 792.0907 Td[('SUM')]TJ 0 -13.5492 Td[('NONE')]TJ +/F46 10.9091 Tf 528.685 198.516 Td [('SUM')]TJ 0 -13.549 Td [('NONE')]TJ ET -1 0 0 1 625.1718 760.9275 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 625.371 167.353 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -625.1718 -760.9275 cm BT -/F48 10.9091 Tf 631.3486 792.0907 Td[('NONE')]TJ +/F46 10.9091 Tf 631.349 198.516 Td [('NONE')]TJ ET -1 0 0 1 708.4295 760.9275 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 708.629 167.353 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -708.4295 -760.9275 cm BT -/F15 10.9091 Tf 714.6063 792.0907 Td[(T)28(yp)-28(e)-416(of)-415(pr)1(olongator)-415(op)-27(e)-1(r)1(ator:)]TJ/F48 10.9091 Tf 152.1938 0 Td[('SUM')]TJ/F15 10.9091 Tf 33.1708 0 Td[(for)]TJ -185.3646 -13.5492 Td[(add)1(in)1(g)-252(the)-252(con)28(tr)1(ibu)1(tions)-252(f)1(rom)-252(th)1(e)-253(o)28(v)28(erlap)1(,)]TJ/F48 10.9091 Tf 0 -13.5492 Td[('NONE')]TJ/F15 10.9091 Tf 37.9997 0 Td[(for)-333(n)1(e)-1(gl)1(e)-1(ctin)1(g)-334(th)1(e)-1(m.)]TJ +/F15 10.9091 Tf 714.606 198.516 Td [(T)28(yp)-28(e)-416(of)-416(p)1(rolongator)-416(op)-28(erator:)]TJ/F46 10.9091 Tf 152.194 0 Td [('SUM')]TJ/F15 10.9091 Tf 33.171 0 Td [(for)]TJ -185.365 -13.549 Td [(adding)-252(the)-251(con)28(tributions)-252(from)-252(the)-251(o)28(v)27(erlap,)]TJ/F46 10.9091 Tf 0 -13.549 Td [('NONE')]TJ/F15 10.9091 Tf 38 0 Td [(for)-333(neglecting)-334(them.)]TJ ET -1 0 0 1 918.8099 760.9275 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 40.6476 l -S +1 0 0 1 919.009 167.353 cm +[]0 d 0 J 0.398 w 0 0 m 0 40.648 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 167.154 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -67.746 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 300.143 99.209 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -299.9441 -692.783 cm BT -/F48 10.9091 Tf 306.121 751.0446 Td[(mld_sub_solve_)]TJ +/F46 10.9091 Tf 306.121 157.47 Td [(mld_sub_solve_)]TJ ET -1 0 0 1 403.5347 692.7831 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 403.734 99.209 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -403.5347 -692.7831 cm BT -/F48 10.9091 Tf 409.7115 751.0446 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 409.712 157.47 Td [(character\050len=*\051)]TJ ET -1 0 0 1 522.508 692.7831 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 522.707 99.209 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -522.508 -692.7831 cm BT -/F48 10.9091 Tf 528.6849 751.0446 Td[('ILU')]TJ 0 -13.5492 Td[('MILU')]TJ 0 -13.5492 Td[('ILUT')]TJ 0 -13.5492 Td[('UMF')]TJ 0 -13.5492 Td[('SLU')]TJ +/F46 10.9091 Tf 528.685 157.47 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ ET -1 0 0 1 625.1718 692.7831 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 625.371 99.209 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -625.1718 -692.7831 cm BT -/F48 10.9091 Tf 631.3486 751.0446 Td[('UMF')]TJ +/F46 10.9091 Tf 631.349 157.47 Td [('UMF')]TJ ET -1 0 0 1 708.4295 692.7831 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 708.629 99.209 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -708.4295 -692.7831 cm BT -/F15 10.9091 Tf 714.6063 751.0446 Td[(Lo)-28(cal)-326(solv)28(e)-1(r)1(:)-441(ILU\050)]TJ/F24 10.9091 Tf 87.8474 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-327(MILU\050)]TJ/F24 10.9091 Tf 44.0257 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-327(ILU\050)]TJ/F24 10.9091 Tf 34.0257 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051,)]TJ -191.1525 -13.5492 Td[(LU)-411(fr)1(om)-412(UM)1(FP)84(A)27(CK,)-411(LU)-411(f)1(rom)-411(Sup)-27(erLU)]TJ 0 -13.5492 Td[(\050p)1(lus)-334(t)1(rian)1(gular)-333(solv)28(e\051.)]TJ +/F15 10.9091 Tf 714.606 157.47 Td [(Lo)-28(cal)-326(solv)28(er:)-441(ILU\050)]TJ/F22 10.9091 Tf 87.848 0 Td [(p)]TJ/F15 10.9091 Tf 5.488 0 Td [(\051,)-327(MILU\050)]TJ/F22 10.9091 Tf 44.026 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-327(ILU\050)]TJ/F22 10.9091 Tf 34.025 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051,)]TJ -191.153 -13.549 Td [(LU)-411(from)-411(UMFP)83(A)28(CK,)-411(LU)-411(from)-411(Sup)-28(erLU)]TJ 0 -13.549 Td [(\050plus)-333(triangular)-333(solv)27(e\051.)]TJ ET -1 0 0 1 918.8099 692.7831 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 919.009 99.209 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 99.009 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 71.712 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -665.2862 cm BT -/F48 10.9091 Tf 306.121 682.9002 Td[(mld_sub_fillin_)]TJ +/F46 10.9091 Tf 306.121 89.326 Td [(mld_sub_fillin_)]TJ ET -1 0 0 1 403.5347 665.2862 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 403.734 71.712 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -403.5347 -665.2862 cm BT -/F48 10.9091 Tf 409.7115 682.9002 Td[(integer)]TJ +/F46 10.9091 Tf 409.712 89.326 Td [(integer)]TJ ET -1 0 0 1 522.508 665.2862 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 522.707 71.712 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -522.508 -665.2862 cm BT -/F15 10.9091 Tf 528.6849 682.9002 Td[(An)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F27 10.9091 Tf 70.6061 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ +/F15 10.9091 Tf 528.685 89.326 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.606 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET -1 0 0 1 625.1718 665.2862 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 625.371 71.712 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -625.1718 -665.2862 cm BT -/F15 10.9091 Tf 631.3486 682.9002 Td[(0)]TJ +/F15 10.9091 Tf 631.349 89.326 Td [(0)]TJ ET -1 0 0 1 708.4295 665.2862 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 708.629 71.712 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -708.4295 -665.2862 cm BT -/F15 10.9091 Tf 714.6063 682.9002 Td[(Fil)1(l-in)-276(lev)28(e)-1(l)]TJ/F24 10.9091 Tf 56.1769 0 Td[(p)]TJ/F15 10.9091 Tf 8.5013 0 Td[(of)-276(th)1(e)-277(in)1(c)-1(omp)1(le)-1(te)-276(LU)-276(factor-)]TJ -64.6782 -13.5492 Td[(ization)1(s)-1(.)]TJ +/F15 10.9091 Tf 714.606 89.326 Td [(Fill-in)-276(lev)28(el)]TJ/F22 10.9091 Tf 56.177 0 Td [(p)]TJ/F15 10.9091 Tf 8.501 0 Td [(of)-276(the)-276(incomplete)-276(LU)-277(factor-)]TJ -64.678 -13.549 Td [(izations.)]TJ ET -1 0 0 1 918.8099 665.2862 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 919.009 71.712 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 71.513 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 44.215 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -637.7893 cm BT -/F48 10.9091 Tf 306.121 655.4033 Td[(mld_sub_iluthrs_)]TJ +/F46 10.9091 Tf 306.121 61.829 Td [(mld_sub_iluthrs_)]TJ ET -1 0 0 1 403.5347 637.7893 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 403.734 44.215 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -403.5347 -637.7893 cm BT -/F48 10.9091 Tf 409.7115 655.4033 Td[(real\050)]TJ/F20 10.9091 Tf 28.6361 0 Td[(kind)]TJ +/F46 10.9091 Tf 409.712 61.829 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ ET -1 0 0 1 459.0892 655.4033 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 459.089 62.028 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -459.0892 -655.4033 cm BT -/F20 10.9091 Tf 462.4347 655.4033 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5678 0 Td[(\051)]TJ +/F18 10.9091 Tf 462.435 61.829 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.567 0 Td [(\051)]TJ ET -1 0 0 1 522.508 637.7893 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 522.707 44.215 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -522.508 -637.7893 cm BT -/F15 10.9091 Tf 528.6849 655.4033 Td[(An)28(y)-333(real)-333(n)28(u)1(m)-1(.)]TJ/F27 10.9091 Tf 72.1515 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5152 0 Td[(0)]TJ +/F15 10.9091 Tf 528.685 61.829 Td [(An)28(y)-333(real)-334(n)28(um.)]TJ/F25 10.9091 Tf 72.151 0 Td [(\025)]TJ/F15 10.9091 Tf 11.516 0 Td [(0)]TJ ET -1 0 0 1 625.1718 637.7893 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 625.371 44.215 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -625.1718 -637.7893 cm BT -/F48 10.9091 Tf 631.3486 655.4033 Td[(0.e0)]TJ/F15 10.9091 Tf 26.5452 0 Td[(\050or)]TJ/F48 10.9091 Tf 17.6061 0 Td[(0.d0)]TJ/F15 10.9091 Tf 22.9088 0 Td[(\051)]TJ +/F46 10.9091 Tf 631.349 61.829 Td [(0.e0)]TJ/F15 10.9091 Tf 26.545 0 Td [(\050or)]TJ/F46 10.9091 Tf 17.606 0 Td [(0.d0)]TJ/F15 10.9091 Tf 22.909 0 Td [(\051)]TJ ET -1 0 0 1 708.4295 637.7893 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 708.629 44.215 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -708.4295 -637.7893 cm BT -/F15 10.9091 Tf 714.6063 655.4033 Td[(Drop)-256(t)1(ole)-1(r)1(ance)]TJ/F24 10.9091 Tf 72.7769 0 Td[(t)]TJ/F15 10.9091 Tf 6.7369 0 Td[(in)-256(th)1(e)-257(ILU\050)]TJ/F24 10.9091 Tf 53.0192 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051)-256(factoriza-)]TJ -146.8095 -13.5492 Td[(tion)1(.)]TJ +/F15 10.9091 Tf 714.606 61.829 Td [(Drop)-256(tolerance)]TJ/F22 10.9091 Tf 72.777 0 Td [(t)]TJ/F15 10.9091 Tf 6.737 0 Td [(in)-256(the)-257(ILU\050)]TJ/F22 10.9091 Tf 53.019 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051)-256(factoriza-)]TJ -146.81 -13.549 Td [(tion.)]TJ ET -1 0 0 1 918.8099 637.7893 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 919.009 44.215 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 44.016 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 -0.1993 -54.1968 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 300.143 -10.38 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -299.9441 -583.194 cm BT -/F48 10.9091 Tf 306.121 627.9064 Td[(mld_sub_ren_)]TJ +/F46 10.9091 Tf 306.121 34.332 Td [(mld_sub_ren_)]TJ ET -1 0 0 1 403.5347 583.194 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 403.734 -10.38 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -403.5347 -583.194 cm BT -/F48 10.9091 Tf 409.7115 627.9064 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 409.712 34.332 Td [(character\050len=*\051)]TJ ET -1 0 0 1 522.508 583.194 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 522.707 -10.38 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -522.508 -583.194 cm BT -/F48 10.9091 Tf 528.6849 627.9064 Td[('RENUM)]TJ +/F46 10.9091 Tf 528.685 34.332 Td [('RENUM)]TJ ET -1 0 0 1 563.7354 627.9064 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4364 0.1992 l -S +1 0 0 1 563.735 34.531 cm +[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q -1 0 0 1 -563.7354 -627.9064 cm BT -/F48 10.9091 Tf 567.1717 627.9064 Td[(NONE')]TJ -38.4868 -13.5492 Td[('RENUM)]TJ +/F46 10.9091 Tf 567.172 34.332 Td [(NONE')]TJ -38.487 -13.549 Td [('RENUM)]TJ ET -1 0 0 1 563.7354 614.3572 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4364 0.1992 l -S +1 0 0 1 563.735 20.982 cm +[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q -1 0 0 1 -563.7354 -614.3572 cm BT -/F48 10.9091 Tf 567.1717 614.3572 Td[(GLOBAL')]TJ +/F46 10.9091 Tf 567.172 20.783 Td [(GLOBAL')]TJ ET -1 0 0 1 625.1718 583.194 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 625.371 -10.38 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -625.1718 -583.194 cm BT -/F48 10.9091 Tf 631.3486 627.9064 Td[('RENUM)]TJ +/F46 10.9091 Tf 631.349 34.332 Td [('RENUM)]TJ ET -1 0 0 1 666.3991 627.9064 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4364 0.1992 l -S +1 0 0 1 666.399 34.531 cm +[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q -1 0 0 1 -666.3991 -627.9064 cm BT -/F48 10.9091 Tf 669.8355 627.9064 Td[(NONE')]TJ +/F46 10.9091 Tf 669.835 34.332 Td [(NONE')]TJ ET -1 0 0 1 708.4295 583.194 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 708.629 -10.38 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -708.4295 -583.194 cm BT -/F15 10.9091 Tf 714.6063 627.9064 Td[(Ro)28(w)-468(and)-467(column)-467(reord)1(e)-1(ri)1(ng)-468(of)-467(th)1(e)-468(lo)-28(cal)]TJ 0 -13.5492 Td[(submatr)1(ic)-1(es)-1(:)-409(n)1(o)-264(reord)1(e)-1(r)1(ing,)-277(reord)1(e)-1(r)1(ing)-263(ac)-1(-)]TJ 0 -13.5492 Td[(cordi)1(ng)-540(to)-540(t)1(he)-540(global)-539(n)28(um)28(b)-27(e)-1(ri)1(ng)-540(of)-539(the)]TJ 0 -13.5492 Td[(ro)28(ws)-334(an)1(d)-333(c)-1(olu)1(mns)-334(of)-333(th)1(e)-334(whol)1(e)-334(m)-1(at)1(rix.)]TJ +/F15 10.9091 Tf 714.606 34.332 Td [(Ro)28(w)-468(and)-467(column)-468(reordering)-467(of)-468(the)-468(lo)-27(cal)]TJ 0 -13.549 Td [(submatrices:)-410(no)-263(reordering,)-277(reordering)-264(ac-)]TJ 0 -13.549 Td [(cording)-540(to)-540(the)-539(global)-540(n)28(um)27(b)-27(ering)-540(of)-540(the)]TJ 0 -13.55 Td [(ro)28(ws)-334(and)-333(columns)-333(of)-334(t)1(he)-334(whole)-333(matrix.)]TJ ET -1 0 0 1 918.8099 583.194 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 919.009 -10.38 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -618.6665 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -618.8657 0.1992 l -S +1 0 0 1 300.143 -10.58 cm +[]0 d 0 J 0.398 w 0 0 m 618.866 0 l S Q -1 0 0 1 112.7264 -30.4898 cm 0 g 0 G -1 0 0 1 -412.8698 -552.3057 cm BT -/F15 10.9091 Tf 412.8698 552.3057 Td[(T)83(ab)1(le)-334(3:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(one-)-1(l)1(e)-1(v)28(el)-333(precondi)1(tioner)-333(used)-333(as)-334(s)-1(mo)-28(oth)1(e)-1(r)1(.)]TJ -ET -1 0 0 1 780.9913 552.3057 cm +/F15 10.9091 Tf 412.87 -41.269 Td [(T)83(able)-333(3:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(on)1(e)-1(-lev)28(el)-333(preconditioner)-333(used)-334(as)-333(smo)-28(other.)]TJ 0 g 0 G -1 0 0 1 112.7264 162.7895 cm 0 g 0 G -1 0 0 1 -593.5743 0 cm - Q -1 0 0 1 -206.2256 -593.5743 cm +ET +1 0 0 1 300.143 121.521 cm +Q 0 g 0 G -1 0 0 1 0 -29.888 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -442 0 obj << +407 0 obj << /Type /Page -/Contents 443 0 R -/Resources 441 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 447 0 R -/Annots [ 445 0 R ] +/Contents 408 0 R +/Resources 406 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 411 0 R +/Annots [ 405 0 R ] >> endobj -445 0 obj << +405 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -444 0 obj << -/D [442 0 R /XYZ 93.9178 740.0018 null] +409 0 obj << +/D [407 0 R /XYZ 93.918 740.002 null] >> endobj -446 0 obj << -/D [442 0 R /XYZ 456.2031 565.8549 null] +410 0 obj << +/D [407 0 R /XYZ 449.315 4358.278 null] >> endobj -441 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F48 214 0 R /F27 179 0 R /F24 176 0 R /F20 171 0 R >> +406 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F46 195 0 R /F25 166 0 R /F22 165 0 R /F18 163 0 R >> /ProcSet [ /PDF /Text ] >> endobj -450 0 obj << -/Length 9699 +414 0 obj << +/Length 7419 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(26)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(26)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 206.2256 0 cm - q 0 -1 1 0 0 0 cm +ET +1 0 0 1 347.964 715.095 cm +q +0 -1 1 0 0 0 cm 0 g 0 G -1 0 0 1 291.3326 108.9954 cm 0 g 0 G 0 g 0 G -1 0 0 1 -291.3326 -1.3948 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 0 107.8 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 -0.1993 -13.5492 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 0 94.052 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -347.7648 -809.1466 cm +1 0 0 1 -347.964 -715.095 cm BT -/F48 10.9091 Tf 353.9417 813.2114 Td[(what)]TJ +/F46 10.9091 Tf 353.942 813.211 Td [(what)]TJ ET -1 0 0 1 451.3554 809.1467 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 451.555 809.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -451.3554 -809.1467 cm BT -/F42 10.9091 Tf 457.5322 813.2115 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ +/F40 10.9091 Tf 457.532 813.211 Td [(d)22(a)67(t)66(a)-377(type)]TJ ET -1 0 0 1 570.3287 809.1467 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 570.528 809.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -570.3287 -809.1467 cm BT -/F48 10.9091 Tf 576.5056 813.2115 Td[(val)]TJ +/F46 10.9091 Tf 576.506 813.211 Td [(val)]TJ ET -1 0 0 1 647.4808 809.1467 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 647.68 809.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -647.4808 -809.1467 cm BT -/F42 10.9091 Tf 653.6576 813.2115 Td[(def)89(a)22(ul)66(t)]TJ +/F40 10.9091 Tf 653.658 813.211 Td [(def)89(a)22(ul)67(t)]TJ ET -1 0 0 1 733.1369 809.1467 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 733.336 809.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -733.1369 -809.1467 cm BT -/F42 10.9091 Tf 739.3138 813.2115 Td[(com)1(ments)]TJ +/F40 10.9091 Tf 739.314 813.211 Td [(comments)]TJ ET -1 0 0 1 943.5173 809.1467 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 943.717 809.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -595.5533 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 347.964 808.947 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 -0.1992 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 347.964 781.65 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -347.7648 -781.6498 cm BT -/F48 10.9091 Tf 353.9416 799.2638 Td[(mld_aggr_alg_)]TJ +/F46 10.9091 Tf 353.942 799.264 Td [(mld_aggr_alg_)]TJ ET -1 0 0 1 451.3553 781.6498 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 451.555 781.65 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -451.3553 -781.6498 cm BT -/F48 10.9091 Tf 457.5322 799.2638 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 457.532 799.264 Td [(character\050len=*\051)]TJ ET -1 0 0 1 570.3287 781.6498 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 570.528 781.65 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -570.3287 -781.6498 cm BT -/F48 10.9091 Tf 576.5055 799.2638 Td[('DEC')]TJ +/F46 10.9091 Tf 576.506 799.264 Td [('DEC')]TJ ET -1 0 0 1 647.4808 781.6498 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 647.68 781.65 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -647.4808 -781.6498 cm BT -/F48 10.9091 Tf 653.6576 799.2638 Td[('DEC')]TJ +/F46 10.9091 Tf 653.658 799.264 Td [('DEC')]TJ ET -1 0 0 1 733.1369 781.6498 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 733.336 781.65 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -733.1369 -781.6498 cm BT -/F15 10.9091 Tf 739.3138 799.2638 Td[(Aggregation)-520(algor)1(ithm.)-1006(Curr)1(e)-1(n)29(tly)83(,)-567(on)1(ly)]TJ 0 -13.5492 Td[(th)1(e)-334(dec)-1(ou)1(pled)-333(aggregation)-333(i)1(s)-334(a)28(v)55(ai)1(labl)1(e)-1(.)]TJ +/F15 10.9091 Tf 739.314 799.264 Td [(Aggregation)-521(algori)1(thm.)-1007(Curren)28(tly)83(,)-567(only)]TJ 0 -13.549 Td [(the)-333(decoupled)-334(aggregation)-333(is)-333(a)28(v)55(ailable.)]TJ ET -1 0 0 1 943.5173 781.6498 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 943.717 781.65 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -595.5533 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 347.964 781.451 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 -0.1992 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 347.964 754.153 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -347.7648 -754.1529 cm BT -/F48 10.9091 Tf 353.9416 771.7669 Td[(mld_aggr_kind_)]TJ +/F46 10.9091 Tf 353.942 771.767 Td [(mld_aggr_kind_)]TJ ET -1 0 0 1 451.3553 754.1529 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 451.555 754.153 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -451.3553 -754.1529 cm BT -/F48 10.9091 Tf 457.5322 771.7669 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 457.532 771.767 Td [(character\050len=*\051)]TJ ET -1 0 0 1 570.3287 754.1529 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 570.528 754.153 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -570.3287 -754.1529 cm BT -/F48 10.9091 Tf 576.5055 771.7669 Td[('SMOOTH')]TJ 0 -13.5492 Td[('RAW')]TJ +/F46 10.9091 Tf 576.506 771.767 Td [('SMOOTH')]TJ 0 -13.549 Td [('RAW')]TJ ET -1 0 0 1 647.4808 754.1529 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 647.68 754.153 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -647.4808 -754.1529 cm BT -/F48 10.9091 Tf 653.6576 771.7669 Td[('SMOOTH')]TJ +/F46 10.9091 Tf 653.658 771.767 Td [('SMOOTH')]TJ ET -1 0 0 1 733.1369 754.1529 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 733.336 754.153 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -733.1369 -754.1529 cm BT -/F15 10.9091 Tf 739.3138 771.7669 Td[(T)28(yp)-28(e)-230(of)-230(aggr)1(e)-1(gation)1(:)-393(smo)-28(othed)-230(or)-230(r)1(a)28(w)-1(,)-250(i.e.)]TJ 0 -13.5492 Td[(usin)1(g)-334(th)1(e)-334(ten)28(tativ)28(e)-333(prol)1(ongator)1(.)]TJ +/F15 10.9091 Tf 739.314 771.767 Td [(T)28(yp)-28(e)-230(of)-230(aggregation:)-393(smo)-28(othed)-230(or)-230(ra)28(w,)-251(i.e.)]TJ 0 -13.549 Td [(using)-333(the)-334(ten)28(tativ)28(e)-333(prolongator.)]TJ ET -1 0 0 1 943.5173 754.1529 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 943.717 754.153 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -595.5533 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 347.964 753.954 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 -0.1992 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 347.964 726.656 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -347.7648 -726.656 cm BT -/F48 10.9091 Tf 353.9416 744.27 Td[(mld_aggr_thresh_)]TJ +/F46 10.9091 Tf 353.942 744.27 Td [(mld_aggr_thresh_)]TJ ET -1 0 0 1 451.3553 726.656 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 451.555 726.656 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -451.3553 -726.656 cm BT -/F48 10.9091 Tf 457.5322 744.27 Td[(real\050)]TJ/F20 10.9091 Tf 28.6361 0 Td[(kind)]TJ +/F46 10.9091 Tf 457.532 744.27 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ ET -1 0 0 1 506.9099 744.27 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 506.91 744.469 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -506.9099 -744.27 cm BT -/F20 10.9091 Tf 510.2553 744.27 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5679 0 Td[(\051)]TJ +/F18 10.9091 Tf 510.255 744.27 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.568 0 Td [(\051)]TJ ET -1 0 0 1 570.3287 726.656 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 570.528 726.656 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -570.3287 -726.656 cm BT -/F15 10.9091 Tf 576.5055 744.27 Td[(An)28(y)-222(r)1(e)-1(al)-222(n)28(u)1(m)-1(.)]TJ/F27 10.9091 Tf 0 -13.5492 Td[(2)]TJ/F15 10.9091 Tf 10.303 0 Td[([0)]TJ/F24 10.9091 Tf 8.4849 0 Td[(;)]TJ/F15 10.9091 Tf 4.8484 0 Td[(1])]TJ +/F15 10.9091 Tf 576.506 744.27 Td [(An)28(y)-222(real)-223(n)28(um.)]TJ/F25 10.9091 Tf 0 -13.549 Td [(2)]TJ/F15 10.9091 Tf 10.303 0 Td [([0)]TJ/F22 10.9091 Tf 8.484 0 Td [(;)]TJ/F15 10.9091 Tf 4.849 0 Td [(1])]TJ ET -1 0 0 1 647.4808 726.656 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 647.68 726.656 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -647.4808 -726.656 cm BT -/F48 10.9091 Tf 653.6576 744.27 Td[(0.e0)]TJ/F15 10.9091 Tf 26.5452 0 Td[(\050or)]TJ/F48 10.9091 Tf 17.6061 0 Td[(0.d0)]TJ/F15 10.9091 Tf 22.9088 0 Td[(\051)]TJ +/F46 10.9091 Tf 653.658 744.27 Td [(0.e0)]TJ/F15 10.9091 Tf 26.545 0 Td [(\050or)]TJ/F46 10.9091 Tf 17.606 0 Td [(0.d0)]TJ/F15 10.9091 Tf 22.909 0 Td [(\051)]TJ ET -1 0 0 1 733.1369 726.656 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 733.336 726.656 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -733.1369 -726.656 cm BT -/F15 10.9091 Tf 739.3138 744.27 Td[(The)-419(thr)1(e)-1(shold)]TJ/F24 10.9091 Tf 72.2629 0 Td[(\022)]TJ/F15 10.9091 Tf 9.9951 0 Td[(in)-418(the)-419(aggregation)-419(al)1(go-)]TJ -82.258 -13.5492 Td[(ri)1(thm.)]TJ +/F15 10.9091 Tf 739.314 744.27 Td [(The)-419(threshold)]TJ/F22 10.9091 Tf 72.263 0 Td [(\022)]TJ/F15 10.9091 Tf 9.995 0 Td [(in)-419(the)-419(aggregation)-419(algo-)]TJ -82.258 -13.549 Td [(rithm.)]TJ ET -1 0 0 1 943.5173 726.656 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 943.717 726.656 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -595.5533 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 347.964 726.457 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 -0.1992 -54.1967 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 347.964 672.061 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -347.7648 -672.0608 cm BT -/F48 10.9091 Tf 353.9416 716.7732 Td[(mld_aggr_eig_)]TJ +/F46 10.9091 Tf 353.942 716.773 Td [(mld_aggr_eig_)]TJ ET -1 0 0 1 451.3553 672.0608 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 451.555 672.061 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -451.3553 -672.0608 cm BT -/F48 10.9091 Tf 457.5322 716.7732 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 457.532 716.773 Td [(character\050len=*\051)]TJ ET -1 0 0 1 570.3287 672.0608 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 570.528 672.061 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -570.3287 -672.0608 cm BT -/F48 10.9091 Tf 576.5055 716.7732 Td[('A)]TJ +/F46 10.9091 Tf 576.506 716.773 Td [('A)]TJ ET -1 0 0 1 588.6472 716.7732 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4364 0.1992 l -S +1 0 0 1 588.647 716.972 cm +[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q -1 0 0 1 -588.6472 -716.7732 cm BT -/F48 10.9091 Tf 592.0836 716.7732 Td[(NORMI')]TJ +/F46 10.9091 Tf 592.084 716.773 Td [(NORMI')]TJ ET -1 0 0 1 647.4808 672.0608 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 647.68 672.061 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -647.4808 -672.0608 cm BT -/F48 10.9091 Tf 653.6576 716.7732 Td[('A)]TJ +/F46 10.9091 Tf 653.658 716.773 Td [('A)]TJ ET -1 0 0 1 665.7993 716.7732 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4364 0.1992 l -S +1 0 0 1 665.799 716.972 cm +[]0 d 0 J 0.398 w 0 0 m 3.436 0 l S Q -1 0 0 1 -665.7993 -716.7732 cm BT -/F48 10.9091 Tf 669.2357 716.7732 Td[(NORMI')]TJ +/F46 10.9091 Tf 669.236 716.773 Td [(NORMI')]TJ ET -1 0 0 1 733.1369 672.0608 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 733.336 672.061 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -733.1369 -672.0608 cm BT -/F15 10.9091 Tf 739.3138 716.7732 Td[(Estimate)-501(of)-500(th)1(e)-501(m)-1(axi)1(m)27(u)1(m)-501(e)-1(igen)28(v)56(alu)1(e)-501(of)]TJ/F24 10.9091 Tf 0 -13.5492 Td[(D)]TJ/F28 7.9701 Tf 9.3348 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F24 10.9091 Tf 4.7323 -3.9588 Td[(A)]TJ/F15 10.9091 Tf 10.9193 0 Td[(for)-250(the)-251(sm)-1(o)-28(ot)1(hed)-251(aggregation)1(.)-417(Cur)1(-)]TJ -31.5729 -13.5492 Td[(ren)28(tly)84(,)-256(only)-237(th)1(e)-238(in)1(\014n)1(it)28(y)-237(norm)-237(of)-237(the)-238(matr)1(ix)]TJ 0 -13.5492 Td[(is)-334(a)28(v)56(ailab)1(le.)]TJ +/F15 10.9091 Tf 739.314 716.773 Td [(Estimate)-501(of)-500(the)-501(maxim)28(um)-500(e)-1(igen)28(v)56(alue)-501(of)]TJ/F22 10.9091 Tf 0 -13.549 Td [(D)]TJ/F26 7.9701 Tf 9.335 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F22 10.9091 Tf 4.732 -3.959 Td [(A)]TJ/F15 10.9091 Tf 10.92 0 Td [(for)-251(the)-251(smo)-28(othed)-250(aggre)-1(gat)1(ion.)-417(Cur-)]TJ -31.573 -13.549 Td [(ren)28(tly)83(,)-256(only)-238(the)-237(in\014nit)28(y)-237(norm)-238(of)-237(the)-237(matrix)]TJ 0 -13.549 Td [(is)-333(a)27(v)56(ailable.)]TJ ET -1 0 0 1 943.5173 672.0608 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 54.1968 l -S +1 0 0 1 943.717 672.061 cm +[]0 d 0 J 0.398 w 0 0 m 0 54.197 l S Q -1 0 0 1 -595.5533 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 347.964 671.862 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 -0.1992 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 347.964 644.564 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -347.7648 -644.5639 cm BT -/F48 10.9091 Tf 353.9416 662.1779 Td[(mld_aggr_damp_)]TJ +/F46 10.9091 Tf 353.942 662.178 Td [(mld_aggr_damp_)]TJ ET -1 0 0 1 451.3553 644.5639 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 451.555 644.564 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -451.3553 -644.5639 cm BT -/F48 10.9091 Tf 457.5322 662.1779 Td[(real\050)]TJ/F20 10.9091 Tf 28.6361 0 Td[(kind)]TJ +/F46 10.9091 Tf 457.532 662.178 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ ET -1 0 0 1 506.9099 662.1779 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 506.91 662.377 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -506.9099 -662.1779 cm BT -/F20 10.9091 Tf 510.2553 662.1779 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5679 0 Td[(\051)]TJ +/F18 10.9091 Tf 510.255 662.178 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.568 0 Td [(\051)]TJ ET -1 0 0 1 570.3287 644.5639 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 570.528 644.564 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -570.3287 -644.5639 cm BT -/F15 10.9091 Tf 576.5055 662.1779 Td[(An)28(y)-222(r)1(e)-1(al)-222(n)28(u)1(m)-1(.)]TJ/F24 10.9091 Tf 0 -13.5492 Td[(>)]TJ/F15 10.9091 Tf 11.5152 0 Td[(0)]TJ +/F15 10.9091 Tf 576.506 662.178 Td [(An)28(y)-222(real)-223(n)28(um.)]TJ/F22 10.9091 Tf 0 -13.549 Td [(>)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET -1 0 0 1 647.4808 644.5639 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 647.68 644.564 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -647.4808 -644.5639 cm BT -/F48 10.9091 Tf 653.6576 662.1779 Td[(4.e0/3.e0)]TJ/F15 10.9091 Tf 0 -13.5492 Td[(\050or)]TJ/F48 10.9091 Tf 17.6061 0 Td[(4.d0/3.d0)]TJ/F15 10.9091 Tf 51.5449 0 Td[(\051)]TJ +/F46 10.9091 Tf 653.658 662.178 Td [(4.e0/3.e0)]TJ/F15 10.9091 Tf 0 -13.549 Td [(\050or)]TJ/F46 10.9091 Tf 17.606 0 Td [(4.d0/3.d0)]TJ/F15 10.9091 Tf 51.545 0 Td [(\051)]TJ ET -1 0 0 1 733.1369 644.5639 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 733.336 644.564 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -733.1369 -644.5639 cm BT -/F15 10.9091 Tf 739.3138 662.1779 Td[(The)-282(d)1(am)-1(p)1(in)1(g)-282(par)1(am)-1(eter)]TJ/F24 10.9091 Tf 117.7581 0 Td[(!)]TJ/F15 10.9091 Tf 10.2526 0 Td[(in)-281(th)1(e)-282(aggrega-)]TJ -128.0107 -13.5492 Td[(tion)-333(al)1(gorith)1(m)-1(.)]TJ +/F15 10.9091 Tf 739.314 662.178 Td [(The)-281(damping)-282(parameter)]TJ/F22 10.9091 Tf 117.758 0 Td [(!)]TJ/F15 10.9091 Tf 10.252 0 Td [(in)-281(the)-282(aggrega-)]TJ -128.01 -13.549 Td [(tion)-333(algorithm.)]TJ ET -1 0 0 1 943.5173 644.5639 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 943.717 644.564 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -595.5533 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -595.7525 0.1992 l -S +1 0 0 1 347.964 644.365 cm +[]0 d 0 J 0.398 w 0 0 m 595.752 0 l S Q -1 0 0 1 159.9538 -30.4898 cm 0 g 0 G -1 0 0 1 -507.9178 -613.6756 cm BT -/F15 10.9091 Tf 507.9178 613.6756 Td[(T)83(ab)1(le)-334(4:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(aggregation)-333(algor)1(ithm.)]TJ -ET -1 0 0 1 781.5847 613.6756 cm +/F15 10.9091 Tf 507.918 613.676 Td [(T)83(able)-333(4:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(aggr)1(e)-1(gati)1(on)-334(algorithm.)]TJ 0 g 0 G -1 0 0 1 159.9537 101.4196 cm 0 g 0 G -1 0 0 1 -593.5744 0 cm - Q -1 0 0 1 -206.2255 -593.5743 cm +ET +1 0 0 1 347.964 715.095 cm +Q 0 g 0 G -1 0 0 1 0 -29.8879 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -449 0 obj << +413 0 obj << /Type /Page -/Contents 450 0 R -/Resources 448 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 447 0 R +/Contents 414 0 R +/Resources 412 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 411 0 R >> endobj -451 0 obj << -/D [449 0 R /XYZ 141.7385 740.0018 null] +415 0 obj << +/D [413 0 R /XYZ 141.738 740.002 null] >> endobj -452 0 obj << -/D [449 0 R /XYZ 551.2511 627.2248 null] +416 0 obj << +/D [413 0 R /XYZ -3820.604 511.808 null] >> endobj -448 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F48 214 0 R /F20 171 0 R /F27 179 0 R /F24 176 0 R /F28 270 0 R /F22 273 0 R >> +412 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F46 195 0 R /F18 163 0 R /F25 166 0 R /F22 165 0 R /F26 249 0 R /F20 250 0 R >> /ProcSet [ /PDF /Text ] >> endobj -455 0 obj << -/Length 11845 +420 0 obj << +/Length 9105 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(7)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(7)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(27)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(27)]TJ 0 g 0 G -1 0 0 1 -412.4511 -24.9066 cm 0 g 0 G -1 0 0 1 206.2256 0 cm - q 0 -1 1 0 0 0 cm +ET +1 0 0 1 300.143 121.521 cm +q +0 1 -1 0 0 0 cm 0 g 0 G -1 0 0 1 291.3326 169.9668 cm 0 g 0 G 0 g 0 G -1 0 0 1 -291.3326 -1.3948 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 0 168.771 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 -0.1993 -13.5492 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 0 155.023 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -299.9441 -870.118 cm +1 0 0 1 -300.143 -121.521 cm BT -/F48 10.9091 Tf 306.121 874.1828 Td[(what)]TJ +/F46 10.9091 Tf 306.121 280.608 Td [(what)]TJ ET -1 0 0 1 426.4435 870.118 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 426.643 276.544 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -426.4435 -870.118 cm BT -/F42 10.9091 Tf 432.6204 874.1828 Td[(d)22(a)66(t)67(a)-378(t)-1(ype)]TJ +/F40 10.9091 Tf 432.62 280.608 Td [(d)22(a)67(t)66(a)-377(type)]TJ ET -1 0 0 1 545.4169 870.118 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 545.616 276.544 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -545.4169 -870.118 cm BT -/F48 10.9091 Tf 551.5937 874.1828 Td[(val)]TJ +/F46 10.9091 Tf 551.594 280.608 Td [(val)]TJ ET -1 0 0 1 648.0806 870.118 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 648.28 276.544 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -648.0806 -870.118 cm BT -/F42 10.9091 Tf 654.2575 874.1828 Td[(def)89(a)22(ul)66(t)]TJ +/F40 10.9091 Tf 654.257 280.608 Td [(def)89(a)22(ul)67(t)]TJ ET -1 0 0 1 731.3384 870.118 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 731.538 276.544 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -731.3384 -870.118 cm BT -/F42 10.9091 Tf 737.5152 874.1828 Td[(com)1(ments)]TJ +/F40 10.9091 Tf 737.515 280.608 Td [(comments)]TJ ET -1 0 0 1 941.7187 870.118 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 13.5492 l -S +1 0 0 1 941.918 276.544 cm +[]0 d 0 J 0.398 w 0 0 m 0 13.549 l S Q -1 0 0 1 -641.5753 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 300.143 276.344 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 -0.1993 -27.0983 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 249.047 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -842.6212 cm BT -/F48 10.9091 Tf 306.121 860.2351 Td[(mld_coarse_mat_)]TJ +/F46 10.9091 Tf 306.121 266.661 Td [(mld_coarse_mat_)]TJ ET -1 0 0 1 426.4435 842.6212 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 426.643 249.047 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -426.4435 -842.6212 cm BT -/F48 10.9091 Tf 432.6204 860.2352 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 432.62 266.661 Td [(character\050len=*\051)]TJ ET -1 0 0 1 545.4169 842.6212 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 545.616 249.047 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -545.4169 -842.6212 cm BT -/F48 10.9091 Tf 551.5937 860.2352 Td[('DISTR')]TJ 0 -13.5492 Td[('REPL')]TJ +/F46 10.9091 Tf 551.594 266.661 Td [('DISTR')]TJ 0 -13.549 Td [('REPL')]TJ ET -1 0 0 1 648.0806 842.6212 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 648.28 249.047 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -648.0806 -842.6212 cm BT -/F48 10.9091 Tf 654.2575 860.2352 Td[('DISTR')]TJ +/F46 10.9091 Tf 654.257 266.661 Td [('DISTR')]TJ ET -1 0 0 1 731.3384 842.6212 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 731.538 249.047 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -731.3384 -842.6212 cm BT -/F15 10.9091 Tf 737.5152 860.2352 Td[(Coarse)-1(st)-483(matrix)1(:)-743(distrib)1(uted)-482(am)-1(on)1(g)-483(the)]TJ 0 -13.5492 Td[(pr)1(o)-28(ce)-1(ss)-1(or)1(s)-334(or)-333(repli)1(c)-1(ated)-333(on)-333(eac)27(h)-333(of)-333(th)1(e)-1(m.)]TJ +/F15 10.9091 Tf 737.515 266.661 Td [(Coarsest)-483(matrix:)-743(distributed)-483(among)-483(the)]TJ 0 -13.549 Td [(pro)-28(cessors)-333(or)-334(repl)1(ic)-1(ated)-333(on)-333(eac)28(h)-334(of)-333(them.)]TJ ET -1 0 0 1 941.7187 842.6212 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 941.918 249.047 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -641.5753 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 300.143 248.848 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 -0.1993 -108.3936 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 108.3936 l -S +1 0 0 1 300.143 140.255 cm +[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S Q -1 0 0 1 -299.9441 -733.8291 cm BT -/F48 10.9091 Tf 306.121 832.7383 Td[(mld_coarse_solve_)]TJ +/F46 10.9091 Tf 306.121 239.164 Td [(mld_coarse_solve_)]TJ ET -1 0 0 1 426.4435 733.8291 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 108.3936 l -S +1 0 0 1 426.643 140.255 cm +[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S Q -1 0 0 1 -426.4435 -733.8291 cm BT -/F48 10.9091 Tf 432.6204 832.7383 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 432.62 239.164 Td [(character\050len=*\051)]TJ ET -1 0 0 1 545.4169 733.8291 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 108.3936 l -S +1 0 0 1 545.616 140.255 cm +[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S Q -1 0 0 1 -545.4169 -733.8291 cm BT -/F48 10.9091 Tf 551.5937 832.7383 Td[('BJAC')]TJ 0 -13.5492 Td[('UMF')]TJ 0 -13.5492 Td[('SLU')]TJ 0 -13.5492 Td[('SLUDIST')]TJ +/F46 10.9091 Tf 551.594 239.164 Td [('BJAC')]TJ 0 -13.549 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ 0 -13.55 Td [('SLUDIST')]TJ ET -1 0 0 1 648.0806 733.8291 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 108.3936 l -S +1 0 0 1 648.28 140.255 cm +[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S Q -1 0 0 1 -648.0806 -733.8291 cm BT -/F48 10.9091 Tf 654.2575 832.7383 Td[('BJAC')]TJ +/F46 10.9091 Tf 654.257 239.164 Td [('BJAC')]TJ ET -1 0 0 1 731.3384 733.8291 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 108.3936 l -S +1 0 0 1 731.538 140.255 cm +[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S Q -1 0 0 1 -731.3384 -733.8291 cm BT -/F15 10.9091 Tf 737.5152 832.7383 Td[(Sol)1(v)28(e)-1(r)-503(use)-1(d)-503(at)-504(the)-504(c)-1(oar)1(s)-1(es)-1(t)-503(le)-1(v)28(el:)-785(blo)-28(c)28(k)]TJ 0 -13.5492 Td[(Jacobi,)-517(se)-1(q)1(uen)28(tial)-480(LU)-480(from)-480(UMFP)84(A)28(CK,)]TJ 0 -13.5492 Td[(se)-1(qu)1(e)-1(n)29(tial)-369(LU)-368(from)-369(S)1(up)-27(e)-1(r)1(LU,)-369(d)1(is)-1(tr)1(ibu)1(ted)]TJ 0 -13.5492 Td[(LU)-494(f)1(rom)-494(Su)1(p)-28(erLU)]TJ +/F15 10.9091 Tf 737.515 239.164 Td [(Solv)28(er)-504(used)-504(at)-504(the)-504(coarsest)-504(lev)28(el:)-786(blo)-28(c)28(k)]TJ 0 -13.549 Td [(Jacobi,)-517(sequen)28(tial)-481(LU)-480(from)-481(UM)1(FP)83(A)28(CK,)]TJ 0 -13.549 Td [(sequen)28(tial)-369(LU)-369(from)-368(Sup)-28(erLU,)-369(distributed)]TJ 0 -13.55 Td [(LU)-494(from)-494(S)1(up)-28(erLU)]TJ ET -1 0 0 1 828.7004 792.0907 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.2728 0.1992 l -S +1 0 0 1 828.7 198.716 cm +[]0 d 0 J 0.398 w 0 0 m 3.273 0 l S Q -1 0 0 1 -828.7004 -792.0907 cm BT -/F15 10.9091 Tf 831.9731 792.0907 Td[(Dist.)-926(If)-493(the)-494(coars)-1(est)]TJ -94.4579 -13.5492 Td[(matrix)-567(is)-568(distri)1(bu)1(te)-1(d)1(,)-627(on)1(ly)]TJ/F48 10.9091 Tf 140.2946 0 Td[('BJAC')]TJ/F15 10.9091 Tf 40.5548 0 Td[(and)]TJ/F48 10.9091 Tf -180.8494 -13.5492 Td[('SLUDIST')]TJ/F15 10.9091 Tf 57.0061 0 Td[(can)-501(b)-27(e)-501(c)27(hosen;)-584(if)-500(it)-501(is)-501(repl)1(i-)]TJ -57.0061 -13.5492 Td[(cate)-1(d)1(,)-415(only)]TJ/F48 10.9091 Tf 57.817 0 Td[('BJAC')]TJ/F15 10.9091 Tf 38.7121 0 Td[(or)]TJ/F48 10.9091 Tf 14.0769 0 Td[('SLUDIST')]TJ/F15 10.9091 Tf 55.8938 0 Td[(can)-399(b)-27(e)]TJ -166.4998 -13.5492 Td[(se)-1(lec)-1(t)1(e)-1(d)1(.)]TJ +/F15 10.9091 Tf 831.973 198.516 Td [(Dist.)-926(If)-494(the)-494(coarsest)]TJ -94.458 -13.549 Td [(matrix)-568(is)-568(distri)1(buted,)-627(only)]TJ/F46 10.9091 Tf 140.295 0 Td [('BJAC')]TJ/F15 10.9091 Tf 40.555 0 Td [(and)]TJ/F46 10.9091 Tf -180.85 -13.549 Td [('SLUDIST')]TJ/F15 10.9091 Tf 57.006 0 Td [(can)-501(b)-28(e)-500(c)27(hosen;)-584(if)-501(it)-501(is)-500(repli-)]TJ -57.006 -13.549 Td [(cated,)-415(only)]TJ/F46 10.9091 Tf 57.817 0 Td [('BJAC')]TJ/F15 10.9091 Tf 38.712 0 Td [(or)]TJ/F46 10.9091 Tf 14.077 0 Td [('SLUDIST')]TJ/F15 10.9091 Tf 55.894 0 Td [(can)-399(b)-27(e)]TJ -166.5 -13.549 Td [(selected.)]TJ ET -1 0 0 1 941.7187 733.8291 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 108.3936 l -S +1 0 0 1 941.918 140.255 cm +[]0 d 0 J 0.398 w 0 0 m 0 108.394 l S Q -1 0 0 1 -641.5753 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 300.143 140.056 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 -0.1993 -67.746 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 300.143 72.11 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -299.9441 -665.6846 cm BT -/F48 10.9091 Tf 306.121 723.9462 Td[(mld_coarse_subsolve_)]TJ +/F46 10.9091 Tf 306.121 130.372 Td [(mld_coarse_subsolve_)]TJ ET -1 0 0 1 426.4435 665.6847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 426.643 72.11 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -426.4435 -665.6847 cm BT -/F48 10.9091 Tf 432.6204 723.9462 Td[(character\050len=*\051)]TJ +/F46 10.9091 Tf 432.62 130.372 Td [(character\050len=*\051)]TJ ET -1 0 0 1 545.4169 665.6847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 545.616 72.11 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -545.4169 -665.6847 cm BT -/F48 10.9091 Tf 551.5937 723.9462 Td[('ILU')]TJ 0 -13.5492 Td[('MILU')]TJ 0 -13.5492 Td[('ILUT')]TJ 0 -13.5492 Td[('UMF')]TJ 0 -13.5492 Td[('SLU')]TJ +/F46 10.9091 Tf 551.594 130.372 Td [('ILU')]TJ 0 -13.549 Td [('MILU')]TJ 0 -13.549 Td [('ILUT')]TJ 0 -13.55 Td [('UMF')]TJ 0 -13.549 Td [('SLU')]TJ ET -1 0 0 1 648.0806 665.6847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 648.28 72.11 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -648.0806 -665.6847 cm BT -/F48 10.9091 Tf 654.2575 723.9462 Td[('UMF')]TJ +/F46 10.9091 Tf 654.257 130.372 Td [('UMF')]TJ ET -1 0 0 1 731.3384 665.6847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 731.538 72.11 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -731.3384 -665.6847 cm BT -/F15 10.9091 Tf 737.5152 723.9462 Td[(Sol)1(v)28(e)-1(r)-242(f)1(or)-243(th)1(e)-243(di)1(agonal)-242(bl)1(o)-28(c)27(ks)-243(of)-242(th)1(e)-243(coars)-1(e)]TJ 0 -13.5492 Td[(matrix)1(,)-610(i)1(n)-554(c)-1(ase)-555(th)1(e)-555(bl)1(o)-28(c)27(k)-554(Jacobi)-554(solv)28(er)]TJ 0 -13.5492 Td[(is)-360(c)27(hosen)-360(as)-361(coarse)-1(st-le)-1(v)28(el)-360(solv)28(e)-1(r)1(:)-498(ILU\050)]TJ/F24 10.9091 Tf 185.6638 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)]TJ -191.1524 -13.5492 Td[(MILU\050)]TJ/F24 10.9091 Tf 33.1819 0 Td[(p)]TJ/F15 10.9091 Tf 5.4886 0 Td[(\051,)-271(ILU\050)]TJ/F24 10.9091 Tf 33.4162 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051,)-271(LU)-256(fr)1(om)-257(UM)1(FP)84(A)27(CK,)]TJ -86.3632 -13.5492 Td[(LU)-333(from)-333(Su)1(p)-28(erLU,)-333(p)1(lus)-334(t)1(rian)1(gular)-333(solv)28(e.)]TJ +/F15 10.9091 Tf 737.515 130.372 Td [(Solv)28(er)-243(for)-242(the)-242(diagonal)-243(blo)-28(c)28(ks)-242(of)-243(the)-242(coarse)]TJ 0 -13.549 Td [(matrix,)-609(in)-555(case)-554(the)-554(blo)-28(c)28(k)-554(Jacobi)-555(solv)28(er)]TJ 0 -13.549 Td [(is)-360(c)28(hosen)-361(as)-360(coarsest-lev)28(el)-360(solv)27(er:)-498(ILU\050)]TJ/F22 10.9091 Tf 185.664 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)]TJ -191.153 -13.55 Td [(MILU\050)]TJ/F22 10.9091 Tf 33.182 0 Td [(p)]TJ/F15 10.9091 Tf 5.489 0 Td [(\051,)-271(ILU\050)]TJ/F22 10.9091 Tf 33.416 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.276 0 Td [(\051,)-271(LU)-256(from)-256(UMFP)83(A)28(CK,)]TJ -86.363 -13.549 Td [(LU)-333(from)-334(Sup)-27(erLU,)-334(plus)-333(triangular)-333(solv)28(e.)]TJ ET -1 0 0 1 941.7187 665.6847 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 67.746 l -S +1 0 0 1 941.918 72.11 cm +[]0 d 0 J 0.398 w 0 0 m 0 67.746 l S Q -1 0 0 1 -641.5753 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 300.143 71.911 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 -0.1993 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 44.613 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -638.1878 cm BT -/F48 10.9091 Tf 306.121 655.8018 Td[(mld_coarse_sweeps_)]TJ +/F46 10.9091 Tf 306.121 62.227 Td [(mld_coarse_sweeps_)]TJ ET -1 0 0 1 426.4435 638.1878 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 426.643 44.613 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -426.4435 -638.1878 cm BT -/F48 10.9091 Tf 432.6204 655.8018 Td[(integer)]TJ +/F46 10.9091 Tf 432.62 62.227 Td [(integer)]TJ ET -1 0 0 1 545.4169 638.1878 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 545.616 44.613 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -545.4169 -638.1878 cm BT -/F15 10.9091 Tf 551.5937 655.8018 Td[(An)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F24 10.9091 Tf 70.6061 0 Td[(>)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ +/F15 10.9091 Tf 551.594 62.227 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F22 10.9091 Tf 70.606 0 Td [(>)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET -1 0 0 1 648.0806 638.1878 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 648.28 44.613 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -648.0806 -638.1878 cm BT -/F48 10.9091 Tf 654.2575 655.8018 Td[(4)]TJ +/F46 10.9091 Tf 654.257 62.227 Td [(4)]TJ ET -1 0 0 1 731.3384 638.1878 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 731.538 44.613 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -731.3384 -638.1878 cm BT -/F15 10.9091 Tf 737.5152 655.8018 Td[(Num)28(b)-27(e)-1(r)-766(of)-765(Blo)-28(c)27(k)1(-)-1(Jacobi)-765(s)-1(w)28(e)-1(eps)-766(when)]TJ 0 -13.5492 Td[('BJA)28(C')-334(i)1(s)-334(use)-1(d)-332(as)-334(c)-1(oar)1(s)-1(es)-1(t-lev)28(e)-1(l)-333(solv)28(er.)]TJ +/F15 10.9091 Tf 737.515 62.227 Td [(Num)28(b)-28(er)-766(of)-766(Blo)-28(c)28(k-Jacobi)-766(sw)28(eeps)-766(when)]TJ 0 -13.549 Td [('BJA)28(C')-334(is)-333(used)-333(as)-334(coarsest-lev)28(el)-333(solv)27(er.)]TJ ET -1 0 0 1 941.7187 638.1878 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 941.918 44.613 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -641.7746 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 17.515 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -611.0894 cm BT -/F48 10.9091 Tf 306.121 628.7034 Td[(mld_coarse_fillin_)]TJ +/F46 10.9091 Tf 306.121 35.129 Td [(mld_coarse_fillin_)]TJ ET -1 0 0 1 426.4435 611.0894 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 426.643 17.515 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -426.4435 -611.0894 cm BT -/F48 10.9091 Tf 432.6203 628.7034 Td[(integer)]TJ +/F46 10.9091 Tf 432.62 35.129 Td [(integer)]TJ ET -1 0 0 1 545.4169 611.0894 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 545.616 17.515 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -545.4169 -611.0894 cm BT -/F15 10.9091 Tf 551.5937 628.7034 Td[(An)28(y)-333(in)29(t.)-333(n)28(um.)]TJ/F27 10.9091 Tf 70.6061 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ +/F15 10.9091 Tf 551.594 35.129 Td [(An)28(y)-333(in)27(t.)-333(n)28(um.)]TJ/F25 10.9091 Tf 70.606 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET -1 0 0 1 648.0806 611.0894 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 648.28 17.515 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -648.0806 -611.0894 cm BT -/F48 10.9091 Tf 654.2575 628.7034 Td[(0)]TJ +/F46 10.9091 Tf 654.257 35.129 Td [(0)]TJ ET -1 0 0 1 731.3384 611.0894 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 731.538 17.515 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -731.3384 -611.0894 cm BT -/F15 10.9091 Tf 737.5152 628.7034 Td[(Fil)1(l-in)-276(lev)28(e)-1(l)]TJ/F24 10.9091 Tf 56.1768 0 Td[(p)]TJ/F15 10.9091 Tf 8.5013 0 Td[(of)-276(th)1(e)-277(in)1(c)-1(omp)1(le)-1(te)-276(LU)-276(factor-)]TJ -64.6781 -13.5492 Td[(ization)1(s)-1(.)]TJ +/F15 10.9091 Tf 737.515 35.129 Td [(Fill-in)-276(lev)28(el)]TJ/F22 10.9091 Tf 56.177 0 Td [(p)]TJ/F15 10.9091 Tf 8.501 0 Td [(of)-276(the)-276(incomplete)-276(LU)-277(factor-)]TJ -64.678 -13.549 Td [(izations.)]TJ ET -1 0 0 1 941.7187 611.0894 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 941.918 17.515 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -641.5753 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 300.143 17.316 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 -0.1993 -27.0984 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 300.143 -9.982 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -299.9441 -583.5925 cm BT -/F48 10.9091 Tf 306.121 601.2065 Td[(mld_coarse_iluthrs_)]TJ +/F46 10.9091 Tf 306.121 7.632 Td [(mld_coarse_iluthrs_)]TJ ET -1 0 0 1 426.4435 583.5925 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 426.643 -9.982 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -426.4435 -583.5925 cm BT -/F48 10.9091 Tf 432.6204 601.2065 Td[(real\050)]TJ/F20 10.9091 Tf 28.636 0 Td[(kind)]TJ +/F46 10.9091 Tf 432.62 7.632 Td [(real\050)]TJ/F18 10.9091 Tf 28.636 0 Td [(kind)]TJ ET -1 0 0 1 481.998 601.2065 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 481.998 7.831 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -481.998 -601.2065 cm BT -/F20 10.9091 Tf 485.3435 601.2065 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5678 0 Td[(\051)]TJ +/F18 10.9091 Tf 485.343 7.632 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.568 0 Td [(\051)]TJ ET -1 0 0 1 545.4169 583.5925 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 545.616 -9.982 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -545.4169 -583.5925 cm BT -/F15 10.9091 Tf 551.5937 601.2065 Td[(An)28(y)-289(r)1(e)-1(al.)-289(n)29(um.)]TJ/F27 10.9091 Tf 73.7389 0 Td[(\025)]TJ/F15 10.9091 Tf 11.5151 0 Td[(0)]TJ +/F15 10.9091 Tf 551.594 7.632 Td [(An)28(y)-289(real.)-290(n)28(um.)]TJ/F25 10.9091 Tf 73.739 0 Td [(\025)]TJ/F15 10.9091 Tf 11.515 0 Td [(0)]TJ ET -1 0 0 1 648.0806 583.5925 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 648.28 -9.982 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -648.0806 -583.5925 cm BT -/F48 10.9091 Tf 654.2575 601.2065 Td[(0.d0)]TJ/F15 10.9091 Tf 26.5452 0 Td[(\050or)]TJ/F48 10.9091 Tf 17.6061 0 Td[(0.e0)]TJ/F15 10.9091 Tf 22.9088 0 Td[(\051)]TJ +/F46 10.9091 Tf 654.257 7.632 Td [(0.d0)]TJ/F15 10.9091 Tf 26.546 0 Td [(\050or)]TJ/F46 10.9091 Tf 17.606 0 Td [(0.e0)]TJ/F15 10.9091 Tf 22.909 0 Td [(\051)]TJ ET -1 0 0 1 731.3384 583.5925 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 731.538 -9.982 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -731.3384 -583.5925 cm BT -/F15 10.9091 Tf 737.5152 601.2065 Td[(Drop)-256(t)1(ole)-1(r)1(ance)]TJ/F24 10.9091 Tf 72.7768 0 Td[(t)]TJ/F15 10.9091 Tf 6.7369 0 Td[(in)-256(th)1(e)-257(ILU\050)]TJ/F24 10.9091 Tf 53.0193 0 Td[(p;)-167(t)]TJ/F15 10.9091 Tf 14.2765 0 Td[(\051)-256(factoriza-)]TJ -146.8095 -13.5492 Td[(tion)1(.)]TJ +/F15 10.9091 Tf 737.515 7.632 Td [(Drop)-256(tolerance)]TJ/F22 10.9091 Tf 72.777 0 Td [(t)]TJ/F15 10.9091 Tf 6.737 0 Td [(in)-256(the)-257(ILU\050)]TJ/F22 10.9091 Tf 53.019 0 Td [(p;)-167(t)]TJ/F15 10.9091 Tf 14.277 0 Td [(\051)-256(factoriza-)]TJ -146.81 -13.549 Td [(tion.)]TJ ET -1 0 0 1 941.7187 583.5925 cm q -[]0 d -0 J -0.3985 w -0.1992 0 m -0.1992 27.0984 l -S +1 0 0 1 941.918 -9.982 cm +[]0 d 0 J 0.398 w 0 0 m 0 27.098 l S Q -1 0 0 1 -641.5753 -0.3985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -641.7746 0.1992 l -S +1 0 0 1 300.143 -10.181 cm +[]0 d 0 J 0.398 w 0 0 m 641.775 0 l S Q -1 0 0 1 111.0143 -30.4898 cm 0 g 0 G -1 0 0 1 -411.1577 -552.7042 cm BT -/F15 10.9091 Tf 411.1577 552.7042 Td[(T)83(ab)1(le)-334(5:)-444(P)28(aramete)-1(r)1(s)-334(de\014n)1(ing)-333(th)1(e)-334(c)-1(oar)1(s)-1(e-)-1(space)-334(correction)-333(at)-333(the)-333(c)-1(oarses)-1(t)-333(lev)28(e)-1(l.)]TJ -ET -1 0 0 1 782.7034 552.7042 cm +/F15 10.9091 Tf 411.158 -40.87 Td [(T)83(able)-333(5:)-444(P)27(arameters)-333(de\014ning)-333(the)-334(coarse-space)-333(correction)-333(at)-334(the)-333(coarsest)-334(l)1(e)-1(v)28(el.)]TJ 0 g 0 G -1 0 0 1 111.0143 162.391 cm 0 g 0 G -1 0 0 1 -593.5744 0 cm - Q -1 0 0 1 -206.2255 -593.5743 cm +ET +1 0 0 1 300.143 121.521 cm +Q 0 g 0 G -1 0 0 1 0 -29.8879 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G endstream endobj -454 0 obj << +419 0 obj << /Type /Page -/Contents 455 0 R -/Resources 453 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 447 0 R -/Annots [ 457 0 R ] +/Contents 420 0 R +/Resources 418 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 411 0 R +/Annots [ 417 0 R ] >> endobj -457 0 obj << +417 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -456 0 obj << -/D [454 0 R /XYZ 93.9178 740.0018 null] +421 0 obj << +/D [419 0 R /XYZ 93.918 740.002 null] >> endobj -365 0 obj << -/D [454 0 R /XYZ 454.491 566.2534 null] +332 0 obj << +/D [419 0 R /XYZ 448.762 4356.566 null] >> endobj -453 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F48 214 0 R /F24 176 0 R /F27 179 0 R /F20 171 0 R >> +418 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F46 195 0 R /F22 165 0 R /F25 166 0 R /F18 163 0 R >> /ProcSet [ /PDF /Text ] >> endobj -460 0 obj << -/Length 4476 +427 0 obj << +/Length 3178 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(28)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(28)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F19 11.9552 Tf 141.7385 704.1363 Td[(7.)-1(3)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ +/F17 11.9552 Tf -203.265 -35.866 Td [(7.3)-1125(Subroutine)-375(mld)]TJ ET -1 0 0 1 264.7607 704.1363 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -4.0349 0.1992 l -S +1 0 0 1 264.761 704.336 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -1 0 0 1 -264.7607 -704.1363 cm BT -/F19 11.9552 Tf 268.7956 704.1363 Td[(pre)-1(cbld)]TJ -ET -1 0 0 1 262.3285 683.5417 cm +/F17 11.9552 Tf 268.796 704.136 Td [(precbld)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -262.3285 -683.5417 cm -BT -/F48 10.9091 Tf 267.7831 683.5417 Td[(mld_precbld\050a,desc_a,p,info\051)]TJ/F15 10.9091 Tf -126.0446 -25.5044 Td[(This)-318(routi)1(ne)-319(b)1(uild)1(s)-319(th)1(e)-319(prec)-1(on)1(di)1(tioner)-318(ac)-1(cord)1(ing)-318(to)-319(t)1(he)-319(requ)1(irem)-1(en)28(ts)-319(made)-318(b)28(y)-319(t)1(he)-319(u)1(s)-1(er)]TJ 0 -13.5492 Td[(th)1(rough)-333(t)1(he)-334(r)1(outin)1(e)-1(s)]TJ/F48 10.9091 Tf 101.9395 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 72.3629 0 Td[(and)]TJ/F48 10.9091 Tf 21.2121 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)]TJ/F41 10.9091 Tf -258.5138 -28.8143 Td[(Argumen)32(ts)]TJ/F48 10.9091 Tf 5.9776 -19.6473 Td[(a)-3689(type\050psb_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.7258 0 Td[(.)]TJ -189.6449 -13.5492 Td[(The)-448(s)-1(p)1(arse)-448(m)-1(atr)1(ix)-448(stru)1(c)-1(tu)1(re)-448(c)-1(on)29(taini)1(ng)-448(th)1(e)-449(l)1(o)-28(c)-1(al)-447(par)1(t)-448(of)-448(t)1(he)]TJ 0 -13.5492 Td[(matrix)-371(to)-372(b)-27(e)-372(pr)1(e)-1(cond)1(ition)1(e)-1(d)1(.)-560(Note)-372(th)1(at)]TJ/F20 10.9091 Tf 195.2263 0 Td[(x)]TJ/F15 10.9091 Tf 10.429 0 Td[(m)27(u)1(s)-1(t)-371(b)-27(e)-373(c)28(hose)-1(n)-371(ac-)]TJ -205.6553 -13.5492 Td[(cordi)1(ng)-322(to)-322(th)1(e)-323(r)1(e)-1(al)1(/c)-1(omplex,)-324(singl)1(e)-1(/d)1(oub)1(le)-323(p)1(rec)-1(i)1(s)-1(ion)-321(v)28(e)-1(r)1(s)-1(i)1(on)-322(of)]TJ 0 -13.5492 Td[(MLD2P)1(4)-333(un)1(der)-333(u)1(s)-1(e.)-444(See)-333(the)-333(PS)1(B)-1(LAS)-332(Use)-1(r')1(s)-334(G)1(uid)1(e)-334(f)1(or)-333(d)1(e)-1(t)1(ails)]TJ 0 -13.5492 Td[([)]TJ -ET -1 0 0 1 196.7172 528.2806 cm +/F46 10.9091 Tf -1.013 -20.594 Td [(mld_precbld\050a,desc_a,p,info\051)]TJ/F15 10.9091 Tf -126.045 -25.505 Td [(This)-319(rou)1(tine)-319(builds)-318(the)-319(preconditioner)-318(according)-319(to)-318(the)-318(re)-1(q)1(uireme)-1(n)28(ts)-318(made)-319(b)28(y)-318(the)-319(user)]TJ 0 -13.549 Td [(through)-333(the)-334(r)1(outines)]TJ/F46 10.9091 Tf 101.94 0 Td [(mld_precinit)]TJ/F15 10.9091 Tf 72.363 0 Td [(and)]TJ/F46 10.9091 Tf 21.212 0 Td [(mld_precset)]TJ/F15 10.9091 Tf 62.999 0 Td [(.)]TJ/F39 10.9091 Tf -258.514 -28.814 Td [(Argumen)32(ts)]TJ/F46 10.9091 Tf 5.978 -19.647 Td [(a)-3689(type\050psb_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(spmat_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 131.726 0 Td [(.)]TJ -189.645 -13.55 Td [(The)-448(sparse)-448(matrix)-448(structur)1(e)-448(con)27(tainin)1(g)-448(the)-448(lo)-28(cal)-448(part)-448(of)-447(the)]TJ 0 -13.549 Td [(matrix)-372(to)-371(b)-28(e)-372(preconditioned.)-559(Note)-372(that)]TJ/F18 10.9091 Tf 195.226 0 Td [(x)]TJ/F15 10.9091 Tf 10.429 0 Td [(m)28(ust)-372(b)-28(e)-371(c)27(hosen)-371(ac-)]TJ -205.655 -13.549 Td [(cording)-322(to)-322(the)-322(real/complex,)-324(single/double)-322(precision)-322(v)28(ersion)-322(of)]TJ 0 -13.549 Td [(MLD2P4)-333(under)-332(use)-1(.)-444(See)-333(the)-333(P)1(SBLAS)-333(User's)-333(Guide)-333(for)-333(details)]TJ 0 -13.549 Td [([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -196.7172 -528.2806 cm -BT -/F15 10.9091 Tf 196.7172 528.2806 Td[(11)]TJ -ET -1 0 0 1 207.6263 528.2806 cm + [(11)]TJ 0 g 0 G -1 0 0 1 -207.6263 -528.2806 cm -BT -/F15 10.9091 Tf 207.6263 528.2806 Td[(].)]TJ/F48 10.9091 Tf -59.9102 -13.5492 Td[(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.5143 0 Td[(.)]TJ -177.5435 -13.5492 Td[(The)-417(comm)27(un)1(ication)-416(d)1(e)-1(sc)-1(r)1(iptor)-416(of)]TJ/F48 10.9091 Tf 165.5646 0 Td[(a)]TJ/F15 10.9091 Tf 5.7272 0 Td[(.)-693(See)-417(the)-417(P)1(SBLAS)-416(Use)-1(r)1('s)]TJ -171.2918 -13.5492 Td[(Gu)1(ide)-333(for)-333(detail)1(s)-334([)]TJ -ET -1 0 0 1 280.2173 487.633 cm + [(].)]TJ/F46 10.9091 Tf -45.971 -13.55 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.514 0 Td [(.)]TJ -177.543 -13.549 Td [(The)-416(comm)27(unication)-416(descriptor)-416(of)]TJ/F46 10.9091 Tf 165.565 0 Td [(a)]TJ/F15 10.9091 Tf 5.727 0 Td [(.)-694(See)-416(the)-416(PSBLAS)-417(User's)]TJ -171.292 -13.549 Td [(Guide)-333(for)-334(d)1(e)-1(tail)1(s)-334([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -280.2173 -487.633 cm -BT -/F15 10.9091 Tf 280.2173 487.633 Td[(11)]TJ -ET -1 0 0 1 291.1264 487.633 cm + [(11)]TJ 0 g 0 G -1 0 0 1 -291.1264 -487.633 cm -BT -/F15 10.9091 Tf 291.1264 487.633 Td[(].)]TJ/F48 10.9091 Tf -143.4103 -13.5492 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-267(prec)-1(on)1(di)1(tioner)-267(dat)1(a)-268(stru)1(c)-1(tu)1(re.)-422(Note)-268(th)1(at)]TJ/F20 10.9091 Tf 216.6391 0 Td[(x)]TJ/F15 10.9091 Tf 9.2894 0 Td[(m)27(u)1(s)-1(t)-267(b)-27(e)-268(c)28(hose)-1(n)]TJ -225.9285 -13.5492 Td[(acc)-1(ord)1(in)1(g)-352(to)-352(the)-352(real/c)-1(ompl)1(e)-1(x,)-356(single/dou)1(bl)1(e)-353(p)1(re)-1(cision)-352(v)28(ersion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5491 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-307(c)-1(o)-28(d)1(e)-1(.)-435(If)-308(n)1(o)-308(e)-1(r)1(ror,)-313(0)-307(is)-308(re)-1(t)1(urn)1(e)-1(d)1(.)-436(See)-308(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 432.0924 406.3379 cm + [(].)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-267(preconditioner)-267(data)-267(s)-1(tr)1(ucture.)-423(Note)-267(that)]TJ/F18 10.9091 Tf 216.639 0 Td [(x)]TJ/F15 10.9091 Tf 9.289 0 Td [(m)28(ust)-268(b)-27(e)-268(c)28(hosen)]TJ -225.928 -13.549 Td [(according)-352(to)-352(the)-352(real/complex,)-357(single/double)-352(precision)-352(v)28(ersion)]TJ 0 -13.55 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-308(co)-28(d)1(e)-1(.)-435(If)-308(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -432.0924 -406.3379 cm -BT -/F15 10.9091 Tf 432.0924 406.3379 Td[(8)]TJ -ET -1 0 0 1 437.547 406.3379 cm + [-307(8)]TJ 0 g 0 G -1 0 0 1 -437.547 -406.3379 cm -BT -/F15 10.9091 Tf 440.9055 406.3379 Td[(for)-307(details.)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [-308(for)-308(details.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -459 0 obj << +426 0 obj << /Type /Page -/Contents 460 0 R -/Resources 458 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 447 0 R -/Annots [ 463 0 R 464 0 R 465 0 R ] +/Contents 427 0 R +/Resources 425 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 411 0 R +/Annots [ 422 0 R 423 0 R 424 0 R ] >> endobj -463 0 obj << +422 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [195.7209 527.2843 208.6226 536.3071] +/Rect [195.721 527.284 208.623 536.307] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -464 0 obj << +423 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[0 1 0] -/Rect [279.221 486.6368 292.1227 495.6596] +/Rect [279.221 486.637 292.123 495.66] /Subtype /Link /A << /S /GoTo /D (cite.PSBLASGUIDE) >> >> endobj -465 0 obj << +424 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [431.0961 401.2768 438.5432 414.9099] +/Rect [431.096 401.277 438.543 414.91] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -461 0 obj << -/D [459 0 R /XYZ 141.7385 740.0018 null] +428 0 obj << +/D [426 0 R /XYZ 141.738 740.002 null] >> endobj 74 0 obj << -/D [459 0 R /XYZ 141.7385 715.0952 null] +/D [426 0 R /XYZ 141.738 715.095 null] >> endobj -462 0 obj << -/D [459 0 R /XYZ 141.7385 606.5072 null] +429 0 obj << +/D [426 0 R /XYZ 141.738 606.507 null] >> endobj -458 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F19 105 0 R /F48 214 0 R /F41 126 0 R /F20 171 0 R >> +425 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F17 103 0 R /F46 195 0 R /F39 116 0 R /F18 163 0 R >> /ProcSet [ /PDF /Text ] >> endobj -468 0 obj << -/Length 11281 +435 0 obj << +/Length 9437 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(7)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(7)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Use)1(r)-378(Interf)89(a)22(ce)]TJ/F15 10.9091 Tf 391.3906 0 Td[(29)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(User)-377(Interf)88(a)23(ce)]TJ/F15 10.9091 Tf 401.542 0 Td [(29)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 11.9552 Tf 93.9178 704.1363 Td[(7.)-1(4)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ +/F17 11.9552 Tf -401.542 -35.866 Td [(7.4)-1125(Subroutine)-375(mld)]TJ ET -1 0 0 1 216.9401 704.1363 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -4.0349 0.1992 l -S +1 0 0 1 216.94 704.336 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -1 0 0 1 -216.9401 -704.1363 cm BT -/F19 11.9552 Tf 220.975 704.1363 Td[(pre)-1(caply)]TJ -ET -1 0 0 1 205.9171 683.5417 cm +/F17 11.9552 Tf 220.975 704.136 Td [(precaply)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -205.9171 -683.5417 cm -BT -/F48 10.9091 Tf 211.3716 683.5417 Td[(mld_precaply\050p,x,y,desc_a,info\051)]TJ -31.4997 -13.5492 Td[(mld_precaply\050p,x,y,desc_a,info,trans,work\051)]TJ/F15 10.9091 Tf -85.9541 -22.6105 Td[(This)-382(r)1(outin)1(e)-382(c)-1(ompu)1(te)-1(s)]TJ/F24 10.9091 Tf 112.644 0 Td[(y)]TJ/F15 10.9091 Tf 9.6497 0 Td[(=)]TJ/F24 10.9091 Tf 12.3947 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)]TJ/F24 10.9091 Tf 6.0606 0 Td[(x)]TJ/F15 10.9091 Tf 6.2348 0 Td[(,)-394(wh)1(e)-1(r)1(e)]TJ/F24 10.9091 Tf 39.3996 0 Td[(M)]TJ/F15 10.9091 Tf 15.9368 0 Td[(is)-382(a)-382(p)1(reviou)1(s)-1(ly)-381(bu)1(ilt)-381(prec)-1(on)1(di)1(tioner,)]TJ -240.4307 -13.5492 Td[(stored)-424(i)1(n)28(to)]TJ/F48 10.9091 Tf 56.9069 0 Td[(p)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)-446(an)1(d)]TJ/F24 10.9091 Tf 30.0922 0 Td[(op)]TJ/F15 10.9091 Tf 15.3966 0 Td[(denot)1(e)-1(s)-424(th)1(e)-424(pr)1(e)-1(cond)1(ition)1(e)-1(r)-423(itse)-1(l)1(f)-424(or)-423(i)1(ts)-424(tran)1(s)-1(p)-27(os)-1(e,)-446(acc)-1(or)1(din)1(g)-424(to)]TJ -108.1229 -13.5492 Td[(th)1(e)-497(v)56(alue)-496(of)]TJ/F48 10.9091 Tf 64.7192 0 Td[(trans)]TJ/F15 10.9091 Tf 28.6361 0 Td[(.)-932(Note)-497(th)1(at,)-537(wh)1(e)-1(n)-495(MLD2P4)-496(i)1(s)-497(u)1(s)-1(ed)-496(with)-495(a)-496(Kryl)1(o)27(v)-496(solv)28(er)-496(f)1(rom)]TJ -93.3553 -13.5492 Td[(PS)1(BLAS,)]TJ/F48 10.9091 Tf 49.3635 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 72.7869 0 Td[(is)-372(c)-1(all)1(e)-1(d)-372(with)1(in)-372(th)1(e)-373(P)1(SBLAS)-372(rou)1(tin)1(e)]TJ/F48 10.9091 Tf 180.6653 0 Td[(mld_krylov)]TJ/F15 10.9091 Tf 61.3325 0 Td[(and)-371(hence)]TJ -364.1482 -13.5492 Td[(it)-333(is)-334(completely)-333(tran)1(s)-1(p)1(are)-1(n)29(t)-334(t)1(o)-334(th)1(e)-334(user.)]TJ/F41 10.9091 Tf 0 -28.3595 Td[(Argumen)32(ts)]TJ/F48 10.9091 Tf 5.9776 -19.6473 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-314(pr)1(e)-1(cond)1(ition)1(e)-1(r)-313(data)-313(s)-1(tr)1(uctur)1(e)-1(,)-317(c)-1(on)28(t)1(ainin)1(g)-314(th)1(e)-315(l)1(o)-28(c)-1(al)-313(par)1(t)-314(of)]TJ/F24 10.9091 Tf 0 -13.5492 Td[(M)]TJ/F15 10.9091 Tf 11.7727 0 Td[(.)-427(Note)-282(that)]TJ/F20 10.9091 Tf 56.5697 0 Td[(x)]TJ/F15 10.9091 Tf 9.4495 0 Td[(m)27(u)1(s)-1(t)-281(b)-28(e)-282(c)27(h)1(os)-1(en)-282(accordi)1(ng)-282(to)-282(th)1(e)-283(r)1(e)-1(al)1(/c)-1(omplex,)]TJ -77.7919 -13.5492 Td[(single/dou)1(bl)1(e)-334(pr)1(e)-1(cis)-1(i)1(on)-333(v)28(e)-1(r)1(s)-1(ion)-332(of)-333(MLD2P)1(4)-334(u)1(nd)1(e)-1(r)-333(u)1(s)-1(e.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(x)]TJ/F20 10.9091 Tf 45.9708 0 Td[(typ)51(e)]TJ/F48 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ +/F46 10.9091 Tf -9.603 -20.594 Td [(mld_precaply\050p,x,y,desc_a,info\051)]TJ -31.5 -13.549 Td [(mld_precaply\050p,x,y,desc_a,info,trans,work\051)]TJ/F15 10.9091 Tf -85.954 -22.611 Td [(This)-382(routine)-381(computes)]TJ/F22 10.9091 Tf 112.644 0 Td [(y)]TJ/F15 10.9091 Tf 9.65 0 Td [(=)]TJ/F22 10.9091 Tf 12.394 0 Td [(op)]TJ/F15 10.9091 Tf 10.777 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(\051)]TJ/F22 10.9091 Tf 6.06 0 Td [(x)]TJ/F15 10.9091 Tf 6.235 0 Td [(,)-394(where)]TJ/F22 10.9091 Tf 39.4 0 Td [(M)]TJ/F15 10.9091 Tf 15.937 0 Td [(is)-382(a)-381(previously)-382(built)-382(precondi)1(tioner,)]TJ -240.431 -13.549 Td [(stored)-423(in)27(to)]TJ/F46 10.9091 Tf 56.907 0 Td [(p)]TJ/F15 10.9091 Tf 5.727 0 Td [(,)-446(and)]TJ/F22 10.9091 Tf 30.092 0 Td [(op)]TJ/F15 10.9091 Tf 15.397 0 Td [(denotes)-424(th)1(e)-424(preconditioner)-423(itself)-424(or)-423(its)-424(transp)-28(ose,)-446(according)-423(to)]TJ -108.123 -13.549 Td [(the)-496(v)56(alue)-496(of)]TJ/F46 10.9091 Tf 64.719 0 Td [(trans)]TJ/F15 10.9091 Tf 28.636 0 Td [(.)-933(Note)-496(that,)-536(when)-496(MLD2P4)-496(is)-496(used)-496(with)-496(a)-496(Krylo)27(v)-496(solv)28(er)-496(from)]TJ -93.355 -13.55 Td [(PSBLAS,)]TJ/F46 10.9091 Tf 49.363 0 Td [(mld_precaply)]TJ/F15 10.9091 Tf 72.787 0 Td [(is)-372(called)-372(within)-373(th)1(e)-373(PSBLAS)-372(routine)]TJ/F46 10.9091 Tf 180.666 0 Td [(mld_krylov)]TJ/F15 10.9091 Tf 61.332 0 Td [(and)-372(hence)]TJ -364.148 -13.549 Td [(it)-333(is)-334(completely)-333(transparen)28(t)-333(to)-334(the)-333(user.)]TJ/F39 10.9091 Tf 0 -28.359 Td [(Argumen)32(ts)]TJ/F46 10.9091 Tf 5.977 -19.648 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.181 0 Td [(.)]TJ -201.1 -13.549 Td [(The)-314(preconditioner)-313(data)-314(structure,)-318(con)28(taining)-314(the)-313(lo)-28(cal)-314(part)-314(of)]TJ/F22 10.9091 Tf 0 -13.549 Td [(M)]TJ/F15 10.9091 Tf 11.773 0 Td [(.)-427(Note)-282(that)]TJ/F18 10.9091 Tf 56.57 0 Td [(x)]TJ/F15 10.9091 Tf 9.449 0 Td [(m)28(ust)-282(b)-28(e)-282(c)28(hosen)-282(according)-282(to)-282(the)-282(real/complex,)]TJ -77.792 -13.549 Td [(single/double)-333(precision)-334(v)28(ersion)-333(of)-333(MLD2P4)-334(und)1(e)-1(r)-333(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(x)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F46 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.728 0 Td [(kind)]TJ ET -1 0 0 1 192.1122 490.9817 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 192.112 491.181 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -192.1122 -490.9817 cm BT -/F20 10.9091 Tf 195.4576 490.9817 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5679 0 Td[(\051,)-525(dimension\050:\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.6347 0 Td[(.)]TJ -252.794 -13.5492 Td[(The)-767(lo)-27(c)-1(al)-766(par)1(t)-767(of)-766(th)1(e)-767(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 164.1766 0 Td[(x)]TJ/F15 10.9091 Tf 6.2349 0 Td[(.)-1744(Note)-767(th)1(at)]TJ/F20 10.9091 Tf 81.5107 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 28.1399 0 Td[(and)]TJ/F20 10.9091 Tf -280.0621 -13.5492 Td[(kind)]TJ +/F18 10.9091 Tf 195.458 490.982 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.567 0 Td [(\051,)-525(dimension\050:\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 154.635 0 Td [(.)]TJ -252.794 -13.549 Td [(The)-767(lo)-27(cal)-767(part)-766(of)-767(the)-767(v)28(ector)]TJ/F22 10.9091 Tf 164.177 0 Td [(x)]TJ/F15 10.9091 Tf 6.235 0 Td [(.)-1744(Note)-767(that)]TJ/F18 10.9091 Tf 81.51 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 28.14 0 Td [(and)]TJ/F18 10.9091 Tf -280.062 -13.55 Td [(kind)]TJ ET -1 0 0 1 166.6079 463.8833 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 166.608 464.083 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -166.6079 -463.8833 cm BT -/F20 10.9091 Tf 169.9533 463.8833 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.9376 0 Td[(m)27(u)1(s)-1(t)-308(b)-28(e)-309(c)27(h)1(os)-1(en)-309(accordi)1(ng)-309(to)-309(th)1(e)-310(r)1(e)-1(al)1(/c)-1(omplex,)]TJ -76.0247 -13.5492 Td[(single/dou)1(bl)1(e)-334(pr)1(e)-1(cis)-1(i)1(on)-333(v)28(e)-1(r)1(s)-1(ion)-332(of)-333(MLD2P)1(4)-334(u)1(nd)1(e)-1(r)-333(u)1(s)-1(e.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(y)]TJ/F20 10.9091 Tf 45.9708 0 Td[(typ)51(e)]TJ/F48 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ +/F18 10.9091 Tf 169.953 463.883 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.938 0 Td [(m)28(ust)-309(b)-28(e)-309(c)28(hosen)-309(according)-309(to)-309(the)-309(real/complex,)]TJ -76.025 -13.549 Td [(single/double)-333(precision)-334(v)28(ersion)-333(of)-333(MLD2P4)-334(und)1(e)-1(r)-333(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(y)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F46 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ ET -1 0 0 1 192.1122 436.7849 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 192.112 436.984 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -192.1122 -436.7849 cm BT -/F20 10.9091 Tf 195.4576 436.7849 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5679 0 Td[(\051,)-525(dimension\050:\051,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.3619 0 Td[(.)]TJ -258.5212 -13.5492 Td[(The)-771(l)1(o)-28(c)-1(al)-770(p)1(art)-770(of)-770(the)-770(v)28(e)-1(ctor)]TJ/F24 10.9091 Tf 164.4241 0 Td[(y)]TJ/F15 10.9091 Tf 5.7399 0 Td[(.)-1755(Note)-771(th)1(at)]TJ/F20 10.9091 Tf 81.717 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 28.181 0 Td[(and)]TJ/F20 10.9091 Tf -280.062 -13.5492 Td[(kind)]TJ +/F18 10.9091 Tf 195.458 436.785 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.567 0 Td [(\051,)-525(dimension\050:\051,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.362 0 Td [(.)]TJ -258.521 -13.549 Td [(The)-770(lo)-28(cal)-771(par)1(t)-771(of)-770(the)-771(v)28(ector)]TJ/F22 10.9091 Tf 164.424 0 Td [(y)]TJ/F15 10.9091 Tf 5.74 0 Td [(.)-1756(Note)-770(that)]TJ/F18 10.9091 Tf 81.717 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 28.181 0 Td [(and)]TJ/F18 10.9091 Tf -280.062 -13.549 Td [(kind)]TJ ET -1 0 0 1 166.6079 409.6865 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 166.608 409.886 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -166.6079 -409.6865 cm BT -/F20 10.9091 Tf 169.9533 409.6865 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.9376 0 Td[(m)27(u)1(s)-1(t)-308(b)-28(e)-309(c)27(h)1(os)-1(en)-309(accordi)1(ng)-309(to)-309(th)1(e)-310(r)1(e)-1(al)1(/c)-1(omplex,)]TJ -76.0247 -13.5492 Td[(single/dou)1(bl)1(e)-334(pr)1(e)-1(cis)-1(i)1(on)-333(v)28(e)-1(r)1(s)-1(ion)-332(of)-333(MLD2P)1(4)-334(u)1(nd)1(e)-1(r)-333(u)1(s)-1(e.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.5143 0 Td[(.)]TJ -177.5435 -13.5491 Td[(The)-380(com)-1(m)28(un)1(ication)-379(des)-1(crip)1(tor)-379(as)-1(so)-28(ciated)-379(to)-380(th)1(e)-380(m)-1(atr)1(ix)-379(to)-380(b)-27(e)]TJ 0 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(d)1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-307(c)-1(o)-28(d)1(e)-1(.)-435(If)-308(n)1(o)-308(e)-1(r)1(ror,)-313(0)-307(is)-308(re)-1(t)1(urn)1(e)-1(d)1(.)-436(See)-308(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 384.2717 328.3914 cm +/F18 10.9091 Tf 169.953 409.687 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 51.938 0 Td [(m)28(ust)-309(b)-28(e)-309(c)28(hosen)-309(according)-309(to)-309(the)-309(real/complex,)]TJ -76.025 -13.55 Td [(single/double)-333(precision)-334(v)28(ersion)-333(of)-333(MLD2P4)-334(und)1(e)-1(r)-333(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(desc_a)-1064(type\050psb_desc_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 223.515 0 Td [(.)]TJ -177.544 -13.549 Td [(The)-380(comm)28(unication)-379(descriptor)-380(asso)-28(ciated)-379(to)-380(the)-379(matrix)-380(to)-379(b)-28(e)]TJ 0 -13.549 Td [(preconditioned.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.55 Td [(Error)-308(co)-28(de.)-435(I)-1(f)-307(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -384.2717 -328.3914 cm -BT -/F15 10.9091 Tf 384.2717 328.3914 Td[(8)]TJ -ET -1 0 0 1 389.7263 328.3914 cm + [-307(8)]TJ 0 g 0 G -1 0 0 1 -389.7263 -328.3914 cm -BT -/F15 10.9091 Tf 393.0848 328.3914 Td[(for)-307(details.)]TJ/F48 10.9091 Tf -293.1894 -13.5492 Td[(trans)-1589(character\050len=1\051,)-525(optional,)-525(intent\050in\051.)]TJ/F15 10.9091 Tf 45.9708 -13.5492 Td[(If)]TJ/F48 10.9091 Tf 10.0575 0 Td[(trans)]TJ/F15 10.9091 Tf 31.4207 0 Td[(=)]TJ/F48 10.9091 Tf 11.2696 0 Td[('N','n')]TJ/F15 10.9091 Tf 42.8752 0 Td[(th)1(e)-1(n)]TJ/F24 10.9091 Tf 23.9969 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9589 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)-278(=)]TJ/F24 10.9091 Tf 18.7878 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(;)-281(if)]TJ/F48 10.9091 Tf 15.2472 0 Td[(trans)]TJ/F15 10.9091 Tf 31.4208 0 Td[(=)]TJ/F48 10.9091 Tf 11.2696 0 Td[('T','t')]TJ/F15 10.9091 Tf -257.5473 -13.5492 Td[(th)1(e)-1(n)]TJ/F24 10.9091 Tf 23.9615 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2425 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)-278(=)]TJ/F24 10.9091 Tf 18.7878 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F25 7.9701 Tf 6.5865 0 Td[(T)]TJ/F15 10.9091 Tf 9.3539 -3.9588 Td[(\050tr)1(ansp)-28(ose)-253(of)]TJ/F24 10.9091 Tf 63.8322 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051;)-279(if)]TJ/F48 10.9091 Tf 19.4309 0 Td[(trans)]TJ/F15 10.9091 Tf 31.3854 0 Td[(=)]TJ/F48 10.9091 Tf 11.2343 0 Td[('C','c')]TJ/F15 10.9091 Tf -257.5473 -13.5492 Td[(th)1(e)-1(n)]TJ/F24 10.9091 Tf 24.8485 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F24 10.9091 Tf 4.2424 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5866 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)-278(=)]TJ/F24 10.9091 Tf 18.7878 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F25 7.9701 Tf 6.5865 0 Td[(C)]TJ/F15 10.9091 Tf 10.7332 -3.9588 Td[(\050conj)1(ugate)-334(tr)1(ansp)-28(ose)-334(of)]TJ/F24 10.9091 Tf 115.0001 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051.)]TJ/F48 10.9091 Tf -294.9017 -13.5492 Td[(work)]TJ/F20 10.9091 Tf 45.9708 0 Td[(typ)51(e)]TJ/F48 10.9091 Tf 19.7771 0 Td[(\050)]TJ/F20 10.9091 Tf 5.7272 0 Td[(kind)]TJ + [-308(for)-308(details.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(trans)-1589(character\050len=1\051,)-525(optional,)-525(intent\050in\051.)]TJ/F15 10.9091 Tf 45.971 -13.549 Td [(If)]TJ/F46 10.9091 Tf 10.058 0 Td [(trans)]TJ/F15 10.9091 Tf 31.42 0 Td [(=)]TJ/F46 10.9091 Tf 11.27 0 Td [('N','n')]TJ/F15 10.9091 Tf 42.875 0 Td [(then)]TJ/F22 10.9091 Tf 23.997 0 Td [(op)]TJ/F15 10.9091 Tf 10.777 0 Td [(\050)]TJ/F22 10.9091 Tf 4.242 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.586 0 Td [(1)]TJ/F15 10.9091 Tf 4.733 -3.959 Td [(\051)-278(=)]TJ/F22 10.9091 Tf 18.787 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(;)-281(if)]TJ/F46 10.9091 Tf 15.247 0 Td [(trans)]TJ/F15 10.9091 Tf 31.421 0 Td [(=)]TJ/F46 10.9091 Tf 11.269 0 Td [('T','t')]TJ/F15 10.9091 Tf -257.547 -13.549 Td [(then)]TJ/F22 10.9091 Tf 23.962 0 Td [(op)]TJ/F15 10.9091 Tf 10.776 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051)-278(=)]TJ/F22 10.9091 Tf 18.788 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(T)]TJ/F15 10.9091 Tf 9.354 -3.959 Td [(\050transp)-28(ose)-252(of)]TJ/F22 10.9091 Tf 63.832 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051;)-279(if)]TJ/F46 10.9091 Tf 19.431 0 Td [(trans)]TJ/F15 10.9091 Tf 31.385 0 Td [(=)]TJ/F46 10.9091 Tf 11.234 0 Td [('C','c')]TJ/F15 10.9091 Tf -257.547 -13.549 Td [(then)]TJ/F22 10.9091 Tf 24.849 0 Td [(op)]TJ/F15 10.9091 Tf 10.776 0 Td [(\050)]TJ/F22 10.9091 Tf 4.243 0 Td [(M)]TJ/F26 7.9701 Tf 11.772 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051)-278(=)]TJ/F22 10.9091 Tf 18.788 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F23 7.9701 Tf 6.586 0 Td [(C)]TJ/F15 10.9091 Tf 10.733 -3.959 Td [(\050conjugate)-333(transp)-28(ose)-333(of)]TJ/F22 10.9091 Tf 115 0 Td [(M)]TJ/F26 7.9701 Tf 11.773 3.959 Td [(\000)]TJ/F20 7.9701 Tf 6.587 0 Td [(1)]TJ/F15 10.9091 Tf 4.732 -3.959 Td [(\051.)]TJ/F46 10.9091 Tf -294.902 -13.549 Td [(work)]TJ/F18 10.9091 Tf 45.971 0 Td [(typ)51(e)]TJ/F46 10.9091 Tf 19.777 0 Td [(\050)]TJ/F18 10.9091 Tf 5.727 0 Td [(kind)]TJ ET -1 0 0 1 192.1122 260.6455 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 192.112 260.845 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -192.1122 -260.6455 cm BT -/F20 10.9091 Tf 195.4576 260.6455 Td[(p)51(ar)51(ameter)]TJ/F48 10.9091 Tf 48.5679 0 Td[(\051,)-525(dimension\050:\051,)-525(optional,)-525(target)]TJ/F15 10.9091 Tf 188.9979 0 Td[(.)]TJ -287.1572 -13.5492 Td[(W)84(orkspace)-1(.)-4466(Its)-1674(s)-1(ize)-1674(s)-1(h)1(ould)-1673(b)-28(e)-1674(at)-1674(leas)-1(t)]TJ/F48 10.9091 Tf 0 -13.5492 Td[(4)-525(*)-525(psb_cd_get_local_cols\050desc_a\051)]TJ/F15 10.9091 Tf 199.989 0 Td[(\050se)-1(e)-1008(th)1(e)-1008(PS)1(B)-1(LAS)]TJ -199.989 -13.5492 Td[(Use)-1(r')1(s)-474(G)1(uid)1(e)-1(\051.)-862(Note)-474(t)1(hat)]TJ/F20 10.9091 Tf 132.3902 0 Td[(typ)51(e)]TJ/F15 10.9091 Tf 24.9355 0 Td[(and)]TJ/F20 10.9091 Tf 22.7342 0 Td[(kind)]TJ +/F18 10.9091 Tf 195.458 260.646 Td [(p)51(ar)51(ameter)]TJ/F46 10.9091 Tf 48.567 0 Td [(\051,)-525(dimension\050:\051,)-525(optional,)-525(target)]TJ/F15 10.9091 Tf 188.998 0 Td [(.)]TJ -287.157 -13.55 Td [(W)83(orkspace.)-4466(Its)-1674(size)-1674(should)-1674(b)-28(e)-1674(at)-1674(least)]TJ/F46 10.9091 Tf 0 -13.549 Td [(4)-525(*)-525(psb_cd_get_local_cols\050desc_a\051)]TJ/F15 10.9091 Tf 199.989 0 Td [(\050see)-1008(the)-1007(PSBLAS)]TJ -199.989 -13.549 Td [(User's)-473(Guide\051.)-863(Note)-473(that)]TJ/F18 10.9091 Tf 132.39 0 Td [(typ)51(e)]TJ/F15 10.9091 Tf 24.936 0 Td [(and)]TJ/F18 10.9091 Tf 22.734 0 Td [(kind)]TJ ET -1 0 0 1 346.6678 219.9979 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 346.668 220.197 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -346.6678 -219.9979 cm BT -/F20 10.9091 Tf 350.0132 219.9979 Td[(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 53.7263 0 Td[(m)27(u)1(s)-1(t)-472(b)-28(e)]TJ -257.8733 -13.5492 Td[(c)27(h)1(os)-1(en)-383(ac)-1(cord)1(ing)-383(to)-384(th)1(e)-384(real/c)-1(omp)1(le)-1(x)1(,)-396(s)-1(in)1(gle/dou)1(ble)-384(p)1(rec)-1(ision)]TJ 0 -13.5492 Td[(v)28(ers)-1(i)1(on)-333(of)-333(MLD2P)1(4)-334(u)1(nd)1(e)-1(r)-333(u)1(s)-1(e.)]TJ/F19 11.9552 Tf -51.9484 -28.1736 Td[(7.)-1(5)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ +/F18 10.9091 Tf 350.013 219.998 Td [(p)51(ar)51(ameter)]TJ/F15 10.9091 Tf 53.726 0 Td [(m)28(ust)-473(b)-28(e)]TJ -257.873 -13.549 Td [(c)28(hosen)-384(according)-383(to)-384(the)-384(r)1(e)-1(al)1(/c)-1(omplex,)-396(single/double)-383(precision)]TJ 0 -13.549 Td [(v)28(ersion)-334(of)-333(MLD2P4)-333(under)-333(use.)]TJ/F17 11.9552 Tf -51.948 -28.174 Td [(7.5)-1125(Subroutine)-375(mld)]TJ ET -1 0 0 1 216.9401 164.726 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -4.0349 0.1992 l -S +1 0 0 1 216.94 164.925 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -1 0 0 1 -216.9401 -164.726 cm BT -/F19 11.9552 Tf 220.975 164.726 Td[(pre)-1(cfree)]TJ -ET -1 0 0 1 237.4167 144.1313 cm +/F17 11.9552 Tf 220.975 164.726 Td [(precfree)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -237.4167 -144.1313 cm -BT -/F48 10.9091 Tf 242.8713 144.1313 Td[(mld_precfree\050p,info\051)]TJ/F15 10.9091 Tf -148.9535 -22.6104 Td[(This)-333(rout)1(ine)-334(d)1(e)-1(al)1(lo)-28(cate)-1(s)-333(the)-334(p)1(rec)-1(on)1(diti)1(oner)-333(data)-333(s)-1(t)1(ructur)1(e)-1(.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F46 10.9091 Tf 21.896 -20.595 Td [(mld_precfree\050p,info\051)]TJ/F15 10.9091 Tf -148.953 -22.61 Td [(This)-333(routine)-334(deallo)-27(cates)-334(the)-333(preconditioner)-333(data)-334(stru)1(c)-1(tu)1(re.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -467 0 obj << +434 0 obj << /Type /Page -/Contents 468 0 R -/Resources 466 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 447 0 R -/Annots [ 470 0 R 472 0 R ] +/Contents 435 0 R +/Resources 433 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 411 0 R +/Annots [ 432 0 R 430 0 R ] >> endobj -470 0 obj << +432 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.7) >> >> endobj -472 0 obj << +430 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [383.2755 323.3304 390.7225 336.9634] +/Rect [383.275 323.33 390.723 336.963] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -469 0 obj << -/D [467 0 R /XYZ 93.9178 740.0018 null] +436 0 obj << +/D [434 0 R /XYZ 93.918 740.002 null] >> endobj 78 0 obj << -/D [467 0 R /XYZ 93.9178 715.0952 null] +/D [434 0 R /XYZ 93.918 715.095 null] >> endobj -471 0 obj << -/D [467 0 R /XYZ 93.9178 555.6591 null] +437 0 obj << +/D [434 0 R /XYZ 93.918 555.659 null] >> endobj 82 0 obj << -/D [467 0 R /XYZ 93.9178 174.0244 null] +/D [434 0 R /XYZ 93.918 174.024 null] >> endobj -466 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F48 214 0 R /F24 176 0 R /F28 270 0 R /F22 273 0 R /F41 126 0 R /F20 171 0 R /F25 267 0 R >> +433 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F46 195 0 R /F22 165 0 R /F26 249 0 R /F20 250 0 R /F39 116 0 R /F18 163 0 R /F23 248 0 R >> /ProcSet [ /PDF /Text ] >> endobj -475 0 obj << -/Length 4158 +441 0 obj << +/Length 3032 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(30)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(30)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -554.1896 -740.0018 cm -BT -/F41 10.9091 Tf 141.7385 704.1363 Td[(Argumen)32(ts)]TJ/F48 10.9091 Tf 5.9776 -19.6473 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.1803 0 Td[(.)]TJ -201.0994 -13.5492 Td[(The)-267(prec)-1(on)1(di)1(tioner)-267(dat)1(a)-268(stru)1(c)-1(tu)1(re.)-422(Note)-268(th)1(at)]TJ/F20 10.9091 Tf 216.6391 0 Td[(x)]TJ/F15 10.9091 Tf 9.2894 0 Td[(m)27(u)1(s)-1(t)-267(b)-27(e)-268(c)28(hose)-1(n)]TJ -225.9285 -13.5492 Td[(acc)-1(ord)1(in)1(g)-352(to)-352(the)-352(real/c)-1(ompl)1(e)-1(x,)-356(single/dou)1(bl)1(e)-353(p)1(re)-1(cision)-352(v)28(ersion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-307(c)-1(o)-28(d)1(e)-1(.)-435(If)-308(n)1(o)-308(e)-1(r)1(ror,)-313(0)-307(is)-308(re)-1(t)1(urn)1(e)-1(d)1(.)-436(See)-308(Sec)-1(ti)1(on)]TJ -ET -1 0 0 1 432.0924 616.7431 cm +/F39 10.9091 Tf -203.265 -35.866 Td [(Argumen)32(ts)]TJ/F46 10.9091 Tf 5.978 -19.647 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050inout\051)]TJ/F15 10.9091 Tf 143.18 0 Td [(.)]TJ -201.099 -13.549 Td [(The)-267(preconditioner)-267(data)-267(s)-1(tr)1(ucture.)-423(Note)-267(that)]TJ/F18 10.9091 Tf 216.639 0 Td [(x)]TJ/F15 10.9091 Tf 9.289 0 Td [(m)28(ust)-268(b)-27(e)-268(c)28(hosen)]TJ -225.928 -13.549 Td [(according)-352(to)-352(the)-352(real/complex,)-357(single/double)-352(precision)-352(v)28(ersion)]TJ 0 -13.55 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-308(co)-28(d)1(e)-1(.)-435(If)-308(no)-308(error,)-313(0)-308(is)-308(returned.)-436(See)-308(S)1(e)-1(ction)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -432.0924 -616.7431 cm -BT -/F15 10.9091 Tf 432.0924 616.7431 Td[(8)]TJ -ET -1 0 0 1 437.547 616.7431 cm + [-307(8)]TJ 0 g 0 G -1 0 0 1 -437.547 -616.7431 cm -BT -/F15 10.9091 Tf 440.9055 616.7431 Td[(for)-307(details.)]TJ/F19 11.9552 Tf -299.167 -28.6283 Td[(7.)-1(6)-1125(Subr)-1(out)-1(ine)-376(ml)-1(d)]TJ + [-308(for)-308(details.)]TJ/F17 11.9552 Tf -51.949 -28.628 Td [(7.6)-1125(Subroutine)-375(mld)]TJ ET -1 0 0 1 264.7607 588.1148 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -4.0349 0.1992 l -S +1 0 0 1 264.761 588.314 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -1 0 0 1 -264.7607 -588.1148 cm BT -/F19 11.9552 Tf 268.7956 588.1148 Td[(pre)-1(cdescr)]TJ -ET -1 0 0 1 282.3738 567.5201 cm +/F17 11.9552 Tf 268.796 588.115 Td [(precdescr)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -282.3738 -567.5201 cm -BT -/F48 10.9091 Tf 287.8283 567.5201 Td[(mld_precdescr\050p,info\051)]TJ -14.318 -13.5492 Td[(mld_precdescr\050p,info,iout\051)]TJ/F15 10.9091 Tf -131.7718 -25.5043 Td[(This)-364(rou)1(tine)-364(pri)1(n)28(ts)-365(a)-364(desc)-1(ri)1(ption)-363(of)-364(the)-364(prec)-1(on)1(di)1(tioner)-364(to)-364(the)-364(s)-1(tan)1(dar)1(d)-364(outp)1(ut)-364(or)-364(to)-364(a)]TJ 0 -13.5492 Td[(\014l)1(e)-1(.)]TJ/F41 10.9091 Tf 0 -28.8143 Td[(Argumen)32(ts)]TJ/F48 10.9091 Tf 5.9776 -19.6473 Td[(p)-3689(type\050mld_)]TJ/F20 10.9091 Tf 97.5157 0 Td[(x)]TJ/F48 10.9091 Tf 6.3742 0 Td[(prec_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 125.9986 0 Td[(.)]TJ -183.9177 -13.5492 Td[(The)-299(p)1(rec)-1(on)1(diti)1(oner)-298(data)-298(s)-1(tr)1(uctur)1(e)-1(.)-432(Note)-299(that)]TJ/F20 10.9091 Tf 218.4534 0 Td[(x)]TJ/F15 10.9091 Tf 9.6296 0 Td[(m)27(u)1(s)-1(t)-298(b)-27(e)-299(c)27(h)1(os)-1(en)]TJ -228.083 -13.5492 Td[(acc)-1(ord)1(in)1(g)-394(to)-394(t)1(he)-394(real/com)-1(p)1(lex,)-409(sin)1(gle)-1(/d)1(oub)1(le)-394(pr)1(e)-1(cis)-1(i)1(on)-393(v)28(e)-1(rsion)]TJ 0 -13.5492 Td[(of)-333(MLD)1(2P4)-333(un)1(der)-333(use)-1(.)]TJ/F48 10.9091 Tf -45.9708 -13.5492 Td[(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td[(.)]TJ -114.5442 -13.5492 Td[(Er)1(ror)-332(c)-1(o)-27(de.)-444(I)-1(f)-332(n)1(o)-333(e)-1(r)1(ror,)-332(0)-333(is)-333(r)1(e)-1(tu)1(rned.)-444(S)1(e)-1(e)-333(S)1(e)-1(ction)]TJ -ET -1 0 0 1 434.3855 398.7098 cm +/F46 10.9091 Tf 19.032 -20.595 Td [(mld_precdescr\050p,info\051)]TJ -14.318 -13.549 Td [(mld_precdescr\050p,info,iout\051)]TJ/F15 10.9091 Tf -131.772 -25.504 Td [(This)-364(routine)-364(prin)27(ts)-364(a)-364(description)-364(of)-364(the)-365(preconditioner)-364(to)-364(the)-364(standard)-364(output)-365(or)-364(to)-364(a)]TJ 0 -13.55 Td [(\014le.)]TJ/F39 10.9091 Tf 0 -28.814 Td [(Argumen)32(ts)]TJ/F46 10.9091 Tf 5.978 -19.647 Td [(p)-3689(type\050mld_)]TJ/F18 10.9091 Tf 97.516 0 Td [(x)]TJ/F46 10.9091 Tf 6.374 0 Td [(prec_type\051,)-525(intent\050in\051)]TJ/F15 10.9091 Tf 125.999 0 Td [(.)]TJ -183.918 -13.549 Td [(The)-298(preconditioner)-299(data)-298(structure.)-433(Note)-298(that)]TJ/F18 10.9091 Tf 218.453 0 Td [(x)]TJ/F15 10.9091 Tf 9.63 0 Td [(m)28(ust)-299(b)-27(e)-299(c)28(hosen)]TJ -228.083 -13.55 Td [(according)-394(to)-393(the)-394(real/complex,)-408(single/double)-394(precision)-393(v)27(ersion)]TJ 0 -13.549 Td [(of)-333(MLD2P4)-334(u)1(nder)-334(use.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(info)-2114(integer,)-525(intent\050out\051)]TJ/F15 10.9091 Tf 160.515 0 Td [(.)]TJ -114.544 -13.549 Td [(Error)-333(co)-27(de.)-445(If)-332(no)-333(error,)-333(0)-332(is)-333(returned.)-444(See)-333(Section)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -434.3855 -398.7098 cm -BT -/F15 10.9091 Tf 434.3855 398.7098 Td[(8)]TJ -ET -1 0 0 1 439.8401 398.7098 cm + [-333(8)]TJ 0 g 0 G -1 0 0 1 -439.8401 -398.7098 cm -BT -/F15 10.9091 Tf 443.4695 398.7098 Td[(for)-332(d)1(e)-1(tail)1(s)-1(.)]TJ/F48 10.9091 Tf -295.7534 -13.5492 Td[(iout)-2114(integer,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 212.0599 0 Td[(.)]TJ -166.0891 -13.5491 Td[(The)-392(id)-391(of)-391(th)1(e)-392(\014le)-392(wh)1(e)-1(r)1(e)-392(the)-392(p)1(re)-1(cond)1(ition)1(e)-1(r)-391(d)1(e)-1(sc)-1(r)1(ipti)1(on)-391(w)-1(i)1(ll)-392(b)-27(e)]TJ 0 -13.5492 Td[(pr)1(in)28(ted;)-333(th)1(e)-334(defau)1(lt)-333(is)-334(th)1(e)-334(stand)1(ard)-333(ou)1(tpu)1(t.)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [-332(for)-333(details.)]TJ/F46 10.9091 Tf -45.971 -13.549 Td [(iout)-2114(integer,)-525(intent\050in\051,)-525(optional)]TJ/F15 10.9091 Tf 212.06 0 Td [(.)]TJ -166.089 -13.549 Td [(The)-392(id)-391(of)-392(the)-391(\014le)-392(where)-391(the)-392(preconditioner)-391(description)-392(will)-391(b)-28(e)]TJ 0 -13.55 Td [(prin)28(ted;)-333(the)-334(default)-333(is)-333(the)-334(standard)-333(output.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -474 0 obj << +440 0 obj << /Type /Page -/Contents 475 0 R -/Resources 473 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 447 0 R -/Annots [ 478 0 R 480 0 R ] +/Contents 441 0 R +/Resources 439 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 411 0 R +/Annots [ 431 0 R 438 0 R ] >> endobj -478 0 obj << +431 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [431.0961 611.682 438.5432 625.3151] +/Rect [431.096 611.682 438.543 625.315] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -480 0 obj << +438 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [433.3893 393.6488 440.8364 407.2819] +/Rect [433.389 393.649 440.836 407.282] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -476 0 obj << -/D [474 0 R /XYZ 141.7385 740.0018 null] +442 0 obj << +/D [440 0 R /XYZ 141.738 740.002 null] >> endobj -477 0 obj << -/D [474 0 R /XYZ 141.7385 694.9697 null] +443 0 obj << +/D [440 0 R /XYZ 141.738 694.97 null] >> endobj 86 0 obj << -/D [474 0 R /XYZ 141.7385 597.4132 null] +/D [440 0 R /XYZ 141.738 597.413 null] >> endobj -479 0 obj << -/D [474 0 R /XYZ 141.7385 476.9364 null] +444 0 obj << +/D [440 0 R /XYZ 141.738 476.936 null] >> endobj -473 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F41 126 0 R /F48 214 0 R /F20 171 0 R /F19 105 0 R >> +439 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F39 116 0 R /F46 195 0 R /F18 163 0 R /F17 103 0 R >> /ProcSet [ /PDF /Text ] >> endobj -483 0 obj << -/Length 2376 +448 0 obj << +/Length 1768 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(8)]TJ -ET -1 0 0 1 99.9481 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(8)]TJ 0 g 0 G -1 0 0 1 -99.9481 -740.0018 cm -BT -/F42 10.9091 Tf 104.0692 740.0018 Td[(Err)22(o)1(r)-378(h)-1(and)-1(lin)-1(g)]TJ/F15 10.9091 Tf 391.3906 0 Td[(31)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(Err)22(o)1(r)-378(handling)]TJ/F15 10.9091 Tf 401.542 0 Td [(31)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(8)-1125(E)-1(rr)-1(or)-376(Ha)1(ndl)-1(ing)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(The)-263(err)1(or)-263(h)1(and)1(lin)1(g)-263(in)-262(M)1(LD2P4)-262(is)-263(based)-262(on)-263(t)1(he)-263(P)1(SBLAS)-262(v)28(e)-1(r)1(s)-1(ion)-262(2)-262(e)-1(r)1(ror)-262(han)1(dli)1(ng.)-420(Err)1(or)]TJ 0 -13.5492 Td[(condi)1(tions)-389(are)-390(signal)1(e)-1(d)-389(v)1(ia)-389(an)-389(in)28(tege)-1(r)-389(ar)1(gume)-1(n)29(t)]TJ/F48 10.9091 Tf 234.4867 0 Td[(info)]TJ/F15 10.9091 Tf 22.9089 0 Td[(;)-417(whenev)28(e)-1(r)-389(an)-389(err)1(or)-389(c)-1(on)1(diti)1(on)-389(is)]TJ -257.3956 -13.5492 Td[(detec)-1(ted,)-397(an)-384(e)-1(r)1(ror)-384(trace)-385(s)-1(tac)28(k)-385(is)-385(b)1(uil)1(t)-385(b)28(y)-384(the)-385(l)1(ibr)1(ary)-384(up)-384(to)-385(th)1(e)-385(top-lev)28(e)-1(l,)-397(u)1(s)-1(er-c)-1(al)1(lable)]TJ 0 -13.5492 Td[(rou)1(tin)1(e)-1(.)-552(This)-369(routi)1(ne)-370(wil)1(l)-370(t)1(hen)-369(dec)-1(id)1(e)-1(,)-378(acc)-1(or)1(din)1(g)-369(to)-370(t)1(he)-370(u)1(s)-1(er)-369(pr)1(e)-1(f)1(e)-1(rences)-1(,)-378(whether)-369(the)]TJ 0 -13.5492 Td[(error)-274(s)-1(h)1(ould)-274(b)-28(e)-275(han)1(dl)1(e)-1(d)-274(b)28(y)-275(terminati)1(ng)-275(th)1(e)-276(p)1(rogram)-275(or)-275(b)29(y)-275(retur)1(nin)1(g)-275(the)-275(error)-274(c)-1(on)1(diti)1(on)]TJ 0 -13.5492 Td[(to)-335(th)1(e)-335(use)-1(r)-334(c)-1(o)-27(de,)-335(whic)28(h)-335(will)-334(then)-334(tak)28(e)-335(ac)-1(ti)1(on,)-335(an)1(d)-335(wheth)1(e)-1(r)-334(an)-335(err)1(or)-335(me)-1(ssage)-336(shou)1(ld)-334(b)-28(e)]TJ 0 -13.5492 Td[(pr)1(in)28(ted.)-567(T)-1(h)1(e)-1(se)-375(opti)1(ons)-375(ma)28(y)-375(b)-27(e)-375(s)-1(et)-374(b)28(y)-374(using)-374(the)-375(P)1(SBLAS)-374(e)-1(r)1(ror)-374(han)1(dli)1(ng)-375(r)1(outi)1(nes)-1(;)-395(f)1(or)]TJ 0 -13.5492 Td[(fu)1(rth)1(e)-1(r)-333(d)1(e)-1(tai)1(ls)-334(se)-1(e)-334(t)1(he)-334(P)1(SBLAS)-333(use)-1(r)1('s)-334(gu)1(ide.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F17 14.3462 Tf -401.542 -35.866 Td [(8)-1125(Error)-375(Handling)]TJ/F15 10.9091 Tf 0 -24.352 Td [(The)-262(e)-1(r)1(ror)-263(handling)-262(in)-263(MLD2P4)-262(is)-262(base)-1(d)-262(on)-262(the)-263(PSBLAS)-262(v)28(ersion)-263(2)-262(error)-263(handling.)-420(Error)]TJ 0 -13.549 Td [(conditions)-389(are)-390(sign)1(ale)-1(d)-389(via)-389(an)-389(in)28(te)-1(ger)-389(argumen)28(t)]TJ/F46 10.9091 Tf 234.487 0 Td [(info)]TJ/F15 10.9091 Tf 22.908 0 Td [(;)-417(whenev)27(er)-389(an)-389(error)-389(condition)-390(is)]TJ -257.395 -13.549 Td [(detected,)-398(an)-384(error)-385(trace)-384(stac)27(k)-384(is)-385(built)-385(b)28(y)-384(the)-385(library)-384(up)-385(to)-385(the)-384(top-lev)27(el,)-397(user-callable)]TJ 0 -13.549 Td [(routine.)-552(This)-370(routi)1(ne)-370(will)-369(then)-369(decide,)-379(according)-369(to)-369(the)-370(user)-369(preferences,)-378(whether)-370(the)]TJ 0 -13.55 Td [(error)-275(should)-275(b)-28(e)-275(h)1(andled)-275(b)27(y)-274(te)-1(r)1(m)-1(i)1(nating)-275(the)-275(program)-275(or)-275(b)28(y)-275(returning)-275(the)-275(error)-275(condition)]TJ 0 -13.549 Td [(to)-335(the)-334(use)-1(r)-334(co)-28(de,)-335(whic)28(h)-335(will)-335(then)-334(tak)27(e)-334(action,)-335(and)-335(whether)-335(an)-335(error)-334(message)-335(should)-335(b)-28(e)]TJ 0 -13.549 Td [(prin)28(ted.)-568(These)-375(options)-374(ma)28(y)-375(b)-28(e)-374(set)-375(b)28(y)-375(usin)1(g)-375(the)-375(PS)1(BLAS)-375(error)-374(handling)-375(routines;)-395(for)]TJ 0 -13.549 Td [(further)-333(details)-333(s)-1(ee)-333(the)-333(PSBLAS)-334(u)1(s)-1(er's)-333(guide.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -482 0 obj << +447 0 obj << /Type /Page -/Contents 483 0 R -/Resources 481 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 486 0 R -/Annots [ 485 0 R ] +/Contents 448 0 R +/Resources 446 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 450 0 R +/Annots [ 445 0 R ] >> endobj -485 0 obj << +445 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 100.9443 748.4526] +/Rect [92.922 739.006 100.944 748.453] /Subtype /Link /A << /S /GoTo /D (section.8) >> >> endobj -484 0 obj << -/D [482 0 R /XYZ 93.9178 740.0018 null] +449 0 obj << +/D [447 0 R /XYZ 93.918 740.002 null] >> endobj 90 0 obj << -/D [482 0 R /XYZ 93.9178 715.0952 null] +/D [447 0 R /XYZ 93.918 715.095 null] >> endobj -481 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F48 214 0 R >> +446 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -489 0 obj << -/Length 347 +453 0 obj << +/Length 174 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(32)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(32)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -488 0 obj << +452 0 obj << /Type /Page -/Contents 489 0 R -/Resources 487 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 486 0 R +/Contents 453 0 R +/Resources 451 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 450 0 R >> endobj -490 0 obj << -/D [488 0 R /XYZ 141.7385 740.0018 null] +454 0 obj << +/D [452 0 R /XYZ 141.738 740.002 null] >> endobj -487 0 obj << -/Font << /F15 123 0 R /F42 129 0 R >> +451 0 obj << +/Font << /F15 115 0 R /F40 117 0 R >> /ProcSet [ /PDF /Text ] >> endobj -493 0 obj << -/Length 4402 +458 0 obj << +/Length 3985 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G 0 0 1 rg 0 0 1 RG -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(A)]TJ -ET -1 0 0 1 102.7965 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(A)]TJ 0 g 0 G -1 0 0 1 -102.7965 -740.0018 cm -BT -/F42 10.9091 Tf 106.9177 740.0018 Td[(Li)-1(ce)1(n)-1(se)]TJ/F15 10.9091 Tf 388.5421 0 Td[(33)]TJ -ET -1 0 0 1 506.3689 740.0018 cm + [-378(License)]TJ/F15 10.9091 Tf 401.542 0 Td [(33)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(A)-1125(L)1(i)-1(cense)]TJ/F15 10.9091 Tf 0 -22.7582 Td[(The)-334(M)1(LD2P4)-333(is)-334(f)1(ree)-1(l)1(y)-334(d)1(istrib)1(utab)1(le)-334(u)1(nd)1(e)-1(r)-333(th)1(e)-334(fol)1(lo)28(w)-1(i)1(ng)-333(c)-1(op)28(y)1(righ)28(t)-333(terms)-1(:)]TJ -ET -1 0 0 1 88.4633 660.4566 cm +/F17 14.3462 Tf -401.542 -35.866 Td [(A)-1125(License)]TJ/F15 10.9091 Tf 0 -22.758 Td [(The)-333(MLD2P4)-334(is)-333(freely)-333(distributable)-333(under)-334(the)-333(follo)28(wing)-333(cop)27(yrigh)28(t)-333(terms:)]TJ 0 g 0 G 0 g 0 G -1 0 0 1 -88.4633 -660.4566 cm -BT -/F48 9.9626 Tf 224.6763 660.4566 Td[(MLD2P4)-1050(version)-525(1.0)]TJ -130.7585 -11.9552 Td[(MultiLevel)-525(Domain)-525(Decomposition)-525(Parallel)-525(Preconditioners)-525(Package)]TJ 57.5337 -11.9551 Td[(based)-525(on)-525(PSBLAS)-525(\050Parallel)-525(Sparse)-525(BLAS)-525(version)-525(2.3\051)]TJ -57.5337 -23.9104 Td[(\050C\051)-525(Copyright)-525(2008)]TJ 104.6068 -23.9103 Td[(Salvatore)-525(Filippone)-1050(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.9552 Td[(Alfredo)-525(Buttari)-3150(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.9551 Td[(Pasqua)-525(D'Ambra)-3675(ICAR-CNR,)-525(Naples)]TJ 0 -11.9552 Td[(Daniela)-525(di)-525(Serafino)-1050(Second)-525(University)-525(of)-525(Naples)]TJ -104.6068 -35.8655 Td[(Redistribution)-525(and)-525(use)-525(in)-525(source)-525(and)-525(binary)-525(forms,)-525(with)-525(or)-525(without)]TJ 0 -11.9552 Td[(modification,)-525(are)-525(permitted)-525(provided)-525(that)-525(the)-525(following)-525(conditions)]TJ 0 -11.9551 Td[(are)-525(met:)]TJ 10.4607 -11.9552 Td[(1.)-525(Redistributions)-525(of)-525(source)-525(code)-525(must)-525(retain)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.9552 Td[(notice,)-525(this)-525(list)-525(of)-525(conditions)-525(and)-525(the)-525(following)-525(disclaimer.)]TJ -15.691 -11.9551 Td[(2.)-525(Redistributions)-525(in)-525(binary)-525(form)-525(must)-525(reproduce)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.9552 Td[(notice,)-525(this)-525(list)-525(of)-525(conditions,)-525(and)-525(the)-525(following)-525(disclaimer)-525(in)-525(the)]TJ 0 -11.9552 Td[(documentation)-525(and/or)-525(other)-525(materials)-525(provided)-525(with)-525(the)-525(distribution.)]TJ -15.691 -11.9551 Td[(3.)-525(The)-525(name)-525(of)-525(the)-525(MLD2P4)-525(group)-525(or)-525(the)-525(names)-525(of)-525(its)-525(contributors)-525(may)]TJ 15.691 -11.9552 Td[(not)-525(be)-525(used)-525(to)-525(endorse)-525(or)-525(promote)-525(products)-525(derived)-525(from)-525(this)]TJ 0 -11.9552 Td[(software)-525(without)-525(specific)-525(written)-525(permission.)]TJ -26.1517 -23.9103 Td[(THIS)-525(SOFTWARE)-525(IS)-525(PROVIDED)-525(BY)-525(THE)-525(COPYRIGHT)-525(HOLDERS)-525(AND)-525(CONTRIBUTORS)]TJ 0 -11.9552 Td[(``AS)-525(IS'')-525(AND)-525(ANY)-525(EXPRESS)-525(OR)-525(IMPLIED)-525(WARRANTIES,)-525(INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)]TJ 0 -11.9551 Td[(TO,)-525(THE)-525(IMPLIED)-525(WARRANTIES)-525(OF)-525(MERCHANTABILITY)-525(AND)-525(FITNESS)-525(FOR)-525(A)-525(PARTICULAR)]TJ 0 -11.9552 Td[(PURPOSE)-525(ARE)-525(DISCLAIMED.)-525(IN)-525(NO)-525(EVENT)-525(SHALL)-525(THE)-525(MLD2P4)-525(GROUP)-525(OR)-525(ITS)-525(CONTRIBUTORS)]TJ 0 -11.9552 Td[(BE)-525(LIABLE)-525(FOR)-525(ANY)-525(DIRECT,)-525(INDIRECT,)-525(INCIDENTAL,)-525(SPECIAL,)-525(EXEMPLARY,)-525(OR)]TJ 0 -11.9551 Td[(CONSEQUENTIAL)-525(DAMAGES)-525(\050INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)-525(TO,)-525(PROCUREMENT)-525(OF)]TJ 0 -11.9552 Td[(SUBSTITUTE)-525(GOODS)-525(OR)-525(SERVICES;)-525(LOSS)-525(OF)-525(USE,)-525(DATA,)-525(OR)-525(PROFITS;)-525(OR)-525(BUSINESS)]TJ 0 -11.9552 Td[(INTERRUPTION\051)-525(HOWEVER)-525(CAUSED)-525(AND)-525(ON)-525(ANY)-525(THEORY)-525(OF)-525(LIABILITY,)-525(WHETHER)-525(IN)]TJ 0 -11.9551 Td[(CONTRACT,)-525(STRICT)-525(LIABILITY,)-525(OR)-525(TORT)-525(\050INCLUDING)-525(NEGLIGENCE)-525(OR)-525(OTHERWISE\051)]TJ 0 -11.9552 Td[(ARISING)-525(IN)-525(ANY)-525(WAY)-525(OUT)-525(OF)-525(THE)-525(USE)-525(OF)-525(THIS)-525(SOFTWARE,)-525(EVEN)-525(IF)-525(ADVISED)-525(OF)-525(THE)]TJ 0 -11.9552 Td[(POSSIBILITY)-525(OF)-525(SUCH)-525(DAMAGE.)]TJ -ET -1 0 0 1 93.9178 91.633 cm +/F46 9.9626 Tf 130.758 -20.921 Td [(MLD2P4)-1050(version)-525(1.0)]TJ -130.758 -11.956 Td [(MultiLevel)-525(Domain)-525(Decomposition)-525(Parallel)-525(Preconditioners)-525(Package)]TJ 57.534 -11.955 Td [(based)-525(on)-525(PSBLAS)-525(\050Parallel)-525(Sparse)-525(BLAS)-525(version)-525(2.3\051)]TJ -57.534 -23.91 Td [(\050C\051)-525(Copyright)-525(2008)]TJ 104.607 -23.91 Td [(Salvatore)-525(Filippone)-1050(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.956 Td [(Alfredo)-525(Buttari)-3150(University)-525(of)-525(Rome)-525(Tor)-525(Vergata)]TJ 0 -11.955 Td [(Pasqua)-525(D'Ambra)-3675(ICAR-CNR,)-525(Naples)]TJ 0 -11.955 Td [(Daniela)-525(di)-525(Serafino)-1050(Second)-525(University)-525(of)-525(Naples)]TJ -104.607 -35.865 Td [(Redistribution)-525(and)-525(use)-525(in)-525(source)-525(and)-525(binary)-525(forms,)-525(with)-525(or)-525(without)]TJ 0 -11.956 Td [(modification,)-525(are)-525(permitted)-525(provided)-525(that)-525(the)-525(following)-525(conditions)]TJ 0 -11.955 Td [(are)-525(met:)]TJ 10.461 -11.955 Td [(1.)-525(Redistributions)-525(of)-525(source)-525(code)-525(must)-525(retain)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.955 Td [(notice,)-525(this)-525(list)-525(of)-525(conditions)-525(and)-525(the)-525(following)-525(disclaimer.)]TJ -15.691 -11.955 Td [(2.)-525(Redistributions)-525(in)-525(binary)-525(form)-525(must)-525(reproduce)-525(the)-525(above)-525(copyright)]TJ 15.691 -11.955 Td [(notice,)-525(this)-525(list)-525(of)-525(conditions,)-525(and)-525(the)-525(following)-525(disclaimer)-525(in)-525(the)]TJ 0 -11.956 Td [(documentation)-525(and/or)-525(other)-525(materials)-525(provided)-525(with)-525(the)-525(distribution.)]TJ -15.691 -11.955 Td [(3.)-525(The)-525(name)-525(of)-525(the)-525(MLD2P4)-525(group)-525(or)-525(the)-525(names)-525(of)-525(its)-525(contributors)-525(may)]TJ 15.691 -11.955 Td [(not)-525(be)-525(used)-525(to)-525(endorse)-525(or)-525(promote)-525(products)-525(derived)-525(from)-525(this)]TJ 0 -11.955 Td [(software)-525(without)-525(specific)-525(written)-525(permission.)]TJ -26.152 -23.911 Td [(THIS)-525(SOFTWARE)-525(IS)-525(PROVIDED)-525(BY)-525(THE)-525(COPYRIGHT)-525(HOLDERS)-525(AND)-525(CONTRIBUTORS)]TJ 0 -11.955 Td [(``AS)-525(IS'')-525(AND)-525(ANY)-525(EXPRESS)-525(OR)-525(IMPLIED)-525(WARRANTIES,)-525(INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)]TJ 0 -11.955 Td [(TO,)-525(THE)-525(IMPLIED)-525(WARRANTIES)-525(OF)-525(MERCHANTABILITY)-525(AND)-525(FITNESS)-525(FOR)-525(A)-525(PARTICULAR)]TJ 0 -11.955 Td [(PURPOSE)-525(ARE)-525(DISCLAIMED.)-525(IN)-525(NO)-525(EVENT)-525(SHALL)-525(THE)-525(MLD2P4)-525(GROUP)-525(OR)-525(ITS)-525(CONTRIBUTORS)]TJ 0 -11.955 Td [(BE)-525(LIABLE)-525(FOR)-525(ANY)-525(DIRECT,)-525(INDIRECT,)-525(INCIDENTAL,)-525(SPECIAL,)-525(EXEMPLARY,)-525(OR)]TJ 0 -11.955 Td [(CONSEQUENTIAL)-525(DAMAGES)-525(\050INCLUDING,)-525(BUT)-525(NOT)-525(LIMITED)-525(TO,)-525(PROCUREMENT)-525(OF)]TJ 0 -11.956 Td [(SUBSTITUTE)-525(GOODS)-525(OR)-525(SERVICES;)-525(LOSS)-525(OF)-525(USE,)-525(DATA,)-525(OR)-525(PROFITS;)-525(OR)-525(BUSINESS)]TJ 0 -11.955 Td [(INTERRUPTION\051)-525(HOWEVER)-525(CAUSED)-525(AND)-525(ON)-525(ANY)-525(THEORY)-525(OF)-525(LIABILITY,)-525(WHETHER)-525(IN)]TJ 0 -11.955 Td [(CONTRACT,)-525(STRICT)-525(LIABILITY,)-525(OR)-525(TORT)-525(\050INCLUDING)-525(NEGLIGENCE)-525(OR)-525(OTHERWISE\051)]TJ 0 -11.955 Td [(ARISING)-525(IN)-525(ANY)-525(WAY)-525(OUT)-525(OF)-525(THE)-525(USE)-525(OF)-525(THIS)-525(SOFTWARE,)-525(EVEN)-525(IF)-525(ADVISED)-525(OF)-525(THE)]TJ 0 -11.955 Td [(POSSIBILITY)-525(OF)-525(SUCH)-525(DAMAGE.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -492 0 obj << +457 0 obj << /Type /Page -/Contents 493 0 R -/Resources 491 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 486 0 R -/Annots [ 495 0 R ] +/Contents 458 0 R +/Resources 456 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 450 0 R +/Annots [ 455 0 R ] >> endobj -495 0 obj << +455 0 obj << /Type /Annot /Border[0 0 0]/H/I/C[1 0 0] -/Rect [92.9215 739.0056 103.7928 748.4526] +/Rect [92.922 739.006 103.793 748.453] /Subtype /Link -/A << /S /GoTo /D (section.A) >> +/A << /S /GoTo /D (appendix.A) >> >> endobj -494 0 obj << -/D [492 0 R /XYZ 93.9178 740.0018 null] +459 0 obj << +/D [457 0 R /XYZ 93.918 740.002 null] >> endobj 94 0 obj << -/D [492 0 R /XYZ 93.9178 715.0952 null] +/D [457 0 R /XYZ 93.918 715.095 null] >> endobj -491 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F48 214 0 R >> +456 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -498 0 obj << -/Length 347 +462 0 obj << +/Length 174 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(34)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(34)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -648.3688 cm 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -497 0 obj << +461 0 obj << /Type /Page -/Contents 498 0 R -/Resources 496 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 486 0 R +/Contents 462 0 R +/Resources 460 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 450 0 R >> endobj -499 0 obj << -/D [497 0 R /XYZ 141.7385 740.0018 null] +463 0 obj << +/D [461 0 R /XYZ 141.738 740.002 null] >> endobj -496 0 obj << -/Font << /F15 123 0 R /F42 129 0 R >> +460 0 obj << +/Font << /F15 115 0 R /F40 117 0 R >> /ProcSet [ /PDF /Text ] >> endobj -502 0 obj << -/Length 9699 +466 0 obj << +/Length 6522 >> stream -1 0 0 1 93.9178 740.0018 cm 0 g 0 G -1 0 0 1 -93.9178 -740.0018 cm BT -/F42 10.9091 Tf 93.9178 740.0018 Td[(Ref)1(erenc)-1(e)1(s)]TJ/F15 10.9091 Tf 401.542 0 Td[(35)]TJ -ET -1 0 0 1 506.3689 740.0018 cm +/F40 10.9091 Tf 93.918 740.002 Td [(References)]TJ/F15 10.9091 Tf 401.542 0 Td [(35)]TJ 0 g 0 G -1 0 0 1 -506.3689 -740.0018 cm -BT -/F19 14.3462 Tf 93.9178 704.1363 Td[(Refer)-1(ence)-1(s)]TJ -ET -1 0 0 1 93.9178 679.7841 cm +/F17 14.3462 Tf -401.542 -35.866 Td [(References)]TJ 0 g 0 G -1 0 0 1 -93.9178 -679.7841 cm -BT -/F15 10.9091 Tf 99.3724 679.7841 Td[([1])]TJ -ET -1 0 0 1 110.8875 679.7841 cm +/F15 10.9091 Tf 5.454 -24.352 Td [([1])]TJ 0 g 0 G -1 0 0 1 -110.8875 -679.7841 cm -BT -/F15 10.9091 Tf 116.3421 679.7841 Td[(M.)-271(B)-1(r)1(e)-1(zina,)-284(P)84(.)-272(V)84(an)28(\024)472(ek,)]TJ/F20 10.9091 Tf 106.4092 0 Td[(A)-302(Bl)1(ack-Box)-301(Iter)52(a)-1(ti)1(ve)-302(Solver)-301(Base)52(d)-302(on)-302(a)-301(Two-L)51(evel)-301(Schw)-1(ar)1(z)]TJ -106.4092 -13.5492 Td[(Metho)51(d)]TJ/F15 10.9091 Tf 34.5937 0 Td[(,)-333(Com)-1(p)1(uti)1(ng,)-333(63,)-333(1999,)-333(233{263.)]TJ -ET -1 0 0 1 93.9178 643.8139 cm + [-500(M.)-272(Brezina,)-284(P)83(.)-272(V)84(an)27(\024)473(ek,)]TJ/F18 10.9091 Tf 123.379 0 Td [(A)-301(Black-Box)-302(Iter)52(ative)-302(Solver)-301(Base)51(d)-301(on)-302(a)-301(Two-L)51(evel)-301(Schwarz)]TJ -106.409 -13.549 Td [(Metho)51(d)]TJ/F15 10.9091 Tf 34.594 0 Td [(,)-333(Computing,)-333(63,)-334(1999,)-333(233{263.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -643.8139 cm -BT -/F15 10.9091 Tf 99.3724 643.8139 Td[([2])]TJ -ET -1 0 0 1 110.8875 643.8139 cm + -51.564 -22.421 Td [([2])]TJ 0 g 0 G -1 0 0 1 -110.8875 -643.8139 cm -BT -/F15 10.9091 Tf 116.3421 643.8139 Td[(A.)-306(Buttar)1(i,)-311(P)83(.)-306(D')1(Am)27(b)1(ra,)-312(D)1(.)-306(di)-306(S)1(e)-1(ra\014)1(no,)-311(S.)-306(F)1(ilip)1(p)-28(on)1(e)-1(,)]TJ/F20 10.9091 Tf 255.0876 0 Td[(Exten)-1(di)1(n)-1(g)-332(P)-1(SBLAS)-333(t)-1(o)-333(B)1(uil)1(d)]TJ -255.0876 -13.5492 Td[(Par)51(al)-51(l)1(el)-472(S)-1(chwarz)-472(P)-1(r)52(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 159.2054 0 Td[(,)-489(in)-457(,)-489(J.)-458(Dongar)1(ra,)-489(K.)-458(M)1(adse)-1(n)1(,)-489(J.)-458(W)84(as)-1(n)1(ie)-1(wski,)]TJ -159.2054 -13.5492 Td[(editor)1(s)-1(,)-318(Pro)-27(c)-1(ee)-1(d)1(ings)-315(of)-315(P)84(ARA)-315(04)-315(W)83(or)1(ks)-1(h)1(op)-315(on)-314(State)-315(of)-315(th)1(e)-316(Ar)1(t)-315(in)-315(S)1(c)-1(ien)28(ti\014)1(c)-316(Com-)]TJ 0 -13.5492 Td[(pu)1(tin)1(g,)-333(Le)-1(ctur)1(e)-334(Note)-1(s)-333(in)-333(Com)-1(p)1(uter)-333(Science)-1(,)-333(S)1(pri)1(nger,)-333(2005,)-333(593{602.)]TJ -ET -1 0 0 1 93.9178 580.7452 cm + [-500(A.)-306(Buttari,)-312(P)84(.)-306(D'Am)27(bra,)-311(D.)-306(di)-307(S)1(e)-1(r)1(a\014no,)-312(S.)-306(Filipp)-28(one,)]TJ/F18 10.9091 Tf 272.058 0 Td [(Extending)-333(PSBLAS)-333(to)-333(Bu)1(ild)]TJ -255.088 -13.549 Td [(Par)51(al)-51(lel)-472(Schwarz)-473(Pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 159.205 0 Td [(,)-489(in)-458(,)-489(J.)-458(Dongarra,)-490(K.)-458(Madsen,)-489(J.)-458(W)84(as)-1(n)1(iew)-1(ski,)]TJ -159.205 -13.549 Td [(editors,)-319(Pro)-27(cee)-1(d)1(ings)-316(of)-315(P)84(ARA)-315(04)-315(W)83(orkshop)-315(on)-315(State)-315(of)-315(the)-315(Art)-315(in)-315(Scien)28(ti\014c)-315(C)-1(om-)]TJ 0 -13.55 Td [(puting,)-333(Lecture)-334(Notes)-333(in)-333(Computer)-334(S)1(c)-1(ience,)-333(Springer,)-333(2005,)-333(593{602.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -580.7452 cm -BT -/F15 10.9091 Tf 99.3724 580.7452 Td[([3])]TJ -ET -1 0 0 1 110.8875 580.7452 cm + -16.97 -22.421 Td [([3])]TJ 0 g 0 G -1 0 0 1 -110.8875 -580.7452 cm -BT -/F15 10.9091 Tf 116.3421 580.7452 Td[(A.)-380(Buttar)1(i,)-392(P)84(.)-380(D')1(Am)27(br)1(a,)-392(D.)-380(d)1(i)-380(Sera\014)1(no,)-392(S)1(.)-380(Fil)1(ipp)-27(one,)]TJ/F20 10.9091 Tf 262.6214 0 Td[(2LE)-1(V-D2P4:)-546(a)-401(p)51(ackage)-401(of)]TJ -262.6214 -13.5492 Td[(high-p)51(er)1(formanc)51(e)-423(p)-1(r)52(e)51(c)51(onditioners)-423(for)-423(scienti\014c)-424(and)-424(engine)51(eri)1(n)-1(g)-423(ap)-1(pl)1(ic)51(ations)]TJ/F15 10.9091 Tf 364.5046 0 Td[(,)-423(Ap)1(-)]TJ -364.5046 -13.5492 Td[(pl)1(ic)-1(ab)1(le)-462(Algebr)1(a)-462(in)-461(En)1(gin)1(e)-1(erin)1(g,)-494(Comm)27(un)1(ications)-462(an)1(d)-461(C)-1(omp)1(utin)1(g,)-494(18,)-493(3,)-494(2007,)]TJ 0 -13.5492 Td[(223{239.)]TJ -ET -1 0 0 1 93.9178 517.6765 cm + [-500(A.)-380(Buttari,)-392(P)84(.)-381(D'Am)28(bra,)-392(D.)-380(di)-380(Sera\014no,)-391(S.)-381(F)1(ilipp)-28(one,)]TJ/F18 10.9091 Tf 279.591 0 Td [(2LEV-D2P4:)-546(a)-401(p)51(ackage)-401(of)]TJ -262.621 -13.549 Td [(high-p)51(erformanc)51(e)-423(pr)51(e)51(c)51(onditioners)-424(for)-423(scienti\014c)-424(and)-424(engi)1(n)-1(e)52(ering)-424(applic)51(ations)]TJ/F15 10.9091 Tf 364.505 0 Td [(,)-423(Ap-)]TJ -364.505 -13.549 Td [(plicable)-462(Algebra)-461(in)-462(Engineering,)-493(Comm)27(un)1(ications)-462(and)-462(Computing,)-493(18,)-494(3,)-494(2007,)]TJ 0 -13.549 Td [(223{239.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -517.6765 cm -BT -/F15 10.9091 Tf 99.3724 517.6765 Td[([4])]TJ -ET -1 0 0 1 110.8875 517.6765 cm + -16.97 -22.421 Td [([4])]TJ 0 g 0 G -1 0 0 1 -110.8875 -517.6765 cm -BT -/F15 10.9091 Tf 116.3421 517.6765 Td[(P)84(.)-367(D)1('Am)27(b)1(ra,)-375(S)1(.)-367(F)1(ilip)1(p)-28(on)1(e)-1(,)-374(D.)-367(d)1(i)-367(S)1(e)-1(r)1(a\014n)1(o,)]TJ/F20 10.9091 Tf 203.7832 0 Td[(On)-388(th)-1(e)-388(Development)-388(of)-388(P)-1(SBLAS)-1(-)1(b)51(ase)51(d)]TJ -203.7832 -13.5492 Td[(Par)51(al)-51(l)1(el)-380(T)1(w)-1(o-l)1(evel)-379(S)-1(chwarz)-380(Pr)52(e)51(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)1(s)]TJ/F15 10.9091 Tf 206.4885 0 Td[(,)-363(App)1(lied)-357(Numerical)-357(Math)1(e)-1(matics)-1(,)-363(E)1(l-)]TJ -206.4885 -13.5492 Td[(se)-1(vi)1(e)-1(r)-333(S)1(c)-1(ience)-1(,)-333(57,)-333(11-12,)-333(2007,)-333(1181-)-1(1196.)]TJ -ET -1 0 0 1 93.9178 468.1571 cm + [-500(P)83(.)-366(D'Am)28(bra,)-375(S.)-367(Filipp)-27(one,)-375(D.)-367(di)-366(Sera\014no,)]TJ/F18 10.9091 Tf 220.753 0 Td [(On)-388(the)-389(Development)-388(of)-389(PSBLAS-b)52(ase)51(d)]TJ -203.783 -13.55 Td [(Par)51(al)-51(lel)-380(Two-level)-379(Schwarz)-380(Pr)51(e)51(c)51(onditioners)]TJ/F15 10.9091 Tf 206.489 0 Td [(,)-363(Applied)-357(Numerical)-358(Math)1(e)-1(matics,)-363(El-)]TJ -206.489 -13.549 Td [(sevier)-333(Science,)-334(57,)-333(11-12,)-333(2007,)-334(1181-1196.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -468.1571 cm -BT -/F15 10.9091 Tf 99.3724 468.1571 Td[([5])]TJ -ET -1 0 0 1 110.8875 468.1571 cm + -16.97 -22.421 Td [([5])]TJ 0 g 0 G -1 0 0 1 -110.8875 -468.1571 cm -BT -/F15 10.9091 Tf 116.3421 468.1571 Td[(X.)-410(C.)-410(Cai,)-429(M.)-410(Sar)1(kis,)]TJ/F20 10.9091 Tf 109.2504 0 Td[(A)-429(R)51(estricte)51(d)-428(A)51(d)-1(di)1(t)-1(i)1(ve)-429(Schw)-1(ar)1(z)-429(Pr)51(e)52(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-428(for)-428(G)1(en)-1(er)52(al)]TJ -109.2504 -13.5492 Td[(Sp)51(arse)-378(L)-1(i)1(ne)51(ar)-379(Sy)1(stems)]TJ/F15 10.9091 Tf 107.9356 0 Td[(,)-361(SIAM)-355(Jour)1(nal)-356(on)-355(Scien)28(ti\014)1(c)-357(Compu)1(tin)1(g,)-362(21,)-361(2,)-361(1999,)-361(792{)]TJ -107.9356 -13.5492 Td[(797.)]TJ -ET -1 0 0 1 93.9178 418.6376 cm + [-500(X.)-410(C.)-410(Cai,)-430(M.)-410(Sarkis,)]TJ/F18 10.9091 Tf 126.22 0 Td [(A)-429(R)52(estricte)51(d)-429(A)51(dditive)-428(Schwarz)-429(Pr)51(e)51(c)52(onditioner)-429(for)-428(Gener)51(al)]TJ -109.25 -13.549 Td [(Sp)51(arse)-378(Line)51(ar)-379(Systems)]TJ/F15 10.9091 Tf 107.936 0 Td [(,)-361(SIAM)-356(Journal)-356(on)-356(Scien)28(ti\014c)-356(Computing,)-361(21,)-361(2,)-362(1999,)-361(792{)]TJ -107.936 -13.549 Td [(797.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -418.6376 cm -BT -/F15 10.9091 Tf 99.3724 418.6376 Td[([6])]TJ -ET -1 0 0 1 110.8875 418.6376 cm + -16.97 -22.421 Td [([6])]TJ 0 g 0 G -1 0 0 1 -110.8875 -418.6376 cm -BT -/F15 10.9091 Tf 116.3421 418.6376 Td[(X.)-234(C.)-234(Cai,)-253(O.)-234(B.)-234(Wid)1(lun)1(d,)]TJ/F20 10.9091 Tf 124.0849 0 Td[(Domain)-266(De)51(c)51(omp)51(ositi)1(o)-1(n)-266(A)25(lgor)1(ithms)-266(for)-266(Inde\014n)-1(i)1(te)-267(El)-51(l)1(iptic)]TJ -124.0849 -13.5492 Td[(Pr)51(oblem)1(s)]TJ/F15 10.9091 Tf 43.2239 0 Td[(,)-292(SIAM)-282(Jou)1(rnal)-282(on)-282(S)1(c)-1(i)1(e)-1(n)28(ti)1(\014c)-283(an)1(d)-282(Stati)1(s)-1(ti)1(c)-1(al)-282(Com)-1(p)1(uti)1(ng,)-292(13,)-293(1,)-292(1992,)-292(243{)]TJ -43.2239 -13.5492 Td[(258.)]TJ -ET -1 0 0 1 93.9178 369.1182 cm + [-500(X.)-234(C.)-234(Cai,)-254(O.)-234(B.)-234(Widlund,)]TJ/F18 10.9091 Tf 141.055 0 Td [(Domain)-266(De)51(c)51(omp)51(osition)-266(A)25(lgorithms)-266(for)-266(Inde\014n)-1(i)1(te)-267(El)-51(liptic)]TJ -124.085 -13.55 Td [(Pr)51(oblems)]TJ/F15 10.9091 Tf 43.224 0 Td [(,)-293(S)1(IAM)-283(Journal)-282(on)-282(Scien)27(t)1(i\014c)-283(and)-282(Statistical)-282(Computing,)-293(13,)-292(1,)-293(1992,)-292(243{)]TJ -43.224 -13.549 Td [(258.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -369.1182 cm -BT -/F15 10.9091 Tf 99.3724 369.1182 Td[([7])]TJ -ET -1 0 0 1 110.8875 369.1182 cm + -16.97 -22.421 Td [([7])]TJ 0 g 0 G -1 0 0 1 -110.8875 -369.1182 cm -BT -/F15 10.9091 Tf 116.3421 369.1182 Td[(T.)-316(Ch)1(an)-316(an)1(d)-315(T)-1(.)-315(Math)1(e)-1(w,)]TJ/F20 10.9091 Tf 123.6182 0 Td[(Domain)-341(De)51(c)51(omp)51(osition)-341(A)25(lgor)1(ithms)]TJ/F15 10.9091 Tf 165.7101 0 Td[(,)-319(in)-315(A.)-315(Is)-1(erles)-1(,)-319(edi)1(tor,)]TJ -289.3283 -13.5492 Td[(Acta)-334(Nu)1(m)-1(eri)1(c)-1(a)-333(1994,)-333(61{143.)-333(C)-1(am)28(br)1(idge)-334(Un)1(iv)28(ersit)28(y)-333(Pres)-1(s.)]TJ -ET -1 0 0 1 93.9178 333.1479 cm + [-500(T.)-316(Chan)-315(and)-316(T.)-315(Mathew,)]TJ/F18 10.9091 Tf 140.588 0 Td [(Domain)-341(De)51(c)51(omp)51(osition)-342(A)26(lgorithms)]TJ/F15 10.9091 Tf 165.71 0 Td [(,)-319(in)-316(A.)-315(Iserles,)-320(editor,)]TJ -289.328 -13.549 Td [(Acta)-333(Numerica)-334(1994,)-333(61{143.)-333(Cam)27(brid)1(ge)-334(Univ)28(ersit)28(y)-334(Pr)1(e)-1(ss.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -333.1479 cm -BT -/F15 10.9091 Tf 99.3724 333.1479 Td[([8])]TJ -ET -1 0 0 1 110.8875 333.1479 cm + -16.97 -22.421 Td [([8])]TJ 0 g 0 G -1 0 0 1 -110.8875 -333.1479 cm -BT -/F15 10.9091 Tf 116.3421 333.1479 Td[(T.A.)-444(Da)28(vis,)]TJ/F20 10.9091 Tf 61.721 0 Td[(A)25(l)1(gorithm)-460(832:)-664(UMF)1(P)76(A)25(C)1(K)-460(-)-459(a)-1(n)-459(U)-1(nsy)1(mmetric-)1(p)51(at)-1(tern)-460(M)1(ul)1(t)-1(i)1(fr)52(o)-1(ntal)]TJ -61.721 -13.5492 Td[(Metho)51(d)-307(w)-1(i)1(t)-1(h)-307(a)-307(Col)1(umn)-307(P)-1(r)52(e-or)51(der)1(ing)-307(S)-1(tr)52(a)-1(te)51(gy)]TJ/F15 10.9091 Tf 211.2457 0 Td[(,)-289(A)28(C)-1(M)-278(T)84(ransac)-1(t)1(ions)-279(on)-277(Mathematical)]TJ -211.2457 -13.5492 Td[(Sof)1(t)28(w)27(ar)1(e)-1(,)-333(30,)-333(2004,)-333(196{199.)-333(\050See)-334(also)]TJ/F48 10.9091 Tf 184.0304 0 Td[(http://www.cise.ufl.edu/)-525(davis/)]TJ/F15 10.9091 Tf 177.5436 0 Td[(\051)]TJ -ET -1 0 0 1 93.9178 283.6285 cm + [-500(T.A.)-444(Da)28(vis,)]TJ/F18 10.9091 Tf 78.691 0 Td [(A)26(lgorithm)-460(832:)-664(UMFP)77(A)25(CK)-459(-)-460(an)-460(Unsymmetric-p)51(attern)-460(M)1(ultifr)51(ontal)]TJ -61.721 -13.549 Td [(Metho)51(d)-307(with)-307(a)-308(C)1(olumn)-308(Pr)52(e-or)51(dering)-307(Str)51(ate)51(gy)]TJ/F15 10.9091 Tf 211.246 0 Td [(,)-289(A)27(CM)-278(T)83(r)1(ansac)-1(ti)1(ons)-279(on)-278(Mathematical)]TJ -211.246 -13.549 Td [(Soft)28(w)28(are,)-334(30,)-333(2004,)-333(196{199.)-334(\050See)-333(also)]TJ/F46 10.9091 Tf 184.03 0 Td [(http://www.cise.ufl.edu/)-525(davis/)]TJ/F15 10.9091 Tf 177.544 0 Td [(\051)]TJ 0 g 0 G -1 0 0 1 -93.9178 -283.6285 cm -BT -/F15 10.9091 Tf 99.3724 283.6285 Td[([9])]TJ -ET -1 0 0 1 110.8875 283.6285 cm + -378.544 -22.421 Td [([9])]TJ 0 g 0 G -1 0 0 1 -110.8875 -283.6285 cm -BT -/F15 10.9091 Tf 116.3421 283.6285 Td[(J.W)1(.)-423(De)-1(mme)-1(l,)-445(S.)1(C)-1(.)-423(E)1(ise)-1(n)1(s)-1(tat,)-445(J.R.)-423(G)1(ilb)-27(e)-1(r)1(t,)-446(X.)1(S.)-423(Li)-423(an)1(d)-423(J.W.)1(H.)-423(Liu,)-445(A)-423(s)-1(u)1(p)-27(e)-1(rn)1(-)]TJ 0 -13.5492 Td[(o)-28(d)1(al)-398(app)1(roac)27(h)-398(t)1(o)-399(spar)1(s)-1(e)-399(p)1(arti)1(al)-398(piv)28(oti)1(ng,)-414(SIAM)-398(Jou)1(rn)1(al)-398(on)-398(Matri)1(x)-398(Analy)1(s)-1(is)-398(and)]TJ 0 -13.5492 Td[(App)1(lication)1(s)-1(,)-333(20,)-333(3,)-333(1999,)-333(720{755.)]TJ -ET -1 0 0 1 93.9178 234.109 cm + [-500(J.W.)-423(Demmel,)-446(S.C.)-423(Eisenstat,)-446(J.)1(R.)-424(Gilb)-27(ert,)-446(X.S.)-423(Li)-423(and)-423(J.W.H.)-423(Liu,)-446(A)-423(sup)-28(ern-)]TJ 16.97 -13.55 Td [(o)-28(dal)-398(approac)28(h)-398(to)-399(sparse)-398(partial)-398(piv)28(oting,)-414(SIAM)-399(Journ)1(al)-399(on)-398(Matrix)-398(Analysis)-398(and)]TJ 0 -13.549 Td [(Applications,)-333(20,)-334(3,)-333(1999,)-333(720{755.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -234.109 cm -BT -/F15 10.9091 Tf 93.9178 234.109 Td[([10])]TJ -ET -1 0 0 1 110.8875 234.109 cm + -22.424 -22.421 Td [([10])]TJ 0 g 0 G -1 0 0 1 -110.8875 -234.109 cm -BT -/F15 10.9091 Tf 116.3421 234.109 Td[(E.)-392(E)1(fstathi)1(ou,)-407(J.)-392(G.)-392(Gan)1(der,)]TJ/F20 10.9091 Tf 143.3316 0 Td[(Why)-412(R)51(estri)1(ct)-1(e)51(d)-412(A)51(dditive)-412(Schw)-1(ar)1(z)-412(Conver)51(ges)-412(F)77(aster)]TJ -143.3316 -13.5492 Td[(than)-358(A)50(dditi)1(ve)-358(Schw)-1(arz)]TJ/F15 10.9091 Tf 106.3811 0 Td[(,)-333(BI)-1(T)-333(Numerical)-333(Mathematics)-1(,)-333(43,)-333(2003,)-333(945{959.)]TJ -ET -1 0 0 1 93.9178 198.1387 cm + [-500(E.)-392(Efstathiou,)-407(J.)-393(G.)-392(Gander,)]TJ/F18 10.9091 Tf 165.756 0 Td [(Why)-412(R)51(estricte)51(d)-412(A)51(dditive)-412(Schwarz)-412(Conver)51(ges)-412(F)77(aster)]TJ -143.332 -13.549 Td [(than)-358(A)51(dditive)-357(Schw)-1(arz)]TJ/F15 10.9091 Tf 106.381 0 Td [(,)-333(BIT)-334(Numerical)-333(Mathematics,)-333(43,)-334(2003,)-333(945{959.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -198.1387 cm -BT -/F15 10.9091 Tf 93.9178 198.1387 Td[([11])]TJ -ET -1 0 0 1 110.8875 198.1387 cm + -128.805 -22.421 Td [([11])]TJ 0 g 0 G -1 0 0 1 -110.8875 -198.1387 cm -BT -/F15 10.9091 Tf 116.3421 198.1387 Td[(S.)-1384(Fil)1(ipp)-27(one,)-1647(A.)-1385(Buttar)1(i,)]TJ/F20 10.9091 Tf 172.554 0 Td[(PS)-1(B)1(L)-1(AS-2.3)-1325(User')1(s)-1325(Gui)1(de.)-1325(A)-1325(R)51(efer)1(-)]TJ -172.554 -13.5492 Td[(enc)51(e)-1150(Gu)1(ide)-1150(for)-1149(th)-1(e)-1149(P)-1(ar)52(a)-1(l)-50(lel)-1149(Sp)51(a)-1(r)1(se)-1150(BLAS)-1150(Libr)52(ary)]TJ/F15 10.9091 Tf 295.2266 0 Td[(,)-1409(a)27(v)56(ail)1(able)-1194(from)]TJ/F48 10.9091 Tf -295.2266 -13.5492 Td[(http://www.ce.uniroma2.it/psblas/)]TJ/F15 10.9091 Tf 188.998 0 Td[(.)]TJ -ET -1 0 0 1 93.9178 148.6193 cm + [-500(S.)-1385(Filip)1(p)-28(one,)-1648(A.)-1385(But)1(tari,)]TJ/F18 10.9091 Tf 194.978 0 Td [(PSBLAS-2.3)-1325(User's)-1325(Guide.)-1325(A)-1324(R)51(efer-)]TJ -172.554 -13.549 Td [(enc)51(e)-1150(Guide)-1150(for)-1149(the)-1150(Par)51(al)-51(lel)-1150(Sp)51(arse)-1150(BLAS)-1149(Libr)51(ary)]TJ/F15 10.9091 Tf 295.227 0 Td [(,)-1410(a)28(v)56(ailable)-1194(from)]TJ/F46 10.9091 Tf -295.227 -13.55 Td [(http://www.ce.uniroma2.it/psblas/)]TJ/F15 10.9091 Tf 188.998 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -93.9178 -148.6193 cm -BT -/F15 10.9091 Tf 93.9178 148.6193 Td[([12])]TJ -ET -1 0 0 1 110.8875 148.6193 cm + -211.422 -22.421 Td [([12])]TJ 0 g 0 G -1 0 0 1 -110.8875 -148.6193 cm -BT -/F15 10.9091 Tf 116.3421 148.6193 Td[(S.)-311(Fil)1(ipp)-27(one,)-316(M.)-311(Cola)-56(j)1(ann)1(i,)]TJ/F20 10.9091 Tf 133.243 0 Td[(PS)-1(B)1(L)-1(AS:)-338(A)-338(Libr)52(a)-1(r)1(y)-338(f)1(or)-338(Par)51(al)-51(l)1(el)-338(Line)51(ar)-337(A)25(lgebr)52(a)-338(Com-)]TJ -133.243 -13.5492 Td[(putation)-333(on)-333(Sp)51(arse)-332(Matric)52(es)]TJ/F15 10.9091 Tf 133.5747 0 Td[(,)-311(A)28(C)-1(M)-305(T)83(ran)1(s)-1(action)1(s)-307(on)-305(Mathematical)-306(Sof)1(t)28(w)27(ar)1(e)-1(,)-311(26,)-311(4,)]TJ -133.5747 -13.5492 Td[(2000,)-333(527{550.)]TJ -ET -1 0 0 1 93.9178 91.633 cm + [-500(S.)-312(Filip)1(p)-28(one,)-316(M.)-312(Cola)-56(j)1(anni,)]TJ/F18 10.9091 Tf 155.667 0 Td [(PSBLAS:)-338(A)-338(Libr)51(ary)-338(for)-337(Par)51(al)-51(lel)-338(Line)51(ar)-338(A)26(lgebr)51(a)-338(Com-)]TJ -133.243 -13.549 Td [(putation)-333(on)-332(Sp)51(arse)-333(Matric)52(es)]TJ/F15 10.9091 Tf 133.575 0 Td [(,)-311(A)27(CM)-306(T)84(ransactions)-306(on)-306(Mathematical)-306(Soft)28(w)28(are,)-312(26,)-311(4,)]TJ -133.575 -13.549 Td [(2000,)-333(527{550.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -501 0 obj << +465 0 obj << /Type /Page -/Contents 502 0 R -/Resources 500 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 486 0 R +/Contents 466 0 R +/Resources 464 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 450 0 R >> endobj -503 0 obj << -/D [501 0 R /XYZ 93.9178 740.0018 null] +467 0 obj << +/D [465 0 R /XYZ 93.918 740.002 null] >> endobj -504 0 obj << -/D [501 0 R /XYZ 93.9178 693.3333 null] +468 0 obj << +/D [465 0 R /XYZ 93.918 693.333 null] >> endobj -187 0 obj << -/D [501 0 R /XYZ 93.9178 697.7693 null] +169 0 obj << +/D [465 0 R /XYZ 93.918 697.769 null] >> endobj -286 0 obj << -/D [501 0 R /XYZ 93.9178 659.6778 null] +258 0 obj << +/D [465 0 R /XYZ 93.918 659.678 null] >> endobj -287 0 obj << -/D [501 0 R /XYZ 93.9178 596.6091 null] +259 0 obj << +/D [465 0 R /XYZ 93.918 596.609 null] >> endobj -288 0 obj << -/D [501 0 R /XYZ 93.9178 535.6617 null] +260 0 obj << +/D [465 0 R /XYZ 93.918 535.662 null] >> endobj -298 0 obj << -/D [501 0 R /XYZ 93.9178 484.021 null] +268 0 obj << +/D [465 0 R /XYZ 93.918 484.021 null] >> endobj -249 0 obj << -/D [501 0 R /XYZ 93.9178 436.6228 null] +230 0 obj << +/D [465 0 R /XYZ 93.918 436.623 null] >> endobj -250 0 obj << -/D [501 0 R /XYZ 93.9178 387.1033 null] +231 0 obj << +/D [465 0 R /XYZ 93.918 387.103 null] >> endobj -393 0 obj << -/D [501 0 R /XYZ 93.9178 349.0118 null] +357 0 obj << +/D [465 0 R /XYZ 93.918 349.012 null] >> endobj -505 0 obj << -/D [501 0 R /XYZ 93.9178 298.8863 null] +469 0 obj << +/D [465 0 R /XYZ 93.918 298.886 null] >> endobj -299 0 obj << -/D [501 0 R /XYZ 93.9178 249.9729 null] +269 0 obj << +/D [465 0 R /XYZ 93.918 249.973 null] >> endobj -190 0 obj << -/D [501 0 R /XYZ 93.9178 214.0027 null] +172 0 obj << +/D [465 0 R /XYZ 93.918 214.003 null] >> endobj -189 0 obj << -/D [501 0 R /XYZ 93.9178 164.1802 null] +171 0 obj << +/D [465 0 R /XYZ 93.918 164.18 null] >> endobj -500 0 obj << -/Font << /F42 129 0 R /F15 123 0 R /F19 105 0 R /F20 171 0 R /F48 214 0 R >> +464 0 obj << +/Font << /F40 117 0 R /F15 115 0 R /F17 103 0 R /F18 163 0 R /F46 195 0 R >> /ProcSet [ /PDF /Text ] >> endobj -508 0 obj << -/Length 5475 +472 0 obj << +/Length 3579 >> stream -1 0 0 1 141.7385 740.0018 cm 0 g 0 G -1 0 0 1 -141.7385 -740.0018 cm BT -/F15 10.9091 Tf 141.7385 740.0018 Td[(36)]TJ/F42 10.9091 Tf 203.2648 0 Td[(MLD2P4)-377(User)67(')-1(s)-377(a)-1(nd)-378(Refe)1(r)-1(e)1(n)-1(ce)-377(G)-1(uid)-1(e)]TJ -ET -1 0 0 1 554.1896 740.0018 cm +/F15 10.9091 Tf 141.738 740.002 Td [(36)]TJ/F40 10.9091 Tf 203.265 0 Td [(MLD2P4)-378(User)67('s)-378(and)-378(Reference)-377(Guide)]TJ 0 g 0 G -1 0 0 1 -412.4511 -35.8655 cm 0 g 0 G -1 0 0 1 -141.7385 -704.1363 cm -BT -/F15 10.9091 Tf 141.7385 704.1363 Td[([13])]TJ -ET -1 0 0 1 158.7082 704.1363 cm +/F15 10.9091 Tf -203.265 -35.866 Td [([13])]TJ 0 g 0 G -1 0 0 1 -158.7082 -704.1363 cm -BT -/F15 10.9091 Tf 164.1628 704.1363 Td[(X.)-408(S)1(.)-408(Li,)-426(J.)-408(W.)-408(Demm)-1(el,)]TJ/F20 10.9091 Tf 125.4471 0 Td[(Sup)51(erLU)]TJ + [-500(X.)-408(S.)-408(Li,)-427(J.)-408(W.)-408(Demmel,)]TJ/F18 10.9091 Tf 147.872 0 Td [(Sup)51(erLU)]TJ ET -1 0 0 1 331.8544 704.1363 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.3455 0.1992 l -S +1 0 0 1 331.854 704.336 cm +[]0 d 0 J 0.398 w 0 0 m 3.345 0 l S Q -1 0 0 1 -331.8544 -704.1363 cm BT -/F20 10.9091 Tf 335.1999 704.1363 Td[(DIST)1(:)-426(A)-427(Sc)51(alable)-426(Distri)1(bute)51(d-mem)1(ory)-426(Sp)51(a)-1(r)1(se)]TJ -171.0371 -13.5492 Td[(Dir)52(e)51(ct)-343(Solver)-342(f)1(o)-1(r)-342(Unsymm)1(etric)-342(L)-1(i)1(ne)51(ar)-343(Sy)1(stems)]TJ/F15 10.9091 Tf 222.3825 0 Td[(,)-320(A)28(CM)-317(T)83(r)1(ansac)-1(ti)1(ons)-317(on)-316(Math)1(e)-1(mat-)]TJ -222.3825 -13.5492 Td[(ical)-333(Sof)1(t)27(w)28(are,)-333(29,)-333(2,)-333(2003,)-334(110{140.)]TJ -ET -1 0 0 1 141.7385 654.5224 cm +/F18 10.9091 Tf 335.2 704.136 Td [(DIST:)-426(A)-427(Sc)51(alable)-426(Distribute)51(d-memory)-426(Sp)51(arse)]TJ -171.037 -13.549 Td [(Dir)51(e)51(ct)-342(Solver)-343(for)-342(Unsymmetric)-342(Line)51(ar)-343(Systems)]TJ/F15 10.9091 Tf 222.382 0 Td [(,)-320(A)28(CM)-317(T)83(ransactions)-316(on)-317(Mathemat-)]TJ -222.382 -13.549 Td [(ical)-333(Soft)28(w)27(are,)-333(29,)-333(2,)-334(2003,)-333(110{140.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -654.5224 cm -BT -/F15 10.9091 Tf 141.7385 654.5224 Td[([14])]TJ -ET -1 0 0 1 158.7082 654.5224 cm + -22.425 -22.516 Td [([14])]TJ 0 g 0 G -1 0 0 1 -158.7082 -654.5224 cm -BT -/F15 10.9091 Tf 164.1628 654.5224 Td[(Y.)-333(Saad)1(,)]TJ/F20 10.9091 Tf 44.5455 0 Td[(Iter)52(at)-1(i)1(ve)-358(metho)51(ds)-358(for)-357(sp)51(arse)-357(line)51(ar)-357(systems)]TJ/F15 10.9091 Tf 202.9803 0 Td[(,)-333(2nd)-333(edi)1(tion,)-333(S)1(IAM,)-333(2003)]TJ -ET -1 0 0 1 141.7385 632.0068 cm + [-500(Y.)-333(Saad,)]TJ/F18 10.9091 Tf 66.97 0 Td [(Iter)51(ative)-358(metho)52(d)-1(s)-357(for)-358(sp)51(arse)-358(line)52(ar)-358(systems)]TJ/F15 10.9091 Tf 202.981 0 Td [(,)-333(2nd)-334(edi)1(tion,)-334(SIAM,)-333(2003)]TJ 0 g 0 G -1 0 0 1 -141.7385 -632.0068 cm -BT -/F15 10.9091 Tf 141.7385 632.0068 Td[([15])]TJ -ET -1 0 0 1 158.7082 632.0068 cm + -269.951 -22.515 Td [([15])]TJ 0 g 0 G -1 0 0 1 -158.7082 -632.0068 cm -BT -/F15 10.9091 Tf 164.1628 632.0068 Td[(B.)-506(S)1(mith,)-548(P)84(.)-505(B)-1(j)1(orstad,)-548(W.)-505(Gr)1(opp,)]TJ/F20 10.9091 Tf 177.8705 0 Td[(Domain)-516(De)51(c)51(omp)51(osi)1(t)-1(i)1(on:)-777(Par)51(al)-51(l)1(el)-516(M)1(ultil)1(evel)]TJ -177.8705 -13.5492 Td[(Metho)51(ds)-432(for)-432(El)-51(l)1(iptic)-432(P)-1(ar)1(t)-1(i)1(al)-432(Di\013er)51(ential)-432(Equations)]TJ/F15 10.9091 Tf 244.3085 0 Td[(,)-434(C)-1(am)28(br)1(idge)-414(Univ)28(ersit)28(y)-414(Pr)1(e)-1(ss)-1(,)]TJ -244.3085 -13.5492 Td[(1996.)]TJ -ET -1 0 0 1 141.7385 582.3928 cm + [-500(B.)-505(Smith,)-549(P)84(.)-506(Bjorstad,)-548(W.)-506(Gropp,)]TJ/F18 10.9091 Tf 200.295 0 Td [(Domain)-516(De)51(c)51(omp)51(osition:)-776(Par)51(al)-51(lel)-516(Multilevel)]TJ -177.87 -13.549 Td [(Metho)51(ds)-432(for)-432(El)-51(liptic)-433(Parti)1(al)-433(Di\013er)51(ential)-432(Equations)]TJ/F15 10.9091 Tf 244.308 0 Td [(,)-435(Cam)28(bridge)-414(Univ)28(ersit)28(y)-415(Press,)]TJ -244.308 -13.55 Td [(1996.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -582.3928 cm -BT -/F15 10.9091 Tf 141.7385 582.3928 Td[([16])]TJ -ET -1 0 0 1 158.7082 582.3928 cm + -22.425 -22.515 Td [([16])]TJ 0 g 0 G -1 0 0 1 -158.7082 -582.3928 cm -BT -/F15 10.9091 Tf 164.1628 582.3928 Td[(M.)-317(S)1(nir)1(,)-321(S)1(.)-318(O)1(tto,)-321(S)1(.)-317(Huss)-1(-Le)-1(d)1(e)-1(r)1(m)-1(an)1(,)-321(D.)-317(W)84(alk)28(e)-1(r)1(,)-321(J)1(.)-318(Don)1(garra,)]TJ/F20 10.9091 Tf 295.0792 0 Td[(MPI:)-342(The)-343(Compl)1(et)-1(e)]TJ -295.0792 -13.5492 Td[(R)51(efer)51(enc)51(e.)-357(V)76(ol)1(ume)-358(1)-357(-)-358(The)-357(MPI)-358(C)1(or)51(e)]TJ/F15 10.9091 Tf 179.3562 0 Td[(,)-333(s)-1(econd)-333(editi)1(on,)-333(MIT)-333(Press)-1(,)-333(1998.)]TJ -ET -1 0 0 1 141.7385 546.3281 cm + [-500(M.)-317(Snir,)-321(S.)-317(Otto,)-321(S.)-317(Huss-Lederman,)-321(D.)-317(W)83(alk)28(er,)-321(J.)-317(Dongarra,)]TJ/F18 10.9091 Tf 317.504 0 Td [(MPI:)-343(The)-343(Complete)]TJ -295.079 -13.549 Td [(R)51(efer)51(enc)51(e.)-357(V)76(olume)-357(1)-358(-)-358(The)-358(MPI)-357(Cor)51(e)]TJ/F15 10.9091 Tf 179.356 0 Td [(,)-333(second)-334(edition,)-333(MIT)-333(Press,)-334(1998.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -546.3281 cm -BT -/F15 10.9091 Tf 141.7385 546.3281 Td[([17])]TJ -ET -1 0 0 1 158.7082 546.3281 cm + -201.781 -22.516 Td [([17])]TJ 0 g 0 G -1 0 0 1 -158.7082 -546.3281 cm -BT -/F15 10.9091 Tf 164.1628 546.3281 Td[(K.)-546(St)-27()527(u)1(b)-28(en,)]TJ/F20 10.9091 Tf 60.6903 0 Td[(A)25(l)1(gebr)51(aic)-554(M)1(ulti)1(grid)-554(\050AMG)1(\051:)-554(an)-554(Intr)51(o)51(ducti)1(o)-1(n)-554(with)-554(A)-1(ppl)1(ic)51(ations)]TJ/F15 10.9091 Tf 310.6702 0 Td[(,)-600(in)]TJ -371.3605 -13.5492 Td[(A.)-493(Sc)28(h)-28()528(ul)1(le)-1(r)1(,)-534(U.)-493(T)83(r)1(otte)-1(n)29(b)-28(erg,)-533(C.)-493(Oos)-1(terlee,)-534(edi)1(tors,)-534(M)1(ulti)1(grid)1(,)-534(Academic)-494(Pr)1(e)-1(ss)-1(,)]TJ 0 -13.5492 Td[(2000.)]TJ -ET -1 0 0 1 141.7385 496.7141 cm + [-500(K.)-547(St)-27()527(ub)-27(en,)]TJ/F18 10.9091 Tf 83.115 0 Td [(A)26(lgebr)51(aic)-554(Multigrid)-554(\050AMG\051:)-554(an)-554(Intr)51(o)51(duction)-554(with)-554(Applic)51(ations)]TJ/F15 10.9091 Tf 310.67 0 Td [(,)-600(in)]TJ -371.36 -13.549 Td [(A.)-493(Sc)27(h)-27()527(uller,)-533(U.)-493(T)83(rotten)28(b)-28(erg,)-534(C.)-493(Oosterlee,)-534(editor)1(s)-1(,)-533(Multigrid,)-533(Academic)-494(Press,)]TJ 0 -13.549 Td [(2000.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -496.7141 cm -BT -/F15 10.9091 Tf 141.7385 496.7141 Td[([18])]TJ -ET -1 0 0 1 158.7082 496.7141 cm + -22.425 -22.516 Td [([18])]TJ 0 g 0 G -1 0 0 1 -158.7082 -496.7141 cm -BT -/F15 10.9091 Tf 164.1628 496.7141 Td[(R.)-408(S.)-407(T)83(uminar)1(o,)-427(C.)-408(T)83(on)1(g,)]TJ/F20 10.9091 Tf 130.124 0 Td[(Par)51(al)-51(l)1(el)-426(S)-1(m)1(o)51(o)-1(the)51(d)-426(A)50(ggr)52(e)51(gation)-427(Mu)1(ltigr)1(id:)-597(A)50(ggr)52(e)51(gation)]TJ -130.124 -13.5492 Td[(Str)51(ate)51(gies)-369(on)-370(Massi)1(vely)-369(Pa)-1(r)52(al)-51(l)1(el)-370(M)1(achines)]TJ/F15 10.9091 Tf 200.3252 0 Td[(,)-349(in)-346(J.)-345(Donn)1(e)-1(ll)1(e)-1(y)84(,)-349(e)-1(d)1(itor,)-349(P)1(ro)-28(ce)-1(edin)1(gs)-347(of)]TJ -200.3252 -13.5492 Td[(Su)1(p)-27(e)-1(rCompu)1(tin)1(g)-334(2000,)-333(Dall)1(as)-1(,)-333(2000.)]TJ -ET -1 0 0 1 141.7385 447.1001 cm + [-500(R.)-408(S.)-408(T)83(uminaro,)-427(C.)-408(T)84(ong,)]TJ/F18 10.9091 Tf 152.549 0 Td [(Par)51(al)-51(lel)-426(Smo)51(othe)51(d)-427(A)51(ggr)51(e)52(gation)-427(Multigrid:)-597(A)51(ggr)51(e)51(gation)]TJ -130.124 -13.549 Td [(Str)51(ate)51(gies)-369(on)-370(Massively)-369(Par)51(al)-51(lel)-370(Machines)]TJ/F15 10.9091 Tf 200.325 0 Td [(,)-349(in)-346(J.)-347(Don)1(nelley)83(,)-349(e)-1(d)1(itor,)-350(Pro)-27(ce)-1(edin)1(gs)-347(of)]TJ -200.325 -13.549 Td [(Sup)-28(erComputing)-333(2000,)-333(Dallas,)-333(2000.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -447.1001 cm -BT -/F15 10.9091 Tf 141.7385 447.1001 Td[([19])]TJ -ET -1 0 0 1 158.7082 447.1001 cm + -22.425 -22.516 Td [([19])]TJ 0 g 0 G -1 0 0 1 -158.7082 -447.1001 cm -BT -/F15 10.9091 Tf 164.1628 447.1001 Td[(P)84(.)-288(V)84(an)28(\024)472(ek,)-297(J)1(.)-288(M)1(andel)-287(and)-287(M.)-287(B)-1(r)1(e)-1(zin)1(a,)]TJ/F20 10.9091 Tf 178.101 0 Td[(A)25(l)1(gebr)51(aic)-315(Mul)1(tigri)1(d)-316(by)-315(S)-1(m)1(o)51(o)-1(the)51(d)-316(A)51(ggr)52(e)51(gat)-1(i)1(on)]TJ -178.101 -13.5492 Td[(for)-357(Se)51(c)51(on)-1(d)-357(a)-1(nd)-358(F)77(ou)1(rth)-358(Or)52(d)-1(er)-357(El)-51(li)1(pt)-1(i)1(c)-358(Pr)51(oblem)1(s)]TJ/F15 10.9091 Tf 223.3438 0 Td[(,)-333(Com)-1(p)1(uti)1(ng,)-333(56,)-333(1996,)-333(179-)-1(196.)]TJ -ET -1 0 0 1 141.7385 91.633 cm + [-500(P)83(.)-287(V)83(an)28(\024)472(ek,)-297(J.)-287(Mandel)-288(and)-287(M.)-288(Brezina,)]TJ/F18 10.9091 Tf 200.526 0 Td [(A)26(lgebr)51(aic)-316(Multigrid)-315(by)-316(Smo)51(othe)51(d)-316(A)52(ggr)51(e)51(gation)]TJ -178.101 -13.549 Td [(for)-358(Se)51(c)52(on)-1(d)-357(and)-358(F)77(ourth)-358(Or)51(der)-358(El)-51(liptic)-357(P)-1(r)52(oblems)]TJ/F15 10.9091 Tf 223.344 0 Td [(,)-333(Computing,)-333(56,)-334(1996,)-333(179-196.)]TJ 0 g 0 G -1 0 0 1 412.4511 0 cm 0 g 0 G +ET endstream endobj -507 0 obj << +471 0 obj << /Type /Page -/Contents 508 0 R -/Resources 506 0 R -/MediaBox [0 0 595.2756 841.8898] -/Parent 486 0 R +/Contents 472 0 R +/Resources 470 0 R +/MediaBox [0 0 595.276 841.89] +/Parent 450 0 R >> endobj -509 0 obj << -/D [507 0 R /XYZ 141.7385 740.0018 null] +473 0 obj << +/D [471 0 R /XYZ 141.738 740.002 null] >> endobj -510 0 obj << -/D [507 0 R /XYZ 141.7385 715.0952 null] +474 0 obj << +/D [471 0 R /XYZ 141.738 715.095 null] >> endobj -289 0 obj << -/D [507 0 R /XYZ 141.7385 670.4335 null] +261 0 obj << +/D [471 0 R /XYZ 141.738 670.434 null] >> endobj -186 0 obj << -/D [507 0 R /XYZ 141.7385 647.3119 null] +168 0 obj << +/D [471 0 R /XYZ 141.738 647.312 null] >> endobj -191 0 obj << -/D [507 0 R /XYZ 141.7385 600.4252 null] +173 0 obj << +/D [471 0 R /XYZ 141.738 600.425 null] >> endobj -284 0 obj << -/D [507 0 R /XYZ 141.7385 562.2392 null] +256 0 obj << +/D [471 0 R /XYZ 141.738 562.239 null] >> endobj -285 0 obj << -/D [507 0 R /XYZ 141.7385 514.7465 null] +257 0 obj << +/D [471 0 R /XYZ 141.738 514.746 null] >> endobj -188 0 obj << -/D [507 0 R /XYZ 141.7385 463.0113 null] +170 0 obj << +/D [471 0 R /XYZ 141.738 463.011 null] >> endobj -506 0 obj << -/Font << /F15 123 0 R /F42 129 0 R /F20 171 0 R >> +470 0 obj << +/Font << /F15 115 0 R /F40 117 0 R /F18 163 0 R >> /ProcSet [ /PDF /Text ] >> endobj -324 0 obj << -/Length1 745 -/Length2 581 -/Length3 532 -/Length 1858 ->> -stream -%!PS-AdobeFont-1.1: CMSY7 1.0 -%%CreationDate: 1991 Aug 15 07:21:52 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMSY7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.035 def -/isFixedPitch false def -end readonly def -/FontName /QUZMMF+CMSY7 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -readonly def -/FontBBox{-15 -951 1252 782}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª/ ùÈ­éÙÀX¸~›id}S5žQ!gt¤ê¡âµŽÃkÑJc;•r´NŒ^ô¢¬µŠ ¦X€5¿.ØSyƒŠ– þ+'êIÃqV˜œ…â:¿r㚉#,Ùô#È ždèBZ£¾÷ÞÖ *R’*"7Ù¨ÝyÝçÒQI¿e©ŒŸâ±ÏrZp(IJÿæ8»¦±#†Çó+£PÖ.¢Õ²NæÂÂCÍ;ý ð+[i-{'¾Ç)ïÜù/•ÝëPphÞ Qãì¸äCæ¾ -A¡øÈœ;Ák5,4C«of^¬^ Ä"ìüXáWeBL‘œ'>¢@¾{.•·‰Ñ'b[¼·>PPë.±Èåó­D§W­,Å=‘{ý #VX†î6ÐÃÝnz¢ïœÄÇñTž`šqÃÂæN&=`¥~Ÿ+GãH —Š¯c†Šê%Ú=TF{vÒð/€—Ò„ÚfwsjÏì «ñj›-$ô{f¶wˆkªxzØeµ÷Žä4ªG·°ñ$JB%ÜÆpý©"&âÆgÂ4B˜ÐW[ßx-–ƒnÊâ)Ç¡~(÷›'?òCE-¨…Š‹ËQeSO9–ËØÙsÛY=`lzü%ži$/neu¶…*­TVyæõBÜ¡ m¢MÉ/¿|ä‹8ySx{+Ë„s®Òߨ39ÓžôÝ:QXE'¬:“c *àÈœ?/úvwC±'káæHÕñ¨0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream +475 0 obj +[892.9] endobj -325 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 511 0 R -/FirstChar 0 -/LastChar 0 -/Widths 512 0 R -/BaseFont /QUZMMF+CMSY7 -/FontDescriptor 323 0 R ->> endobj -323 0 obj << -/Ascent 750 -/CapHeight 683 -/Descent -194 -/FontName /QUZMMF+CMSY7 -/ItalicAngle -14.035 -/StemV 93 -/XHeight 431 -/FontBBox [-15 -951 1252 782] -/Flags 4 -/CharSet (/minus) -/FontFile 324 0 R ->> endobj -512 0 obj -[893 ] +476 0 obj +[674.8 778.2 674.6 1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 530.4 539.2 431.6 675.4 571.4] endobj -511 0 obj << -/Type /Encoding -/Differences [ 0 /minus 1/.notdef] ->> endobj -321 0 obj << -/Length1 803 -/Length2 1857 -/Length3 532 -/Length 3192 +477 0 obj +[877 323.4 384.9 323.4 569.5 569.5 569.5] +endobj +478 0 obj +[458.3 458.3 416.7 416.7 472.2 472.2 472.2 472.2 583.3 583.3 472.2 472.2 333.3 555.6 577.8 577.8 597.2 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 791.7 791.7 583.3 583.3 638.9 638.9 638.9 638.9 805.6 805.6 805.6 805.6 1277.8 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000] +endobj +479 0 obj +[566.2 523.3 571.8 644 590.3 466.4 725.7 736.1 750 621.5 571.8 726.7 639 716.5 582.1 689.8 742.1 767.4 819.4 779.9 586.7 750.7 1021.9 639 487.8 811.6 1222.2 1222.2 1222.2 1222.2 379.6 379.6 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 379.6 379.6 963 638.9 963 638.9 658.7 924.1 926.6 883.7 998.3 899.8 775 952.9 999.5 547.7 681.6 1025.7 846.3 1161.6 967.1 934.1 780 966.5 922.1 756.7 731.1 838.1 729.6 1150.9 1001.4 726.4 837.7 509.3 509.3 509.3 1222.2 1222.2 518.5 674.9 547.7 559.1 642.5 589 600.7 607.7 725.7 445.6] +endobj +480 0 obj +[531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 295.1 826.4] +endobj +481 0 obj +[826.4 295.1 826.4] +endobj +482 0 obj +[470.1 429.5 467 533.2 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 694.5 660.7 490.6 632.1 882.1 544.1 388.9 692.4 1062.5 1062.5 1062.5 1062.5 295.1 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 826.4 531.3 826.4 531.3 559.7 795.8 801.4 757.3 871.7 778.7 672.4 827.9 872.8 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8 474.4 479.5 491.3] +endobj +483 0 obj +[525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] +endobj +484 0 obj +[777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 500 500 611.1 500] +endobj +485 0 obj +[444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 570 517 571.4 437.2 540.3 595.8 625.7 651.4 622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.7 361.1 572.5 484.7 715.9 571.5 490.3 465] +endobj +486 0 obj +[613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 306.7 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 511.1 306.7 306.7 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 460 664.4 463.9 485.6 408.9] +endobj +487 0 obj +[319.4 436.1 436.1 552.8 844.4 319.4 377.8 319.4 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 319.4 319.4 844.4 844.4 844.4 523.6 844.4 813.9 770.8 786.1 829.2 741.7 712.5 851.4 813.9 405.6 566.7 843.1 683.3 988.9 813.9 844.4 741.7 844.4 800 611.1 786.1 813.9 813.9 1105.5 813.9 813.9 669.4 319.4 552.8 319.4 552.8 319.4 319.4 613.3 580 591.1 624.4 557.8 535.6 641.1 613.3 302.2 424.4 635.6 513.3 746.7 613.3 635.6 557.8 635.6 602.2 457.8 591.1 613.3 613.3 835.6 613.3 613.3] +endobj +488 0 obj +[638.9 638.9 958.3 958.3 319.4 351.4 575 575 575 575 575 869.4 511.1 597.2 830.6 894.4 575 1041.7 1169.4 894.4 319.4 350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 575 575 575 575 575 575 575 575 575 575 575 319.4 319.4 350 894.4 543.1 543.1 894.4 869.4 818.1 830.6 881.9 755.6 723.6 904.2 900 436.1 594.4 901.4 691.7 1091.7 900 863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6] +endobj +489 0 obj +[583.3 555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 500 500] +endobj +490 0 obj +[489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8] +endobj +491 0 obj +[350 300 500 500 500 500 500 500 500 500 500 500 500 300 300 300 750 500 500 750 726.9 688.4 700 738.4 663.4 638.4 756.7 726.9 376.9 513.4 751.9 613.4 876.9 726.9 750 663.4 750 713.4 550 700 726.9 726.9 976.9 726.9 726.9 600 300 500 300 500 300 300 500 450 450 500 450 300 450 500 300 300 450 250 800 550 500 500 450 412.5 400 325 525 450] +endobj +492 0 obj +[625 625 937.5 937.5 312.5 343.7 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 812.5 875 562.5 1018.5 1143.5 875 312.5 342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7 593.7 500] +endobj +493 0 obj << +/Length1 1483 +/Length2 9915 +/Length3 0 +/Length 11398 >> stream -%!PS-AdobeFont-1.1: CMMI7 1.100 -%%CreationDate: 1996 Jul 23 07:53:53 +%!PS-AdobeFont-1.1: CMBX10 1.00B +%%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.100) readonly def +/version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI7) readonly def +/FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def +/Weight (Bold) readonly def +/ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /PIOLWB+CMMI7 def +/FontName /IZMJER+CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 84 /T put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 85 /U put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put dup 101 /e put +dup 56 /eight put +dup 102 /f put +dup 12 /fi put +dup 53 /five put +dup 52 /four put +dup 103 /g put +dup 45 /hyphen put +dup 105 /i put +dup 107 /k put dup 108 /l put +dup 109 /m put dup 110 /n put +dup 111 /o put +dup 49 /one put +dup 112 /p put +dup 46 /period put +dup 114 /r put +dup 115 /s put +dup 55 /seven put +dup 54 /six put +dup 116 /t put +dup 51 /three put +dup 50 /two put +dup 117 /u put dup 118 /v put +dup 119 /w put +dup 48 /zero put readonly def -/FontBBox{0 -250 1171 750}readonly def +/FontBBox{-301 -250 1164 946}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸM×v9ß2¤Ö#:œ¯i±QßÓ?À–.¬n>¿¸­%j”zGm >Nj›S]Éñ¾Ñ)Å7uÕÖ‡‡¥Œ“ŸÕÚU±•¹QhÈ4)½-‡‚×p#êz£™É{8YãаGP¸9 ññ¼)Ü"¼­PìÆ£Æ3ГzYèYåZùõgp_P÷C߬CÄçÜ”DÎþC'šý<|”(‰£Ròÿ€l/ø³ëIÕxªXÏüMYz©”í„»è²ntÔŸlõAv·)|Ú*iQ€P3|ºTxë˜LÝ" ®ÙʃÃ?¼ÈAwõ·pŸÆÒ‹:rï÷)ˆÁ6,ç›Nœ{?åˆé‚J¼oÑA剳‘Js¤(0T9†$ø“Õ¶Ã'§î'0ÞÞj—°œ%&Æ4öLŸ„wÍQcK¦HüpöYÉ ÀBÀÖ¶ŒÑß6Ö$ób¸ZXÖZŽmýX>ù§šB# µ9Žëxôµ¨šÒ¥à6IUJ½eG#˜ÿ݆>@P1o(ýß‹UøÖc˜Cо¤"‰ø[ØD‰´.ÇÅ)Ó>çè;@Ly›ŽŒˆ—‡ÍÅÍ—¿ˆ`50/¬—+Rª1›¯&e7ØH¿ê?ž¡Û6Ÿy÷@Vxžó™!+Ô ãÈSkä,ŒÆ×ýÎM8Ú±kp/ ñh(”Ç!:ÿÔŸÃH'5˜…²II,LIlí9°®ª#ozð)”‹ç®bÿúz“¼¡¡&õÚ2eöŠpDQ/‹T‘UÝ^ riFÅQdþ‹'@8¾„—¸ÑNL5‰`ññëNC§‡ø®Amÿ·îô3ÂIÒQûþ™AJ¼Ùqla_YÐ&¢ÆíP„èmj‹Naz!vœ¥×4à°÷%.™ª™Ý§„Çèã\Ö–ŒÝb`Û+#·ð`‹\ܠḄ¦FÒr=„Z -¬ŠšLç2-·Ãàêq; ]˜Æ¼®±n²l›²•,ÅLt4‹žœä–-`_ÛM¾ùÁ–yç檭õÁ -RBéÙŠ€1äjùý¼•GO._í=] Viæ°šlê@¦øÒå%fÀé½…YB1ëq4MèÅkºÛ—¥í$_’ÔêN>÷à‚B0¢}á\äSZh«–?sÈ€¯‚O“ËwJªXmQ¦6ž½²8›XN3A?¶Œ¾Â(Y}ND§$R{óÕ¿‚&è¦ ÝÕ\ËÔìëñ€šù\á‘z½Þº¿ˆmå—±*¶P äk«ð¯-‡ì£°‹›è´BÀF‘ *Íñ♹8ÊcýšlmÎþot‘÷g³J‚(OƒóÑlj^– Øðü~^&¹Y´üç0ìÜTI\žÍ1¬'6ÆØ“Bcx˜3|'ÅÞ]PxªTi\ú[¼`¼ßýß»,·Ï}Ìy*•ãÚ1PAÄ@H³1}c >­¾¦Iä|N¶_ŸDÅåkغãš^ï©~+($ÑïÙ65)øœ¾qAŒahˆÒJƒÒ¾ùU“¸Ð(Á¬qísš3F•ªjÃékXµìÖõ[;Õ8vâ;;ñ¨$=Nž™Ynú… \XÖ=ˆ(iv/…Á·Qg¦“¼_,\ðüç-÷]C 3­ÓˆG;¨öV-¾ˆòÑÚî|yn^ç4ÆÒÏ@Édx¬¬]Ö*Ú~Ð.|8îÿùÌD?,©ÕÀõ㋽ö»5¾©ØçÁÑ`aøû”0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -322 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 513 0 R -/FirstChar 84 -/LastChar 118 -/Widths 514 0 R -/BaseFont /PIOLWB+CMMI7 -/FontDescriptor 320 0 R ->> endobj -320 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /PIOLWB+CMMI7 -/ItalicAngle -14.04 -/StemV 81 -/XHeight 431 -/FontBBox [0 -250 1171 750] -/Flags 4 -/CharSet (/T/e/l/n/v) -/FontFile 321 0 R ->> endobj -514 0 obj -[675 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 542 0 0 0 0 0 0 361 0 706 0 0 0 0 0 0 0 571 ] -endobj -513 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 84/T 85/.notdef 101/e 102/.notdef 108/l 109/.notdef 110/n 111/.notdef 118/v 119/.notdef] ->> endobj -318 0 obj << -/Length1 752 -/Length2 1167 -/Length3 532 -/Length 2451 ->> -stream -%!PS-AdobeFont-1.1: CMR7 1.0 -%%CreationDate: 1991 Aug 20 16:39:21 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /OSJUQO+CMR7 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 43 /plus put -dup 49 /one put -readonly def -/FontBBox{-27 -250 1122 750}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\õ¸Ê»ŸülÃñé®2ò4ë`þ}ãI•±¬ÿRBŽ¢ ŽÔýsã“\ëÔ­pÀˆzEÈG®ÞA‘ÌÛ‹a4_Ðpý0ÄóuØAÝEG)¢Q³ö®|ˆ‚8B‚ýÖ*èîþÞdGWjú'¤‚©Ê×0Viäx²†ò#(ò®„ï=äœ@'q¢IªÁúT5i -(Ñ´t†`È ?á¿E<øG¢KO„d¦<ê섪"ý^t„~Bkh•}Ñõ -_2…áùXñÇðâoî|c™Ž¡2‹É„WÈ FÒÂü4bI¦dìû¢ÎP6Χ5ŸÊÀö†Ã»'îúEÕH÷½LæbjOƒÆŸé:S$:x6/0ŽÌ€Ý Iá7Íɬºã’‚âjzMŒ›•ò'½¢¢¯©ÚëóPC€²¢ÏŸë.š?³½>€ŸÆ)4‡§E^³¸yÒ´½F”+±$8–&G"ËYl?e½Y¹jt±+²šT¯I2! nþXKÀt`‰Ë±~h„]{> Qîäaãiσ\¾mFÇU#GŽvh2uöÙnÃ8½­WÕ;Rõ4¬ŸàEjÑ1‚B4²b¬ «¤;bëÚ9y[®lþ—V:Pªáñ•ˆ‡9òg`†©\šJ~ óO>%V‰0­ø ݬ;cJÔºjYr¤t’6Ïy«¤ql4˜QoÙ«~ØôoÁ†‹_=6xßqªw,ñ÷Ý",kñŽðÏ·§oÆÑ -Ó#ÁvI«7_ ÏÍfz°”âÇË!yÄ(3)Éä5ç¤*к Y³øb#a€³M?ÎØ3G%wºÍG*LÕÇ4}. f0ôFópË)¨@Cÿ™”Þê—,W š”€Ú'˜’Ó §—'—]8Ñ7¦Go´}yÈ-IõÞ‚Î%³Ðú ;ÂdŒÝ»í·‡ýƒyåï%‰•I«+³-tŒ7šóÊˬ'Åä$· ì;›9ð†ûWJ]µ.ôIùuŒò®Zò8CôpÛ-ÿ–ç$X‰ ÊÓ½„TÔÖ¶c+÷…DßEA1ñâ_oKC5³à—Ýö@Æâ‡Ç{®¡ !^þqñ‘ü¹©î‚RˆBÖ­ÍdºŠpÿ’ï=Ìþ‚?E‹‡­ „Á¶™OS°97õ­òºkøîúÖò,+³Ä©Iö^+͆S# -ia®s”1 +'_¥ÝÔm Ã'©ädº,ÁÒ]XÒé{&ßíØ41ú¼Y9HY‡_\½*2Õ|$Êg}å/MØ#ž9§]ržîZRaà^3cs!7烬y¡D6ÅÇ$1/Ñnh¨0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -319 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 515 0 R -/FirstChar 43 -/LastChar 49 -/Widths 516 0 R -/BaseFont /OSJUQO+CMR7 -/FontDescriptor 317 0 R ->> endobj -317 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /OSJUQO+CMR7 -/ItalicAngle 0 -/StemV 79 -/XHeight 431 -/FontBBox [-27 -250 1122 750] -/Flags 4 -/CharSet (/plus/one) -/FontFile 318 0 R ->> endobj -516 0 obj -[877 0 0 0 0 0 569 ] -endobj -515 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 43/plus 44/.notdef 49/one 50/.notdef] ->> endobj -278 0 obj << -/Length1 935 -/Length2 2339 -/Length3 532 -/Length 3806 ->> -stream -%!PS-AdobeFont-1.1: CMEX10 1.00 -%%CreationDate: 1992 Jul 23 21:22:48 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.00) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMEX10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /BMKFPS+CMEX10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /parenleftbig put -dup 1 /parenrightbig put -dup 26 /braceleftbigg put -dup 80 /summationtext put -dup 88 /summationdisplay put -dup 110 /braceleftBig put -dup 111 /bracerightBig put -dup 112 /radicalbig put -readonly def -/FontBBox{-24 -2960 1454 772}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\õ¸ÊƧ¾µÐ"våÿ¯*áÞo$1”Ð|¬Ã#ó`ˆ¡ݧ’ó2Y†ý°«ßÈŽK@瘉!ÕQìgëÊDÀVWðÜ‘>{0¥óá3{i‡þ¼Eù‰ÈÜmÀ­W~?ÐÕB ®(Ç4ñ0Á3´„"¾Ô†9¢·NLòçâJ™óGàô9LæN¬µIWn‰NRê¾Y[ÉdmŒ+«IfN•|=‰ÄÇcÕèßú¬G5‚ÊàyJ©i,dRhŠt§¦§­ ¸©x<#^Áê!V&³1‚qEÞ1[nÁ³Ø¶{3#÷aêôÂ#»!LLk-(PAÐh1ŸIƒvØïºYˆK£1Œ[ÉV„òàYÀѲ¤Y*óa¸¬F®nH¼ ˆŽD‡hƒPé­PtîHH'ä¬ÃŒ¼=³(ÝÕ³A¯šf(º8J—‹˜H:cüÄXÐã¼æýƒ~ °Û˜zkc·F8üŸ!¥ŒhGž…"VpלÝå¬ wõ©”Êp _ñùÆ>ýà#5ðJ ر*àfvÃbª£•Íï -Ià3YeòûA˜I—™ÎÌȪ]%RdxLÓ ->‚•ˆŽû -Ý׺ÄZîîÍÿzG¨ŽiØLžW&Á¬i£K_ èîNߟJÞ‡h $ØÕ·>ðN­E—|¨­sÔÝEÞf£¸%†L5X€Ý& È–Ñ«†’YtŽ˜öqN$&žÕó(4Fd:ùñÎgÛ/]>§~ç4Ò¾Ö#ùsæ„ ­,<&fÝMÑÁÃ/‚c…å_ ÉHãuK{HƒÝ«û€RV·Ô—ôÓÙ-ÇR?J-" sèmk¸Û<3C"†©8&Ž vÙâ§ø$âq¼iÇB·Â³^ «;]5“8ìåf(!êœ(vo3švã Ø)W•]¤gn§ÓlÙ¾:j©tÏl+r÷ŒA”Á¼Ò¨¨ÁЩ‡¾N?€KF•òXød“qu€h ‚ì¬Ç]¯ò)yHcƒ"Q—ëS}D9É9AWÌ*”œJ®Å¼%·O¹™ðOÊÛÉŠ_v}ÊéKby é'²/\S!ÀÄ>G÷9¬)4:ЖãW¯¤ˆwuЮèz ­~sr»Ý ~)FáVã7rn_ã²¾h¼f±˜¯<¥Êž ÑÓ#ÓxEÙ,®uaÈøõç)~fŸ®#GÇùñÍÍ`ÞšÛ¥uÂi ˆÅßs”ƒ%ÛÂåΈ)Õû ÄP4ˆöÄZ؉8 -A _gPsB1uUÿ±÷8íIÏúuÐT† -Å…Ûþ_=½ -—-Øèz7ÔIœ¯"þ ‚=sy·´$%‡&sÅ«Ž =ôa±‚ò3-… æ•:%‘¾qqÀßiéù±_¦Ö¸ÐÛ¸™¸¤ -> wŸœ·æßL¬ÇDKâ×{gö& -4²N%pî.¯óh‹‡ìó7‰ãMHSF`ÐYv9Î>±m.(²çd®Fn˜ oè 53MT -«<çÃST Iµ¼<ÀW&à¹cúI>ðgàÞ »À Ë -§ÁCÄA‰ÛkmSù:…d_ŠQ=]MxY5œpÛÊöQÀâ…«wu)«rWØ)-nÒ[$‹q¸¡tóšR;¯ø…~æMè¤Ü‡´V Z¯Æ—kS…’uŽàMì(Õ+Ð<û0îž¹­Ìí—Z7_UïÉ>Ö÷_èul¼q$UƒŸê(³÷h(2:Sù2Â;ïÍÌÊGáoÿµÄ~9Õšç³}uVãÖ-«Ù^Ÿ­ÀÇ%äP vUöXKb…|«%–4ñ&‹‡¶ª¯ aŸ_œ0Tï—Ãù¢wñ}GßÀLPžÒR3ø­=Vgy K'òøCEÄCݽ½HÛV îÂxñEÁv}›Â=soÇ\{¡ëÚ¾Ž"™×c>QœF@òµ(í ÄþYð:©Üûe&ˆl`°ZÈ+I«ülrà^™Ë–¸N®€ë”G ÜЗDòasðô5õ1ŠÓ£ÿ»ÚÚì¦É ?–D}|éç^ÅME>¨®B˜R™ÊÈ’ö÷ýãq§ `4°ØI"h±¡oˆ=Ëy†`]W·«Ûð”Ž1`ÑžÕ{±t»rÒ§Äà‚ –’¨ôtŸv ›« -¤zFí9)[?h|)b•gÉä3Œ½×.&ìæŸïBºj: X3;™àáÓG¯÷k„š(´ƒB,ûÖvç0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -279 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 517 0 R -/FirstChar 0 -/LastChar 112 -/Widths 518 0 R -/BaseFont /BMKFPS+CMEX10 -/FontDescriptor 277 0 R ->> endobj -277 0 obj << -/Ascent 40 -/CapHeight 0 -/Descent -600 -/FontName /BMKFPS+CMEX10 -/ItalicAngle 0 -/StemV 47 -/XHeight 431 -/FontBBox [-24 -2960 1454 772] -/Flags 4 -/CharSet (/parenleftbig/parenrightbig/braceleftbigg/summationtext/summationdisplay/braceleftBig/bracerightBig/radicalbig) -/FontFile 278 0 R ->> endobj -518 0 obj -[458 458 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 750 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1056 0 0 0 0 0 0 0 1444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 667 1000 ] -endobj -517 0 obj << -/Type /Encoding -/Differences [ 0 /parenleftbig/parenrightbig 2/.notdef 26/braceleftbigg 27/.notdef 80/summationtext 81/.notdef 88/summationdisplay 89/.notdef 110/braceleftBig/bracerightBig/radicalbig 113/.notdef] ->> endobj -275 0 obj << -/Length1 777 -/Length2 1473 -/Length3 532 -/Length 2782 ->> -stream -%!PS-AdobeFont-1.1: CMMI6 1.100 -%%CreationDate: 1996 Jul 23 07:53:52 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.100) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI6) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -end readonly def -/FontName /AXIIQG+CMMI6 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 14 /delta put -dup 67 /C put -dup 105 /i put -readonly def -/FontBBox{11 -250 1241 750}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÖ¨ð[G¯•ï(©ÅaÛܘÄ|õRPé6n¶ý=: ªbãÕÙ9s2m4{~ÜC‘ÉßD…¸ü˜Ô%Åx’Ýð4,¡C v•ƒjÖû-ÄÁ?x”vä„ynhQ¯`¦?°ÞfÕ\ñ -Ö[“BËhnVGXÉadÿ§±èÇ&óÇ»D»Òƒš¤gWGßaá0¥^)|¥ð*?ùZòõHqr@w©8~'‡š–I­_o3P¬¢f4½Î!ìÐãYåê^afRoëà 0 Ÿ½Á¼/›bïîăEª˜øЪT·¤€çBfQ†\ŽDNÛyŒ~ -öå§íˆeaÕ‰‹R†a}8ÒÎÉU‰Z ySráºq'tû©±5Òàã\ÿ~…¹å;ª (Ï?¯^ËAK®Þ”fñ¸êöÇ:*mÈVoö2˜ø¬õ)õA]«­³foþLÓ˜t\7¸g3&Ü5é#eªŒ5qeÿ];¨unwï¨E«ÿâ9È,}éïî#WºD‹=«Ö^ä'Ìžß›]J›q],Tˆm–« þ|Í>=V¾ÈDÕZ*Z±†ˆ4×£Ù†§âDó˜‚%Ý6öV½6ðá>Îñ" Ó¡[¼%Rëq2t5—·h]òQS2TšyIA@»Ò©cÖ'é÷ |œþ3Ý1ÎOd~ -ÉZTò³_Ãhï]ßá“Åâŵ÷¾ù -à^×µGºS76×ã1Ñz'ˆã²C½UHÕè g¡ G(µ¿ ô‚?â’W ûf±%™[*&¿TÀ”è&¿€õ":|6éóÊAæ $< UßD‰Ô5 >Ó0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -276 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 519 0 R -/FirstChar 14 -/LastChar 105 -/Widths 520 0 R -/BaseFont /AXIIQG+CMMI6 -/FontDescriptor 274 0 R ->> endobj -274 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /AXIIQG+CMMI6 -/ItalicAngle -14.04 -/StemV 85 -/XHeight 431 -/FontBBox [11 -250 1241 750] -/Flags 4 -/CharSet (/delta/C/i) -/FontFile 275 0 R ->> endobj -520 0 obj -[566 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 884 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 446 ] -endobj -519 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 14/delta 15/.notdef 67/C 68/.notdef 105/i 106/.notdef] ->> endobj -272 0 obj << -/Length1 786 -/Length2 1479 -/Length3 532 -/Length 2797 ->> -stream -%!PS-AdobeFont-1.1: CMR8 1.0 -%%CreationDate: 1991 Aug 20 16:39:40 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /SBCCLH+CMR8 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 48 /zero put -dup 49 /one put -dup 50 /two put -dup 61 /equal put -readonly def -/FontBBox{-36 -250 1070 750}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\ôéÒ@[œÕ6]nÎÕ×hÖmlha‹ŒH+4Œ£Ž›¹ºüú­œ/?Ð3¶&˜nÔ=œ“a6E¸#’ÕÊá|´~.‚ÜÔ…Ë¡w,ä"»rƒ­g[eH§êi¨ƒìª>žÎu†ÖÏ -ŒÕWÇåת>©~ºÓ–Ñ¿ÏJmdv‡Aíê -[û¿4|ܾ.×V–z¶ÛÄ_¢£1. F¥ýf« |Xÿîĸ9^Rw] -ü×ÛŠ³31S\D¤ËKZÍW`– äP”Š^êÝ3ê ’eÛŽÈ Í8`2?Òl;ˆÈŠ!eXxh -Dfú@=$»—*I¸BÁ€äÒXÉÔ!ÐWx-b1ƒ £™³ÅòòÝC; p™À}½âhÐÿíQi¼Ð=H²ðX­bØgŒbmÇ£óR,™º–>ù_ŠÑ¸°ÓQ! -äÂÅZØž¶Ar“]< £˜óîîÃQ–jt8ï?îB,mN3v լǵ+í˜Kú­6ï t‹Ð{äAJc—Q%ÒrúØ?væÿø60¾RmXsŤ+pú‘Ǹiñ:þUësõ‚ƒ‡“¸Ì)káÜÏPýWË\~Ú;’í” 7 T“.ÅN ¹„ü¤«}.¡‚¼ñ&:¢D°~ÀêzŸpŸ0C„Ë_§HòO­šzCÔêBy½AOve1k`ÃG|f2¾þ8—µŒ'j0&®òuk6sw,› I´Ù5¨&{oƒ¶®¤ÚÄõ³P}p2ªd -«ãC¤é½ÏAœ§!8ˆ²Zô⓪ÎÙ¦½ÇŽaÚBLeÌ…÷b¾±ls†ëLK›1B¹f/HÏ[UÜD&Ÿ—V{˜FB16³¥h¹X"·lñÍLÐÆMÅTÌ.„?³pSêþ˜Z˜Ïž@‡«+½/kb/t9{ä¾ú ÌQ£ 2l6TµåHµý[æ¿ý .ñ*”‰!9† ¦wm€ð·ÃéŽ4‘†Šk%glÝqðÛ×ÏQOc±[l~bï›â'ëDÌø‹‹_Ý¡^b—`ýê & O–°[écN™ÒåDObÂkº×frîɉH·ÙÈ®»·ÉË¡l½üY]zÓù&Q¶=PÌ~’ôélMârþéO¿å„9yÓh¼å7OonôXl«i—'w —¨h.uésƒ-4ý{´Žè -9âcÃO `+Þ÷‚§¼ñ‚Ëm†ãø.f›)K¾›ZÒœÑ/©ÝªÈ«M»f?ŒPG,|óϹ®q-ƒ³™‰÷Z‡¦ÈÏy#nžábòly@Jn¸zÅ2¢œGÉE]=̤Ž+&@ë<Ñ~ÆÄãõ³h'ßu Í&¾÷ÅBÐ3+*/hì¬:,•ÃñuvÞ½¹GƒCîb-øÈ÷Ĉí–izzÿeŽ«ÞõÔ =–‘•ÚôË»ài¬¿ºKŠ¢á_±ëxÌÆæjx¡Ð%¼­ZUí«L¹ˆà1ú„(Sܦe]/™­^åáìÀÇ ÙÃamaÏ[Š‘±a²`û¾ÙTQ)|F¨½ÍÇ‹•êú+•ìÏmCð›[êPß+¨<Âý!ˆw ÉfR”< àIFVpGž‘æjgÿn•œ¹ rÎ-îìbì¥béGÛ±l\¯hë|—è±í•ÓXÌ#;øˆhPjnð<*§ZÍMGœK²à8ÿõp~ƒ­> endobj -271 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /SBCCLH+CMR8 -/ItalicAngle 0 -/StemV 76 -/XHeight 431 -/FontBBox [-36 -250 1070 750] -/Flags 4 -/CharSet (/zero/one/two/equal) -/FontFile 272 0 R ->> endobj -522 0 obj -[531 531 531 0 0 0 0 0 0 0 0 0 0 826 ] -endobj -521 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 48/zero/one/two 51/.notdef 61/equal 62/.notdef] ->> endobj -269 0 obj << -/Length1 765 -/Length2 745 -/Length3 532 -/Length 2042 ->> -stream -%!PS-AdobeFont-1.1: CMSY8 1.0 -%%CreationDate: 1991 Aug 15 07:22:10 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMSY8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.035 def -/isFixedPitch false def -end readonly def -/FontName /WAGXZO+CMSY8 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -dup 2 /multiply put -readonly def -/FontBBox{-30 -955 1185 779}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª/ ùÈ­éÙÀX¸~›id}S5žQ!gt¤ê¡âµŽÃkÑJc;•r´NŒ^ô¢¬µŠ ¦X€5¿.ØSyƒŠ– þ+'êIÃqV˜œ…â:¿r㚉#,Ùô#È ždèBZ£¾÷ÞÖ *R’*"7Ù¨ÝyÝçÕü! ƒž[Rß»*|]Ž~Š [êCÖ¨ía¯[#Ô™ Ø÷«jY!4ØJÀ‡¦Í€õÝÙÒ"¬±Â3&§ejc\J$Í2Ëýø62¸ª6áwõIaàUÇI¯òränÌFB/€Ð“(Hp%#ûÚÌO.,ÊÕñsü¾nݸt­%\ÕåÀøb9?Ë_\ œ<+µˆn6ü<Ì!H<:Á“HZFéÒ+× ”äÔZÝ›ñÌ\ö¥ VT¬ àÚ=µc±8@º0÷.Qã¼€cˆºø<}93’¼¼"wqÍË—n“0%0ú?Kï4—Ô0*H8JÎÿÁU”bê_`Ü$^„™Øæ—²À”ÎíònáZƒr ìæOïA«èݧ¾5ñNºÔ ï¿ÃÎ{IÖþu-œñcNhÜĨ)ËCnm ’ƒK@øÜŠ‚-Bͱ{R{›9éɖη I_õ€¢Ó&þ8Í"–Ýù´Ç9 ÞCsû Hë¤'³o ý)©ìGÕm ‹`ŠOÆ/=õ™‹=~?0å´ÑΕ,Õ~\Tö%ëÌqK)èor89îrø±Ù¥ŽõBÈPüYÜÔ¥‚ T¿lÕpë4űêãI=+r¼p%«Æ ˜À!í»<¸Ê'y1# – ¶Šõ0æwªy»rÈ(X¸|ãX> endobj -268 0 obj << -/Ascent 750 -/CapHeight 683 -/Descent -194 -/FontName /WAGXZO+CMSY8 -/ItalicAngle -14.035 -/StemV 89 -/XHeight 431 -/FontBBox [-30 -955 1185 779] -/Flags 4 -/CharSet (/minus/multiply) -/FontFile 269 0 R ->> endobj -524 0 obj -[826 0 826 ] -endobj -523 0 obj << -/Type /Encoding -/Differences [ 0 /minus 1/.notdef 2/multiply 3/.notdef] ->> endobj -266 0 obj << -/Length1 994 -/Length2 4891 -/Length3 532 -/Length 6417 ->> -stream -%!PS-AdobeFont-1.1: CMMI8 1.100 -%%CreationDate: 1996 Jul 23 07:53:54 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.100) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI8) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -end readonly def -/FontName /NFUDKK+CMMI8 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 14 /delta put -dup 65 /A put -dup 67 /C put -dup 69 /E put -dup 72 /H put -dup 76 /L put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 105 /i put -dup 106 /j put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 114 /r put -dup 115 /s put -readonly def -/FontBBox{-24 -250 1110 750}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÖ¨ð[G¯•ï(©ÅaÛܘÄ|õRPé6n¶ý=: ªbãÕÙ9s2m4{~ÜC‘ÉßD…¸ü˜Ô%Åx’Ý÷Sd,Õ&©jÎÚA x"±ÐŸ—”æmѬ,+;ÆþÅboB|Õ®œTÇ÷bÃoI³Âåæ*ûVÜî‡DZ©BÁJæÑþ©ÏŸª2a{YŒå‡ï0Qâ(÷/e@­™§AòGÆ€挄éÑп™ª]w}ˆ§ÓÎÒêgô®a輕çÚ8.‚ݲ° ÝcS,tã¾^ÅU ¼»j³‚†×q.’o†–ƒr¸!N›]@Ájß -ýGÄ“75uÆÊ‘ämˆÞ$æ‚ÞÄKWêŠøNWÔVF2PØ,KPË» 6™2aƒóÔbw;S³ÉæÛBÖ³ö{‚ Õu&D“C½ùúÏhN¾ã›e^±½L2Ib^ÇžY6þ2Ùò"CSò¤l5Xï!ok²£º÷R¾ì6ÄD UjïìôTº|»§S{ËëÂG3:‰‰6A…|Ùõžº °£ÙºJ 3•3kLÚK¦EnMpúÙ½«·òq¼lHÙßZo®xV ވ˘U§>ŽU©Ïó^îo°\WáóŽbY<&~…~S'_ZÁþ `¤žgקZW(U7ÛTg°4{{Ór§»ˆ ÷çsÄ^=ç²ò£Pé0ëœê¨Ð@õ._ßÌ^×–c]ÀDÉd0“š‹«ƒXžä,¡a÷<øä5Âݦ°u0ÅoHdêxÇwÄâÂôE}…g»í£/ú÷ è(Š ™ã¼:.‚ÙÈ€€Vj™{E§~$>>o !4;_Àú¸Hd¨[+öªhÜ)DÒn…çï«ï¨Ïý“ÀâH:B§øhV¿aK›õ’ 1ñºéxg LÔ”}w“¡ÑÂå“Zõ¿êŠ“Ú»›ÌµFê1GR !0n@0›nWJìTîwèïÅʳÅ'B-âÜM;xøùðëZ¤ŠO½ åYXÀÊ%55ðÖ’›qŽÂzÈ#ŽÝ!4=ÄôÏpËãÈ•4S¾Ý€„Õ2£öú2º/Ò‹jÙœÎÏÚftÁñ<ǨQ–ס»µÁÐ 6vû»»y²ø¬´˜eÑ8죵…CíJUÌx± ©ÏÕÍâ[‹Ĥ"\oM•I‘[KKŸ!t@WdT7’(Ä?Ÿù+¿¿O'³•É}«Ä“¢€"}Sí"ƒF€Åšsˆ³6ndïâaT4M!¿Ÿ…RVîÔeDg=ã}¢¦2´¬òžw;,§ŽÃEC^&?­ž~Î܉NGÝFï‹íøš–ù²Ge`&¶D(®ƒ¬N:=|•$ZÃäÀR1­n—¿†²ÈPÀÌ»À= °?¼¬_ÌxÙGoÒº¹à‡¯ VìmZC*X0…1>}Ãê\g`lИÜÍ6Ë`Ø]ð\;¨ +NÝ/ã˜$pjZVÆŠ^áØY>¨‹º>¥ü†—Ž,Û.'aòš0:_…ÁÃ8z瘱åβyr u¸Ñê¥t^žñ -›cb+¯Ð å1%b>а€§“h“-X?”®}°ú¦†ÃÿÌsk‘=p³n¼°Hãât(êóz.»éö Ç¥há4®í’Ž7r߇í’€—É=‹±=B;¥-½ ànsGË\7”1ß÷Ä\L Õ“«› µAÞ¸¡zŒo%ÉílÏJ³W@!ÊŸý;ø• À4r¨àM22|Ø`%*Ù:c˜¤'¾ ùËNùö¶f;UÏoÛkÛÌJ[ Š]-ñ‰º[ªLÉÃlΔûŠÏA:x» ÝEÃ1žè'BèÉ–ˆô`@Ýœ¿ -ëóqÑk3A"l=ñ^üþ§yןë}AŠdt´úÛÎù6j%¼Kƒü¤`‰t"Oâ¾k$ëc’I˜fU7;(G‘ €“F©×RòD@$t)|Le{U)ŠÙé½qŒÖGp‡V#Ä}ú¸—¿ïf2óÙ Þþ×m1Ó“¢ÑÓÆõ"‘qSU[(BæúÓl./µ}ôl'/Pþð(œ¨g8^`µ!¹æÁ™ˆ”´¥íWb´³>¹î“%$W£¶Ñ‹·AhW2ytƒ½ÈßÙjªº¨[Îkøµ¶B4ÖÍg¯ã¢ó•ÍwL¬y‡.Š‚I¡KlgÛ &ФÂÿ„bïˆõ›J Un±&žÏ}$ ’M@ÃìXlŒD²sk›†f×B›™> œ$L:B£±y\Æu‹¶7œ²”’] lThpÌš0G1ë‚T>_“æ<©S’5ÅÅŠ ¶b*¯ÌuIÛÈÆÈÉëVWÉ—‹U¯=A=×<ú¬IcÌðU_1Új{Ÿ”Ç0-z„ i‚&¢Ën;ùÙù:öƒûèRÀßEÓŸ;yÞ°Xº Û©h¹(šðh•&ƯÞW^ª[°`éÑèË¿ßq¢u·H[ÖXôµÓ?Æ硺¢¸Ò‰ µÄ&ª¤ëï;VqÍxÛ‰ ¥Q÷ +ªÇoç -.¤÷Å8iŒÇ5Ž~°{‹­øÝôäÜŸ½àãÂÝ“S›§p½ôói5ni*nêç@Õ*™g3ø¡ÂÒ(S`¨¬Ä"Ömÿ–|H»¦J ɽ­»Væ¯%ïébZžjA ²xM§äë—ËD¤LðâLaR(`,06ûÇƆôÉ·W‹Ç_ñUo¾ÅøJlÀüó/ÞGÉT6? ©©ù‡²xdR`qÚ ´x]…͵êHƒ¶(Ä §Q»@¼$LT•ãg9±åx+1û͵Æìlò:õÄÙ™ÞT¸XIGü;ìp 6)m¯n’¨äÉ·b¬D«úÔ)éú|ÕoìÛ -=פQ‡`°ŽZ™¥·¹k ²Þ«}ù^4}dç‘O.+1ÀoÍãð2’ô!WÒR…ÉÅt[¦ŸºÄ¢(bvÞ!®‹r{V¿.Åqa'Á¯åºŒŸxL -dÅi).[Võ;‘'c1:{å¾6@Ä]PZ×,Vciß6•å]´«(ÏfÚ9îÁq¶ÀŽÚ™¦,oÒ²ç‡ °BJ« exéù°@²©ãèþ¹èÿË©#Gïr ú¤èÑk¢œP8Lg/õðÓ·!¸<Š]ÛÕ"Êbò®X_ <ÎÈu°7÷‡÷²’ØœëÍ߇\Ál.ƒ&÷D“ÃÐ/uGîûŽN³,´ã(E¢ÞzR9Z>ÂÓ}ïÔƒqbäW„çÉŸ"ÏŸ@†0Þê‹Æy-γ¡#ô3j?¯$Ùùî<Çqôÿ¨•œoŠPj.9älMü¼ŠL‚Çq¤³¤åŠ6;Û&?±E´D)‰Û! çÑ]¹Mliå«£¼çÁ‹dgYJ -‚£}Ö=¢ÀlºÝ÷ ì¼æ}ùñ÷”á?ȃʗ¥‘hfÞrüæàÓɽXüDcÊ¡“ŒÈfEØÚŒÆw±moh)füpD†!hÝÁ‡ü¸DÒìâë÷¤‘PLµ&zY¸¾˜[ö9XõGËÞ FÝ ozµ¶ŸvƒäÏ.²ïW~j>Y´:6aéts½ØNrü»oÀ÷h8H`’2à›‹s~ƒ)Š×Óƒ½yooí2>¡Ò>†ÂYQðµóœW–u>;öÿÀ-Ùœ<ä,ïE3rÅÚý/gº.Š¼§ÖÃ#RÏ/ÃÆÅÀffÁ1㸺|zMæT!øDÔz—Ùü/x‡*úà)²;bkZkµá±ÒŽ1økLQŸ\œ“ ý°5µìÝ’ÃÉå/X¹Ð»WÒõ–ÝíbŒ~îE‚Ê.Câ6äµòcWS‰‚ñ©|Lµߦž "èãæ¢cž,¤/Tá2ɺSÙzóì¼=Œþ~ÌžgÑ+f)9A’XŠäÕ(3×™FY²9Óê[€'ÖvÍÀӒÄ„ÁÇ7k’5™z>›-ã¶ÕGh=UE¯Q#Ǹ“LñΞ÷–Þ< 9¸c@<Þ´‡mdkF²t¼TÐTá iŠ­w¤Xó-4á^;qK¹L}ºèï®IB¶¹÷R†Ä& HÔxç1ÙÐNwö ÈîÏò¨þv̸³¡§ËH>úi,œÐÕN~I’G£Å-PC½D•¦‹0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -267 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 525 0 R -/FirstChar 14 -/LastChar 115 -/Widths 526 0 R -/BaseFont /NFUDKK+CMMI8 -/FontDescriptor 265 0 R ->> endobj -265 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /NFUDKK+CMMI8 -/ItalicAngle -14.04 -/StemV 78 -/XHeight 431 -/FontBBox [-24 -250 1110 750] -/Flags 4 -/CharSet (/delta/A/C/E/H/L/O/P/R/S/T/i/j/l/m/n/r/s) -/FontFile 266 0 R ->> endobj -526 0 obj -[470 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 796 0 757 0 779 0 0 873 0 0 0 723 0 0 806 674 0 800 646 619 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 362 430 0 317 940 645 0 0 0 479 491 ] -endobj -525 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 14/delta 15/.notdef 65/A 66/.notdef 67/C 68/.notdef 69/E 70/.notdef 72/H 73/.notdef 76/L 77/.notdef 79/O/P 81/.notdef 82/R/S/T 85/.notdef 105/i/j 107/.notdef 108/l/m/n 111/.notdef 114/r/s 116/.notdef] ->> endobj -213 0 obj << -/Length1 2088 -/Length2 13404 -/Length3 532 -/Length 16024 ->> -stream -%!PS-AdobeFont-1.1: CMTT10 1.00B -%%CreationDate: 1992 Apr 26 10:42:42 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.00B) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMTT10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch true def -end readonly def -/FontName /ORKUKI+CMTT10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 33 /exclam put -dup 34 /quotedbl put -dup 36 /dollar put -dup 39 /quoteright put -dup 40 /parenleft put -dup 41 /parenright put -dup 42 /asterisk put -dup 43 /plus put -dup 44 /comma put -dup 45 /hyphen put -dup 46 /period put -dup 47 /slash put -dup 48 /zero put -dup 49 /one put -dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 56 /eight put -dup 57 /nine put -dup 58 /colon put -dup 59 /semicolon put -dup 60 /less put -dup 61 /equal put -dup 62 /greater put -dup 64 /at put -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 74 /J put -dup 75 /K put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 80 /P put -dup 81 /Q put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 85 /U put -dup 86 /V put -dup 87 /W put -dup 88 /X put -dup 89 /Y put -dup 91 /bracketleft put -dup 92 /backslash put -dup 93 /bracketright put -dup 95 /underscore put -dup 96 /quoteleft put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 103 /g put -dup 104 /h put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 112 /p put -dup 113 /q put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -dup 126 /asciitilde put -readonly def -/FontBBox{-4 -235 731 800}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ_ùc‹‚2BžØ·Ïj=‡š-8Ý\DgùÝŒ] ³¦¿/%b›®Á™®‹ÔºnÙ»÷Ú¿ÐáSº±ÁyÔüâ b*ÍçÇL(Ð9sWí«F Rë:E·¬Mks­ƒH…02§Eô”?›Oíe+ƒZ¤—'¨´zÿK΃µ¶…–оi‚·f Ë<àÂ,¬ÝE“òDÁNìZ|JÄ#’ø¼BWþ¯3ô¿ê‘ÿÏ—MÖìp¢ÄÁäó(¡ë%ä5%ûÀ~(Ì5öBk}Aêj „Ýc'S•¥ªéáÈ-8ŸÑ*!èi™yž$©”G.¡®w g ¾ ªÒJ0Ùn¥r -û;Òà¬Á¡ Kèr^×ã©o™x¼7p4Ù= C‘åyÃOùü#yËŸ[¾©â4éê¨9'nÀÙ*¹xÁxÛ/J}û¥oÖ¯†pë6OÞÊû¯e}hà1‘W6Ϋª‹¥À¬%(ƒi]I½‰«ïèiš -ãí…´ŠË""žb3™É=çÙ5sJÚÚzbÁÔJÕ>£[Wåеü H ä2"ÛŽüÕÓùº0O¨y9.à¼Àá¦t³¡ü:=×$E€Çª Æ]t¥þoŒ¿`% -Ì'EK¿—ÊKœƒ¥fr•‡RíK^yá†`vO^†ðžúŸv…òõ~ÈZwR‡³ iÞNMWçÐ3HS¢p+§T,q!s0Ï(عÆ;U–©´+3çÙ"”J8q3ƒÓdŠJñ`£°Èó7›¤7+âçêIªºu®îÅÝáØ¿hH<=!'€«¹TÌ–€2.«rá% -v ÈÚrdïä c[[ Hu,>’½àdÄ*,RŒŠ`8'ξðÉD À4ÚÙÁŸ²}³™½®â SYe8X|vŒ{ }"--Šó¦G<ÄÀÖÃàÛIŒëŒ›ÑÅÍHjPÚ¡ Ç}b†#UãòÒTâ|ÄBrŠ ®ÉÓñzéÎ2 1z,æ¶.R/½ó÷Ñ ‡…Nk³ß}~i‹±|Äk>dvIš—ª¼‡mD‰‰R•M&·ñ†OTÏ`Ü¡M”ßæõ aæXc¶:rNê…S؆–á'GSkˆ,¢åÛ Ä>a càÖµpeW¸1“J¾m=Ì6·dgae­Ÿ·R#¦¸l¶/`˜Nj5NENªžÄ~QJ—ÊÇSYm#ØÁM$Ú÷ã¨ÿéË_#ê8ˆÙ˜žw¶É 8H¿Èž2€'{’Gº× [þa%ºQ†E%1µº”l$ûks@+Ê¢·@óU³4ëx ®R3óO×ïè¿šš¦#0G ªL - G(‰‚»Å•!8BÂcÈÔzœí^‚¡í<õgC]µIœÑ’Œ$v´½Ô>4«8…ÇG‡`xÑ°N–¸çEò@ÌûPC@€aø9gà­.7ÒQ‡úŠÆ$à»hWøû¤J\àÚUÐ`Óz„¦§åõ›¿ ‰< )ÜÉQÅKÌtïX’cs[§)&:SÂ[Þ¬¢]+39n¨\q•¬¼“ñ¦xÖÒ†µ 3–Jœyó>Dg"^ݘ³X4dò{ åúãÓh‹s¿KA_”éË&ÁF05nÈ—=È:#Îãê7GÛ…Júp\ãSž=j¡é48Ä¿ìIÜgi'9óÓ)2+$„Þ¥ÃüÙ\±†Äš»Ò®'çÎÈ°;Ó cE§¿¾³ÜzŸMþhi®å#1“P]+îä>áûN\Úr®®€&fÁÄB¯ób­f›³šI) h[&€²]­Ú/òŠ4ù­¨Z¼¶îµãƒùYÐk0°&Àgv£r¶ï&×Ýtÿ¸AØgDÑ=Q:ÙÂt`{0ø¡Àa¬ª]ÇU$©qpÌH«ìs¢S@%%üÂ+tv ¶ñ Eÿu ð$ïåÇà`”óÐi ÷3SμƒúºíÃVÜï,Vw-a?vgª»)ô÷K}ko†üz|¯n«B 7mÆi”k 8Ø[ ô¡yôa ­·©6o!:zÙ~­üù4…]:1!jíôl0ËRlæ*aÓAƒÎ-d—~Ô‡ %Ë~ôØn†ó:†™ ‰•ÛqK‡V“Äs=ýÞ-0üчg#}œ$;ÿAKðhjP½ª#Ué^¡ÝŠí8¤u«¨fiåÒžæÄ6=]êŒL|ï¸\' Õ‹ŸOΓY©WîÛ}@<´~­c3zÃEc·!ï±ïN‘¥jÛHßÀÅß Ê7ägjð~Õ…Nø}Á¢8Áü`Lå–4_R±ã©ƒ`pJø[ -¦6>ùbE½©@¦ÝGG(è ›&¼â6GqL\#Ç¿{Ê'2¨:´ ›Ë¦•5§)!#øW:tÄ)à÷ï1¯%à“@¹gŽovØiåŸWv0Bƒ%‰±ºŽÀî¡ÁÁÕf©m§šLgìP$”Ô¾TGèhþÞ -†•þšwú|=ÏŠʼúh`@eã•’ýDË–­aûr&­|£[J ߀”ýæ ÷ìïO j®'þFÈÓÚ™3æu°ƒ¢Ð§¾¤;ôëÿLÆ/ËÛ7)]Ÿú4·ýAb r´3‰,Ì–‚ÒI’M’¥”¶.I‚v6Ãy,m²zɱ ~èúËŽþ»€MìT1ÈŒò©f…øÅ‹ƒŸªúèÏÍa¶ì€Ìíö:Šô¼/̼Ö±‘Èœ¨ 'sòÃ. -)G X’ÉÜJ»ñµÃytC÷KØ]˜n TM—ew©±–‡Ì%ša{zs:o óú;L“@ªð<¿tæ–"ÊC#6‘ÕñÒ– Vh8'yòo¶,c ‘/}bhM<Ë©ƒõ›K7_ˆœ2×9MX#›Ì†˜vXŽmíᘥsÉ|PÝ1ÂôŽð¬œÙæ£ibÅwKÔ‹¹ÙXŸÆ¤;^UCOqårò¬6ÂÈF3Ý>’u˜¡ÃýM‡0—§&á:óJ¦#n•ú©5„ºÑ‘çŽ}¸&»z÷]ö‚PÊ¡¯ð5#c¥°©Ü­´MØâ«ÍE³ôVIÃÅÊÄÚ„dè$”Šöt¯–ÆÇRIØQtñ,šž¿§½D%žö<³:´|–¬ÊÖîà(%IT 7ý©ñú1 ÅJLg3êþÝiˆnÔåîÂF&‚[Qáî^—rV_ŽWv4T=„°² †Æ°x\³é°@RªU©¢u'*äšþR¹.4¶€p˜»'‰·8G{ˆ)ů²ºùâÿ )¿µ“ þ/„¤On.¥ÃÑyQ+9i`ç¾·9£øܤ*ÛÝ–vWÈ¥ßÒ"ÞæÕ´–‘‰;Q$Ú¥óºWm˜‡Â2¶¶$o¶_YyÓ\Ø Ï;›S34zÍ2=õºQK+GOYéÂB©”µÒ¢ ó_qX¤û¬|’ïµù±½×.p|¼JôjšmÈÒ„ü´¤É¥¹ù î‘ÑèÊ´’õ.£7w«!J4°a]ùÖö¡¶o -BQ2^m¬ü†*(ïpð'™¥P3Zé8¾‡º«S¾cðJ*Tô§2d±P£”¾¢d µö…è5‡lÃúa*/òº Sßïõ:¹ÕS¯àíؾça¡| ÑÜìÝËÍ6ùÊ_ßf,üÈ—zÊ%Î3| Uù £zVÖ5áœð¤ªÓQ jq2# ®ÑT£_x$¤â¸[ii Šå4ªŒj¢£J>¥åËÇcÖ•:«"?uí[yŸÊF)Í•c²Oï;uQäë;·{ƒÅ£´Ëürú(­å¥½m„v/cøFxsíëGDXˆìmøß~ã¢ØÔ¶9,U‹nŒñÄ®CÝ’ùf™î>="#ŒˆøBÑÓ‰‘2%d¼h¶ ÿ—ÞºÒVH-„Q)?Š•<ÈÉ¿Þj®ýç‘æ°ŠñÌí03þ",éâƒ'?×æEœmôÇwß1ÜuHµ‡tu}|Õì–QBòWdàQf,á[Æ°¡š#dÃâ|°muVc è -‚™F%«ë†x‹íKØÆ•:8|s,È&D¹ŽQe;?ƒÝÖɯ` Þá^€÷é (4¶m/ ¾?p€µq6ûöváÛ£±èÔ}…¤®%=iLì÷[]ÓJ/2v×J8FÁËï¹ÇBá'ño®Û\÷ÓQJ”©jºÝïÿ.lGò×òt$À¤›*iT2´©ànÍ$ÇÌè]™KtËñîr‘ŽX¹Û!¨V}Âriçéܺ¸5D;sº_û>N¸òb8€ž¼ÄY¦opUN‘Uõ' >VàT ‚ùq˜ÁÝB1»g¯¼¤„oq»üùþé—uõhë¬~ö3tO3—÷iŽ4=«BÆ×ö]®Æ÷gì8D6ÿêæÔë©L|W~ÉK?LÔ\™ÞFç?iæ<;ŠJSýLS;.ax—ñ --ë¹eÀS±lSV"57Q§:•]-¥ÁÞIÄo-pÁÌUWøÑb;âùÖv—$]ÓFBØ3Óó°ƒ!~ƒÅäªâäGS )+C£¥P&œDqÁ݇ËÏÜýÎrƒEUž9¾¬?£ºký•ÕÊÝÑr$F+Ö)¦ßU)ÙŽ{x…gc'¿*5Å‹õ>èäv‚•c6¶õÿÐÏl%d‚ê=³ÎÆÏáN(2ÂåçGz0ÃGcÏ÷€ÎÂ>cX±”Á—GRßî„*/̸Nkë @á›ãÑókv”md¾Ðdz¾žýj£ù¤ÍÂ.é Á˜;+ÚÎ×K³¼3íð§3öþ'ìI15˜DŠ÷ª%øh›èw"RŒ§Ø'Ü¿ÿ{y2uÿÁwtÒþ¸uÌØÎî‹æs[M͵ó3Eœ:!Þ±ªw­¹'ëG #{•ú¼-{¸\‹qróäQQî7i¶ŽýÙ¼yµ¢g‚e÷rt“Šéß@ß -Ã?⿪òÈù‹™_ÿa‰z®†Åàˆ-L7„G×BÞÄDRlµ¡AîxCO0bz¥ Õ ¼AQ·ìY6>×Q¤RhCVâ$ÈÐʽòú»ðO#U[§ÕüÌ!â*°Rá_³ÿj­ow“YW«¤½dvÇÕªžÉ;:ãönæL…Í4ˆç–Bòl©¸‘ää3¿MìjçóSCüL+úa¤Û²Âéä±à©ôÊbu,Ú]ôÅ cp²©ÌT§É‰‚!Äõÿ𛃌'₲"Ú)ú{³ÆËOK'yz0'Ôo|.®X0Íq ãΑæë’™b jB±/h‚3B”à9tŽCùåO©Ý`É¥Mi“Tè€Áhýboæ›R¾sŤ -q;–TÁøôxOÓÁ¨ÙÒƲµêXCpƒ:€¥$ ÏÑBnÒ -m¡”´¿Ñ#·+V+J>ìÂ7kس[¶¾ÑóýQ_’cÒgŒÄ.ó’N#µ“'õüì Hò¥¿±Ö]K8?>b¼Õ`‹¬¦[zªŽþæ/ç3 䮀o£'¹*›I¤ œ,Æ€hì8Z¨ä¹ñúnË.c¢·¹²Ìį׺ª®×™#l·K½²˜÷¬g. -Œ4ã#d Kñ€X–ê+jν Fû¶­ßO鉎•çä¶Vmß››x„ÕSìõÉžW¡TÆœéý5Š–âå6wÁÊ®‘aztA¯”Ü‘;}?+.¶ú¯ÞûöÙ\¿ù䃻c-³JuG0xHÙ½9MªG"¬?’M‹í‚ Å| ®‚5h󀺽*ˆ™{Àso‘q÷•’Û[=ËûÕŠF{Wñ ¢„ ¡j%¦Ïòf_i »fùÿUÞ„¨sœùcp¡©¡<Ö¥TTX -‘«jNõ8h¿–ac]næßÕ}O}ndO÷ -±ŸÅÉùËîºÿô5Õn±O^µñíxQÓêTwÇŒÛÄÙË/twæ°ÔLÕöÔQÍ_ñÍra¸#¿9…¯5¥˜¬÷TÜÚøµÓ}Ð g7qtˆØ¡\ˆÙy}O|D•ðŸdˆpcç\AÚÐÛod#”2è§~¾³dÆ" ¯yÉ’Ee¾œ\“êBînq×ïçZ0JT[àÐÂ=Cž­ÛTò§¦ö³Õ/K -Wš0¡G¤­ Ï„G¸eјÒJ¤ôðÿWYÇK\¹›»„WB*j³Æž†$XBk‹z8'V«Qn`e¼“Æùó8‡’O ÞK?•…n'ðÁûz\M|¥CžK ÊâþnI ‘æ‚.2Ï&õr©:oã0%h^’Tÿ=™F583|H1ÃðJuR˜©8cÉë' õòœÿC]Ç$WH»Çħq-#ŒçT…;¿´l%{df‚¯jÔLÏiÙ›o7å/ ¸z)™Ý Páä…ÅôƒÒÚßF=W•(øÂÛõ@-Û -_zŽ7Q‹4Ü€EÕ׋Œ”Ò:hHèµY@5HSðŠx„’dò0—…c"ÇÚƒÝûóãž¿ý¾~ê}€/¶¨ÄN(¡R’{©ä¿Âµ¥ÆDHIöÆ"^>º•49éúNýþØWÙõ®£6‚>€PRËùáÅîåïtÃG ¸ˆÚ!GCÍÈnI£#E!‹?Ò FŒ5acÅÔåù,†E‚)Á~Ž};Ÿî‘ÇŒ Š<®HO’:±…/Ȇîø=[Á­Ñˆ‚«3·(Ъˋ§ËåãjÊ ³t[™ 9ÚOë†4ËÆõP˜=«þ1?«?“χRÆvz‹6  Θmq•â?döÎ{Ï‘X*û†HðìÖ€ì U¹ºwöÈÖc{‘E}+ø™ÚfäÕÏ’3ï¼ömcŠbC]ÉþSô™3ˆ á´-ôOÎDÄKŠÍŒ]T&HR7²2s: ÁB‡ÞÚ»`„î, -!³røáM\m#hÕÔ%/…]LÊ©Àx§” x`Hù9_*ÿî~WKôêJÜ;g-áEƒâ1[2¤²‚Õ+lвÇÃ'r±vŠ2/’mâIRøا0;Oï0«|èû¥Ú½ð'-hMqœ!ÏV1q†?þd˜—`7yÜ3rk‹\%f ’Œ&¸˜k¤„ìrè€Kòóf"ä,g *{µ÷›ú¼¸U6 paQsCÏ—ü}“ÎŒ™gÕn»&”ð1‹ƒ?êh¿Z˜ÇpKmâÇåètÁ_r'Ó§Ú ò­Â‹šKÒ) ÉM«ô[1„‚á°‚xèáwI’96KTì±H;.JJÒ ç–äãa¾0xà|«‹ò“Ö¡B!,\ÎÉÚ)w­ ðT%¨K#Dé§t°ø“YçAÙú=<,| -鎩+÷WœQE=ºì&àÿÉÕm‚ßõU#„üŽO¬‘,¿w‘ôŸóÔ+„Cƒš«C)]Âqî[øúù&§6„¶½SÛ A…L;µ ˜]Ù™éS½‰è Ä%8æHMz•ð—.?ë{ÅA\ÏÛýr(ÀââcNˆnÑåDhµÃ‘æ•äd -!'Š+Â)y5Èûb÷¥²HªâÌëQ:¯Sî•]º¿ê@Ë™ÇÐt”x B@TƒÇ+K _Om‘ã¯ÂõkP]û·D°‘ÁlÇñ)°C˜aÛ_îe©ñ .“QªcK]U ®ždõQ¢øvm¸yܵ¯òŸ? x_Uì„’™Ûüái™GÐŽ9(G‡NeðäŠÐ=½“Q5ƒéðj®’éÞ”£wA p6À®×K_¯{h2jeæ¾£ž| f­°‡ãm3:³ïÞŠ¨v"rŒäL-ãùiDG_à&´ö0ÑÜ„”f¡ÒŒŸ¿IŽ¢‹Ú=ñl­"á£s‰*s,µ72,àWQòýœ¢Å -±š+MÇÄM¸4t²“ͲDê"È:Ѹ/ᙀÉj¿vœ±La»Pì<ê5žLˆ-ÝŠñEWsl›êüm®&VåcŒÌ†àÔ2-f‘=›tŽÅùÙ0ûõʵ1½ðH*ÀÞ²¾VžÂ沨ÌHlWåHaª§ïǤº{v§1¼QVžvýŒ=ÀäKø« ­JÈšq/i&çì_—æb/ ‰ä»ˆJö¯ýÍMPšçg÷‰BÙÝþ ¾Œl 8”xÛØ¡¶/HaF­f3Z6΄ÎYÅgÿfÖö®hr€V@wjàËòžž¹^›2 áÚaÏ6Å•bpÔh“ÿ°ËÒ›%nuWçB.M6pÿ 2bª°Yoz׋.ai)‡lÕÌXu„qƒL6ïb%;34jDd±¹FG¶KÊšœ§%)‚³‹’·VÐqÌŒ¢cù°¿Ì&Áïö:ŒDuÝ9BšïgAñÉȳ½ƒi†&ݾk£1uQBs•(} Øžý½ÝHþ%X“¡ ÃqñB»Êh>¢]3ð#šGCeŸt• ±Ðˆ×ÅÁ…äWo¯P7L²°Æ0Ó¦k½E8¾o /2ö}‰6••rž•¬²ÁJŸ;£+ÎÓúðX1ݾ7šÈäsE -?|û4&$,دÒôP wtb×CëöMj—ôï6'€î¥ã)5p$AH‘ŸàQLÿAù_þÊ¥B3ÌFÎ9"l»¦:H”qøTuçãf5æ^1…í¯«£©µvÄ’Z\)Ã?aýâŽeáÕ#œB\›Oç”øðùöÀëA[äÿd£÷¹áë} Jc(²€“„ã‰øçr˜„R[Ø8¦›†cé|Ö¨²×óÅìÇ>0U¬)´ÉÔ—ë=Ç\ŽòÈì ŸŠþ9ÒüÖ»÷Vht Ú‚ÙŽ“!zêñÇÊ U¤÷Hª,¶Œ#"¬›ö‹®C£S -àËfûaC;}æd-KŽ¡ÂQ)9ÅOÑT³rpÑô40ã‘ÕW`ö"´B› àÖšãƒÅ°O 0íßµÅ0 ÿ?%˜\ šh‰.؇‚ÈìÿÄ°qŠ°Äž¾)Ï -6¤‡ ìÃy˜º–EŠÏ¦ÌUPDP:VVZÜÌ’<"5h²ÞÇ‘õ[Œœn¢?ÛtÈ5ƪ‰Ÿåþ@mÒl›p¹ЖA!’›XÙP;:ŤŽÂŽ´×áE‘p`p¯šùóÿ`Z³c<—ÂÞ õU!ýÒ¥ˆ ¾'ó(‘êͳ±ýœ»=ˆñ¨×—¥>³Ÿ8Ò¢Dïš¿?'ã½`lȱÖq%íî…åßíq·‹7PìlhuÝeöð™ Ó…ß# Ÿ¿Oiß+·j1¹«ø°ä¦šä;;l‘0ER|hòßa‹gó@g®=ìþ㟠;çäÏd“‹mà+)ê:òhí(t¬fc„¯qœ÷lÌ{}–çç7§§BTÞ¤¼¾­ÑKi7Ît{‡Dî2a;7Æ'èæý÷ Üö`ƒ Nj`ÇOV$F£xþTí.ôb¢pC…æÕ‡7gmœÚ\zb¨3ix<Ù¯ÁÚG»fB3ŽÇ(øûGçäy£2!b„ÛʬDس£ìüÖPI?Þa±¦È*B˜ÝYslºi^uˆ©MP A×çwjë/iwh‡-α‚°PÈ3Ù(yÐW>…7{äò’:¯ŒR¦«ï­…‰[S«Yj!ÎÀ¦ÔÌzf¨Á‡‡ `¬2,$&‡Dyç£7‘m¡^I©` t¨ö‚Ýé›ÝzŠÑÌ×!qKÃÇù`ÅT¬–·M±™É­¤7€>xäú¢Ñ­tð(™¨‚\ï}qpµ%^ [*ó½cöEt`뀾9K‡M–S(’^/,(Hz» µ$KÞr pyä»Ð3ìÁ¤¦|ÿ!D]ùÜô·@Té¸< -#ÁTn†pm¡ŒÏL%2þš*_‚dy…פ¼2 »ÿdvå²ìŠ²Ï-Z¯|—›Þ&ö‰ rðÒÃu¾†\î1fç¥ãÏØVò-dÙA{¼Nó0ŠÞ¡ÞþøÏÁ&YŸÓê}yÀaðsôð¼ÿñ™›=ÿ`³tÈ¡ÿa\Ê>flhΈó¦Ý,²Â‹Y4^ê‰*ÎôX}Î9׆׈ò‹&ÃÊq]Ê‘ÎþôŸàèÞôÞìŠ#鮥ijïç7=&t“Çf5/ÛfÐz:ÃU´Ù É[ä¬í¡m>ž°A-¼ÆT -õdÁÝÿv﯎®x—î«SÌî  S«æ^ÄÖgg\i è -‰³ãøB'¨º–8v’JðÈ "îÿS¼Ûžœu¹NÀ£t’D ²ŒÞ—Æi±¬jBókt¿~ÝÆ_(9ÃÎb`ƒbß?µ#mVß\æÒ”eЙÏèGj½Å¯©nwa|Oîøl·~z(• –7uZw“‰ñK¤%VsvO÷aåX7:­k%¡}GF^C±Ê0×σÁ~ Ó’×AuÞs‰YÅoIO`)¹Uøœƒ´‡!'í&‹ÈÒ7eIÑ¿¨ÇNçöF¥†C¸¶K4»’#_Vê)«•Ú›Gá”dǪðÕOR‹¯ûÃ¥ª~í -IÆóŠßTtòE½MÃX¯¹â h#8[Ȩ~ÒÈn$Ÿåƒ³o»úc>­h6;N‰ †f»±é<„ÇváT9 3S'QéL£ÙèÚZØ}Ì8zÙ_9Ï*<ÄWÇí&³.ùtÿì ‰ç±Ëc/òBŠµh gí £xèöÁ·MÉ?™Œ‰9g»ú1º*³ C½·Í|T‡~²wWg^½[?†M¸ÅŒæËÀ¯ƒ=º¬ýŠ.ù•ÅìÞp¯ÀZ¿Ñœ_ǦݴÀ/˜ûdm'ÿ;Ñéâq³îÉ‘'lMx!ÒîÚ²s,Ð £é>OBÑ+ò0u­«¤8/¸fÇ âR±\¶”L¥’ÙVG -åUÈHMÛ/Òï6ˆÚ¯f½§|œP(ùD™™íº ZGžÐìŠt;+UçCÌ#7 ? ˆ0¢º™é¤¥Ôd¬—¼±&—^lms -2†â³1Æ Ú‹'P5jhs$ò\ ¡ìÀlÏ _yâ¬bT‘®„l'kœ) _ ê…3M€Qk ÉQ&tzïÊÚcA_‘ÎΊ¹^šMb}®°gßM<íLš£EÄBwøýÔ:¶nqS7¯K ’‘ ^ü³„2ܦçßüFd.jR£%¾ÁèÛX­Ì/®Owº/_ ÷i!#s[ìôYÒ‡Mê³ûé Ôè¨ïL¡¨Ž8飳”ÁÕÈk½Q åÌæC¿Ö™Å\øëS¬iâ<*MÎûi6Èt2]ƊІ_ÁS‡û@@h&q$4zÿ«.þTÒãþ4s¹ÅrŠå¤6ø)„¢Ì÷_i8FÚAš ‚3 ÉS€%ô©àˆyw¨k~ëñÇn¼¸Ä5àŒ|—Y÷—Õøk™ÉefË¥•#¾šC_ºz …Q%Š“xÑÈ{éΊå­U®´Ño‚¯2BQwÌßúΠó†Ña]ºÇºã0 &%b*`ä<„™$Íæ´í€óg¡)_¿ZÇèPâ¶õ¡°*(P³D€™ÂŠŸ¦î†ª·ì†F㔢ŒzgX oÛÂñ2+®hÈ™›iÌ+’AHApDç]¡bÚ\öÊ=®ÓhO ÃÁȲâZ ¿9²Ô¼î5 >+óFø9†yÎì.ò>Ÿ¬uèë`]ÕºŽ?àT9ÿc¼‚ùÔ¾­±ÛòX UæW_ö -2ÞÿòmÀ,³;“(}#uß.ýZfüå9¼ñ‘Ì%E¦ßzà® û4ŽÛÕÅe$@BŠ(©ÇþøAb³¼¾þÃ5-o"²ÕÓWx‹ü3qÈìH¶›²> w+­p¨B<êÃÃË—¦×¸nFN´Oþ -"—}£®FÕìvc -™¢/W÷ÔóàY®Ûaû¿þ"^[Ë[´´¥†æ¤&O9y\¨"\¨ÒRÇï9òo­lújöFð­OåQÙžåò“úO{9Ô ‡~CÅ‹U4oK¨´_¤ ÙB…Á/"®ÕdÌ★#5<÷qÞÖQfÿ[/u2²9¯™=ãòìûF…Û,ŸJŒp5¢ {sG2wñB#@š­ÀXYq0;<í(¸}:屣̻Ž +R+ò\¯h±S2xæOPÇ‘‡ë;OLV©¤r`Èâ ù`0|²M$™¸Â -E/ÌîvðÓ{D,Yâ+#œЬܑ®iÙß:µìœñW=L\ç^¶ÐQ½†X%y¢œ¯4R§ëH«u⣄<ÇÖ' ö‚¹Ë«tC—.˜yšzuøÑŽ÷¢‹SP‚_ä€çy•‹(äÜ,­‚àDæXåÁko>Õ¼¨[:[7WžÑo×`8¦äinNÝt}®4ï2œ’¬ÊYr3šæ½ê .ÏI»¯kþaÏÕÐî:R141omLRodñè ÂV)–ˆfÊ!Þ‚¬PõBU-@*¹?á›ÿzcƒ[•ë÷€TÄÍAÜþ-­“Ïúx—âÖQç÷gP©IÿK}γ?È™ÎBóvv‹NUâ¸91‰6ôM™D>ªå‹pEMøæ¨?"¤š1Zj焸DN°÷ÝôÈS¥7VbÇRVñÒû‰³YÚ=Y2Ò2¯*(x‘š@)›”ÑÍá_í1Bebv[ºV~ï®æqÌÖB¥?„·%µKGU_¨7N2ïÉÚŸ×b…=‘åü†­}JˆˆÃ«¨¦¸»¹8É»ÅçºLç·"4}'Í¡¨Û‡ý¾E(§aJpö¹X5ÑQ¡øŽZÓTÂNë¿$‘‹dµûŒïW}¢I‹>„`œñhÌÜ+Ö×ù²ÉLÝZm]ÿI‚A­4Ä)«‘Ét"˜ü‰fÉ9väD­Wª4VRW|Á½ÀÜ,<Ⱥ%ò‹·PÚK(‘^?cZ\So>šÓÿT©E€†JÁ{éÏ[¹å‹÷ˆ*Kuö7Î÷{ hÂÌJQ…4Só3«5ÆÜÞ™3+V ß[2•'žñ<Œy•ÛI›j¥í«¹Ù[ 8ü ó±ò9IIì,`ôeTt¢“Ï.LçÎ$ȪwíS@†ßÿüÞÃÃÙœ$JèC (÷ÎÏQè þE;8Àî ElÄT ¿lB²”é(½€!`ó'IÇ”¿n— #I!þªÜÛ=´5žªÿê?SW_Ç%Ò^“Â"STD¡ÄºQwÞP‰ƒ7a_ ±ÊÅ!¥?ÀýRPa1è‹ëÌ•[Za_m˜õ’tànoöu^s%—Ùe­zFﯕ¹en¤D;BÚ·ö`6öwýŸRê—ž5{hh×3–á~G„t•ŒDq寃Äà›h!ÜÑÔRQ0²bOþã †§Ó™5jE‚C ]]X»›ƒZÁ2Xu¿u1’núáöé ÂVáÁ#ÌÝ决‹q2Fr…åºÅüê³±¼w¨íC©¿uôó$g3§,†æ̪¾2œÊE¢cüÁ(^]ÛsM{à…¨›G´Ô­XÀa¤aÒ¿“Ès¹+¾ipk^dÆ™”€ÖÈCu~·lñw\Ú$Ž`^øUé]$õXNp„ú,n¹q6æQØ•Ê*’LY{;Ìvú»>\RÌ…yemÅ’Š+“Í»ïN½*{êÞ®ÒËA ¤ªU–*­ -Øò$K[î!Ù.ÉݦØ~é!LnÈ$æÞ“ã;w¸[y¾º@H„X&Ëg«Ý"dút†¦ûÒo¸—G.I´Ë~§5®éó^=•²Üé‹ñax}¡ùfPìOå* ç¥ 6Zfíxwtxœ¸§)ü|o†Ošø®x…]´Ô~¼J»PtÝjɬ€£x0€\à4xC냫! -‘ô—‹s*ë½ „gÑR(÷=Ö“ ÕAÄáÍm mðu±ŠÔÝEÂ6V}þ.£òàáŒ×ɼÌä*Ce¢šY•N -Þ‚»Ó÷ÛÜïsÆ‹]Ô<5&uwét—½.¤ÓW ˆ°JíÓÁ0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -214 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 527 0 R -/FirstChar 33 -/LastChar 126 -/Widths 528 0 R -/BaseFont /ORKUKI+CMTT10 -/FontDescriptor 212 0 R ->> endobj -212 0 obj << -/Ascent 611 -/CapHeight 611 -/Descent -222 -/FontName /ORKUKI+CMTT10 -/ItalicAngle 0 -/StemV 69 -/XHeight 431 -/FontBBox [-4 -235 731 800] -/Flags 4 -/CharSet (/exclam/quotedbl/dollar/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/eight/nine/colon/semicolon/less/equal/greater/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/bracketleft/backslash/bracketright/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/asciitilde) -/FontFile 213 0 R ->> endobj -528 0 obj -[525 525 0 525 0 0 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 525 525 525 525 525 525 525 0 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 525 525 525 0 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 525 ] -endobj -527 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 33/exclam/quotedbl 35/.notdef 36/dollar 37/.notdef 39/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five 54/.notdef 56/eight/nine/colon/semicolon/less/equal/greater 63/.notdef 64/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y 90/.notdef 91/bracketleft/backslash/bracketright 94/.notdef 95/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef 126/asciitilde 127/.notdef] ->> endobj -178 0 obj << -/Length1 1016 -/Length2 2355 -/Length3 532 -/Length 3903 ->> -stream -%!PS-AdobeFont-1.1: CMSY10 1.0 -%%CreationDate: 1991 Aug 15 07:20:57 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMSY10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.035 def -/isFixedPitch false def -end readonly def -/FontName /GNFTBS+CMSY10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -dup 15 /bullet put -dup 21 /greaterequal put -dup 26 /propersubset put -dup 27 /propersuperset put -dup 50 /element put -dup 54 /negationslash put -dup 60 /Rfractur put -dup 91 /union put -dup 102 /braceleft put -dup 103 /braceright put -dup 106 /bar put -dup 110 /backslash put -readonly def -/FontBBox{-29 -960 1116 775}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª/ ùÈ­éÙÀX¸~›id}S5žQ!gt¤ê¡âµŽÃkÑJc;•r´NŒ^ô¢¬µŠ ¦X€5¿.ØSyƒŠ– þ+'êIÃqV˜œ…â:¿r㚉#,Ùô#È ždèBZ£¾÷ÞÖ *R’*"7Ù¨ÝyÝçÓò¸—Ç=cîÍÚLIPsFŠ'Ñf> bôaöä -]fvÑÑ+QæAÁÔèâwdüOŒ¿[xìˆ"‡%ñÄS¦xõŠ~{×ÊpÒˆë¡õ|O -¿BÅÝÐÄÇâ/€G¾LÈã3hûÈ+N–g0Þ3²æ¸ËjäU±¯1‡ÿè¥~ø¦akœ·”Dìzq§»=÷U}.K¶˜Y碌à ֻ1?ÔÙCùŸ NÌŠ2Muµö–¸hŽë/åí4ÌÖÐG¤ã€m |Q]· -OaFþÁåÞ‹Åp4ò|ð¹ä¿dÒŠ=“fH1y¤äw&a%sA­Ï*¾ç'ËÞÇV¶jÓ_߶ã{ݬ¦ƒpæ@ã$lð÷¤c”¥+^4±á®P *óÏÕ$•²¾hš0P¤TŠpÓÿÏêÚ|Œ/‡‰dWÕVº£ÝQs&Å¥=*ÚìJa¾Bª´rÀ,°'‰£@jüe<ÃB½D! JÕ„Ü¥ÅYž·\?VVzÑ|½­ã!à£jIÒß5‘$ }+Ã>És$ß<}.Ìï)æ&:2&O‹Äò>mKOÔ‡1Aò5…Pã@© -xÔÅ@ØCõ¬ƒÛ1+,g­ØAªSpF¨Âñð+†ÿ: "[Ç .@€qÓ5t,GJ.ÔT'";ðÅ@_é,°Ã›Ù×·eã$<Æ8™•rÎP5• -=$AYÎ`-§‚C1$—ÉŒ› ¬èt©\jÑKŽÐ\D‘Ùµjé¥Ì?.™çB¨,ÆžVJÂZü(9ÂHêÜ¢³»FÂœY5› y…ÖÞSý)—“ÚÉs2¯‘0Ú¾‚œÉ61<œã&¬Cˆ.o¡øºŽÐc9€ýîWÄ”–dÞ\?G=€ÀV&’ôXŽ?Ye4ŸKw.e „º/›Ÿ ¦ -шC!Öý«î¶ ª¼Ž§—%¦ÎåvyúÈ|Ë–Rë¸ëÑâë©ötÆÜ/I¿EVÍà5AlÑ·XÊ!Í-íÀøëvEê šQðÀ6”„æNûh›†-´#iÄwGЀÑO§·JÎ}¶ÊùÊÚò™¨‘K¶ÛMéM¸P©¹Š‰VâUè2Ë8¿Fܶ]³Ü—ÒLÉj4mãpñ#Íx‹vlSŠQo]›#Õ#Í3ñ žw£Â¤kêÒÞɉQX|:©¦–RœíÄþ$´îÌ69¯ã ám¾lw=#,Z éIÝ3ZF«++Í–²¯+"ňUÙ-$°Â¶„„ÁÿH‰^yE3´„BP˜?ˆÍÛ«fñÕü&ÛIPS*rp©³7†Ös'® -ÿ²×Ȇn#à%¯ëMø/ndñ'ù¿J-ï‚Q͉ªãMË-½Z1*Šö|F:åµY¡´+çë‡ØLÂuhÂǖΨ°|Á¼Y—áûÝ÷é2HMšVîž:a§5qh~C{wW7x"”`›dþcF‰Øï ’£žV %v7”Mùv:MÄG=â@­ -ëQþkö隦ª%Α%Ö‹<«Ký‘ë˜q•&/ò—dÄÔ‘;òª…௽³Œ5kŽÅ¯‘m¾ÄÉS‰EmÏ€lÍ©m­'”´Š%ºÝ4q9ÞúгÉzJ™m¿A±!»±W‚KYf·¹ZÄK©BÝÛ -RËÙÍÂm*š¦­UÊÎÑxQ:ž7ëk5°2¥¿œ‘Ð6Ï8¢Mzê‡áñZ[Ålõô&éz#aE¿cB›Ê$=­95,ß?i2iCø‰ìy¢$ÿft0õwÓ" â¿,”¤š¾‹hCi‹@éÄ8q¹) @ç{Ý(µÍG}K¨U$¯ïÞ$ý””×0íÒWîc=^V_è0g¨‚’?Û]U -oSÔnp°#qþ·p®ÒßÐö Ó3˜6‹ÏÔ{·üÉ„ Ï``У6Õ–øA Ø榮ùå{ÀM°cþWHÄ.õvM Ÿ¨@ `4¦òÒdmY¯·i ×[¢ø¤co š‘ûàs™ÛÈ&ë2:Xx èÕÚös‘5Žd’’Ògû#tX…nnÿÓËçÿáU)ñ‰áG\ÁIìrš{òžÓc/\£]A„Ú•ÑcÐu0lª`¨ùUÇË©—¡Å—·dB“Ä€¾}aÆìawqòËq—¿ÈC…6¢"d›XÆÅ› ×bó]Ôì÷ðì««4ŪÁ͇ù.÷)~”ÑuÍÖïOÀ§íˆxË1$jœo &i•Ÿú I"aÐy\…Üv’¸*[Ñ5`Þmôzhê1íúíˆç…(lª -yµ‚ô£œþ[ gïI𬥦Påº,¾EHšJ¾z̘Z®Äoìõ¦k¹ûO3ƒè½ D&ò'à5÷îcÕCW¶…Å¡OKf^ÎTÕ/ñlíJ§ö±A­|6¬ þÿĬ`YüS@QÈ¿á†dEHºðÚ`ŒÙLä$Ý-bH¥3Ô•®þºSüMH7Iàb=Äae}ÆL*"Vô:­«ðÐá-õÂ<²þŸ7?†+›¸‡g„mJÛ -‚ „6Ùœ[°‚õœAñ#=š˜MdP'¬òV\'ÈÙC E4à« ©9\d{­ñ$eMqvƒ“¹¹bN6Õ«p–•E°È˜Œœ§$3c–ʨÇpRÆ]Z£<¥Ðt€ú*!'Ä›…À–4ÈÑÈa{K ¾£?J¾eRÓûraÀÎ&>6.å“ɯÜ*]Ì#ßO0¼ãË^ž»ÏN+k]üž¹¹1<«øÃÅ®ƒ*g×5]_$9Ï^6oMd§ÈGØð—âŸóèjô0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -179 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 529 0 R -/FirstChar 0 -/LastChar 110 -/Widths 530 0 R -/BaseFont /GNFTBS+CMSY10 -/FontDescriptor 177 0 R ->> endobj -177 0 obj << -/Ascent 750 -/CapHeight 683 -/Descent -194 -/FontName /GNFTBS+CMSY10 -/ItalicAngle -14.035 -/StemV 85 -/XHeight 431 -/FontBBox [-29 -960 1116 775] -/Flags 4 -/CharSet (/minus/bullet/greaterequal/propersubset/propersuperset/element/negationslash/Rfractur/union/braceleft/braceright/bar/backslash) -/FontFile 178 0 R ->> endobj -530 0 obj -[778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 0 0 778 0 0 0 0 778 778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 722 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 0 500 500 0 0 278 0 0 0 500 ] -endobj -529 0 obj << -/Type /Encoding -/Differences [ 0 /minus 1/.notdef 15/bullet 16/.notdef 21/greaterequal 22/.notdef 26/propersubset/propersuperset 28/.notdef 50/element 51/.notdef 54/negationslash 55/.notdef 60/Rfractur 61/.notdef 91/union 92/.notdef 102/braceleft/braceright 104/.notdef 106/bar 107/.notdef 110/backslash 111/.notdef] ->> endobj -175 0 obj << -/Length1 1281 -/Length2 8108 -/Length3 532 -/Length 9921 ->> -stream -%!PS-AdobeFont-1.1: CMMI10 1.100 -%%CreationDate: 1996 Jul 23 07:53:57 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.100) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -end readonly def -/FontName /VOERAL+CMMI10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 14 /delta put -dup 18 /theta put -dup 33 /omega put -dup 58 /period put -dup 59 /comma put -dup 62 /greater put -dup 65 /A put -dup 68 /D put -dup 69 /E put -dup 71 /G put -dup 73 /I put -dup 77 /M put -dup 78 /N put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 86 /V put -dup 87 /W put -dup 97 /a put -dup 98 /b put -dup 101 /e put -dup 105 /i put -dup 106 /j put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 112 /p put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -readonly def -/FontBBox{-32 -250 1048 750}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÕ™=ü 0)xfáÍ -1›kÙXž9JS:6ÔV ™ =!™X>¹¸KMîãÑ)9ã!™ ÒI‚}–HWIUöª¡c©l=G¥e°ÂZ¿m>nÁ‡ä°Q‚k°Ð2=”1p·•%R`ùý%ò$ô]ûûÞ÷ÿ‹¿ïc{!®W+8›?v(+ë)Ì0ÓˆÇ!Yah“çtA?HÞ @‹ÆmÎ?á|¹øM X9Õ€Ö¨ˆ#Ù2 -é:ùm— ,MZ+²¸Ç’\Ex9YÄn<á¢ðêÄ¿‹›2^FC[Þ`¼T×+ȬµÀ£D¬‡]ǸFF£$¸oØãB!>;A\äT hŽÙÁÒxìh½|5úù«:6Òü;åÏ–UÇ·í§6~åƒkŽ.ìT*{8î¾K¬`yÐ8¬³ÇÉ'—dT|-Q—k«©K©†myñ9 •ª9°ð1 |½ôA¸ÅfŸr ¯(Kõ*)Æ%_ʬñtPû¢`.rY?¼¿Ânrnä®ù{v2¼O_5;\gþÒ>§R¤¥{ïñ×4‰_ -: áØã9pEz–~ÿ„öØGu E¸Ì[Ùn窙ÝÉài9ヽ¤u#=X­&>¿¯Â~J~П°ƒUöêtå0°t1Cò¨qs-bØ5±ŸÒÇýð„Õ 4AšÆG˧÷OE1Ü»Ú"®ê?»»@~ -ÌR½Æ ¢”ÌO“ë‹öÔ>›¨XÕO8‘ŠÈ' IVÕ‘ðTnPü¯¦ÛÐ ‘#õìÔ«3³ÛL®3z‰ŽÙ›oH9@ÉuDøˆêðËë JÀsÐf*¨+ ­5èx/…Jöl ÀþñÍÑdc!¹=2~SØŒ è%ú•ªW½qœìJ¨&¹ªY\ƒœFbÕ.”'JbÉ¢“>úôBžå؉úùp‡,ý#€¦ËõåÚ  AjDBWÜ›3mT~ø9,ÙOg–j†»§”®›²„”_¨”b]’eZ9ààUuhÄäsŒÙ‹1λ2ñ¹Ãåv6ܪ%j(„MÚ¹aã›,Ä{yˆ—‚[,zå¨ìøç0lÕH ¡®á«YÇÄR¸ßÙoi„¯NZ»%Ã^ï£;fçFm˽8Ÿþ=ž%”VÍôÝÐxÿZõê$&é­dnÊà=ÏÂ5)3±‰ž#o(ßÿl )`¬j1Br“O8@â1'B~ܬ…ãs¹±¥.zYžÉ,/@(‡;ÉFþºÖ]s{¯Rú³Þ¬h¨È²»Õ7œ*“q®l•¨t ’â3.9@¦WhŠÌÙÔÇ zß—ï¡ñ$Š~¼)Ip†À›1HlÂŒfû²h,Ñóôý®<`=¤<‹d‚ð7;‡`~]ñ­_Ì-­´ïƒfÏ8äÁò¡EƒÌãlI×?…|%¹ñ¯©ÒÉ(m ‘r,ߢÅTþ„kyÒÔÐ]ø£áÀ$ú-{=*fP wéЇ¬oÛða¾Ïi­Òs&`^Æp~|Œë†ìµ9·ð ÇBâ†Ü”W -À7WRÃßÜâ=Ò 1”ƒCÓØŽñÜa<Ó+©cçñÑ}6Jó_õ•¼â`#ÉHÖ°Ö¼¿IM Ç„5Ááj¦øvÒÐDKÍ3†ãÞFш]¡†¿äE6&R¶†-svìgÚßÈ;RÂŒNæT-Sºu>ã `Jp{P· ¤mÍ7™„±zBÓU9·úYÈcZ yÎÖ2”u›ÝP&ú¥¬Ü`x ¦"¨ Oµïžv÷<©óEpê’†£”óoJ-/Ag",Θ³Ó•Ð'¥Y¾ÆEú0jb*7ÍÀ%~Ò)ÁØ嚟ûj]çQ ïÓøæ‚»ö/Ú‚}ûóâ+]nÍWÖvuSX{ ¾²0‚A¼K¿Ýùo«,%|´„Y Å4À¡_Ä–­tøQ=¶A›ÿÏõå‰ ÇR mksþŠ!6[œQjО„†'.©|X‚ºY‡øÝi÷w’d°'h<Óæzx[¿¨éÆ™2×&†Œ=ùÆDÌí àY¼;aüâr?üÈ¡ƒij«•qà¡«âqŸç¥’B“3äG맨Såõ’5ú^T -\ܸ.„: þóVäh(o¹~:P·XÙž³ Ç4dHldPÀ²ç 'Ô [Á¾p¤sà¿Ó÷Ö^¢ Ì<À?°k¡µ3*D cÃ"(‘ {MÞ¼_ïG;@δÇ7µ|ŠEa¶±Ù<Ù† Fš±Ñ¢yÏži¢‰‚NºÍ”ýŠ"´ m_Rñ,iä¡CXÎÃìëI‰Xù¹&ÃÛVÓ{IJä®& 2úæœqw·Ü±ëª I·Ó—þ2¢# -¬†Þö—wQ‚€6dLÃΕ¶Ä¬‹ôº«ãCÌL—3¤ôŸB\y%mL_š£F9βæU·µ‰Æ$34«d…”ÚsØÖ‚Ž¶†ò\†½›É4ër;Ô‹f •ÂCE™›)g5Í&&pâ¦Ê d"Cˆ´Úüªb±¢ne.†:”¬Pû½Ý®2ŠÎ Ÿ4d:˜L!"_HÊæq)ú*´VÔð—ôG‡?¡‹úXóÕ24–}ç¯w»ç¶=‘‡}RŽ$ž¤?»FÅýˆšU€Þ!nôqi:`^‘ÉÚgýƒ˜u®ÏYq«i~ú+\î8 ²Ø;3 àMŸƒÉÎÐV:=v˜…È3’r–cóÝk]ò2¬2JLè½!&.“ç(±I€rÝNá@6Œ§{Ô‘ÔKßžXt –LÄœ|v|>+ï®âü„ñR¥jZµ‘a·ÉÙnLŒ/OcC æ…(ª*¢+‹ÖÚ‹ËÖYÅzÍÔaT|ød¬1Åeì4‹‘té“P|±ä”øª¤E©;å0ª ³ŒNs(àãžÈÌìZ¦è‚¸!*²)ZVx ²£ôT'A¸FµÐKCÁE°Î;2ôSþ-°¸P*ÅüçkWÒ¶ ɧtÿYMK[œk¨(GÓ £Ñ–ÏeäN”#•`EH6RÌt6RÑHÞàî–"óJ’å¾6°¥n$UÛ-MÆbMá­ð…üzX3ɲŽ‰Rqö©f’êÒ[¥|_èµúþTý°{]„øÓ‚ãÎÈ~˜Æ‡ý3Š93ÈÒS(ÉÑÙÑü6¥«és•Ãžîæï²kçȈ Ä.ø’8fø¶r3392Î:"s¶b[à-le$b,’äC3Žs˜£O¤"¬’«wœ-h`îwåE§¹Ã¯û|ÌŒ|½.Æ äÈü/œÌ›íÞ‚"ßš:5%jY€Uš‘Ï<¢îD“ìŠð;Kr´½_jaàa°ˆ—0R>ן |•wvª)Hvà·ÍZ>ÈY~›£1›ØN#^²§Ì’&XxÒæ®t¤(º÷ARÛKuÜo®ŸáÀ áÇRTø¼ˆ2SÂð“²i[K'£‡tLÀ)H¸›iK#¨é~ú–(kÃg' 0·ñ1Œ$…z›l½ºi±Â%•í=«¬Õa9È{³ÆL7ø”u˾9ƒ´·ÏyˆÇCL5æ=sSv¾sQñ‡¥³à\4鑪€ã?×ýomý÷Š™3á0We¼“‡‡Ä¥'Th}»-}Ÿ膽iýošÛÎ2¡Gåïä6ƒÈš‹Rç ¢ÊPm{êÚ˜ãä<¦¶ÜcrïÔÍ)ž“ÇùùÖ¬ùÚ"•ý¨®Û ås-Ë#«ÇÇ'Px „¦Éq$Ù±°|{¬Ò—‰š7Yë†Y¾WÑŽÐÖeš/‡óßCõå{‚à:œç*_ÕÀÔ%a6#¬åÓæ²÷à”çÒÍ´^Nt2úp`Bú¶D+ò(ß -ñH -X¤*W"ñYÚåæ)–Õ*ÛÆãpñ1°Î¢‡ˆmE«(µ™ì^PÔÝ1iýXeãʸuK̼¬¡C‹ö—\ÿ–@Ûí­A6£*“ÀUªéýe_ð6ÉÁ\U”bJ'µ_á |ŒÍÝ%¾OìçZ5†Ý[ œ «*u÷‡v{âB,3'åGs¾øDu«kAÁh)¾_ЗVÝ2ëçÖ;ÜѾ©¾¼C¦D[Z}òz†et²`Q¥nqŽ?à¢ÝC˜9ê à>¸pÈeb÷XÅ@iÀH?Þé•pY b\é½/b©ø#‚,‹áhA@kóÿùoÏg>¯®6ŸžŠ—"¥~›Ö°JI? DԀ߰àœýÄjŒŠãY7c€r‘µMÃ)8¹¨tGf¶QET'JˆåÙqš}üñ¨¤î¢qe_EW>:VJ¤¹ï,é²öÉT*ªÊVWÆv/ô^m7¥©_}ȾonPlY?J½O_t±5dñ¢ª¢J™ .õÅþl5©%‰(—`w,,išŸw‹ BWc[Ω¾˜¦œCZÐóv>÷3 -QUûF1’\€+þ’é³iÛJ¼„xÉ…ß°Âå:!€jçð©nU¶æ2ó":¶V$´®8H¹Tbéjš/ëm­×Á‡+(è¹¹pˆZf9gWo?ôY˲ëWh+j}Ág¼ÖóµgƒÉZŸ¾@ú¶MfýÕB?—s nʹ5sè¢GæZ†ÉâDïÉ¥«ÅÀŒ@^\§½H&ÐZã$2óG-4¾à¼º{2ý$Œ/ƒnÝÍÁžJ (ãMº$%ÅB>±ñáû¾¦_ÞøÙU#|¥Ø™©½€E›©gàÇžGÒѨç›áífC#¶ó=3à‚úw涪EئƴøÃñSQÝÃy«Vq×ý¨ÿò9ðG ÑäÊ$üêÿž¸„;ôöEcÆ/*š±’7Œ±á$jôãJõXA-†c+±EÒ$Ñÿ³Gý¼TSgCý‹Œi#ÎaÄ'à—ÈqÚô-ÊÇ~ÛxÓoîF€s³4h *¸eúñ´e½ƒ˜O·Óiî´8Eí¢V:´pC/ÝÏþ=×?£d>·áHd* méßäŸÎt„È&ðMr=õ=á¹|ˆÑ2$á>ë©Ájã7ì_¾v0·h7ôíú»+mXº€ ©A"Ý@F^±yi+™µ;6–!~žñÝ’XëIkDe2OrÁlþ‘¶BYB/ܬïN¼Þ¯®eð:W•U&ªÑß„Ê+ü7nQâeH®C%Ÿ…ÂÝL=švþ§òܼæ~ç‚ò š·›r`Т9¿<àyu9ÝäMŶ¯ÙÖ“±2ÅÕÛ9(1ë8HO¼Ç6붭$m•^'«Cî`ÊIV/ ‚™1ÎTÔ¹T5y^F„™ƒ­MŒ„ĵRªu¿ÊÌVN:Ο§åÇ66Cð®éR·aŸÃjo$XÔEuRÀìl/¸{~ª§±ÁN`Ø,j](‘Ÿåµ¡ -JU¯GlóC½üÖÒÝh f8tç.Š¿æ»—`/Mº´#˜Ä8/;¯Tüuçò9´JŠ…ÍsÌöñט£x´Š?…Ãÿ¢øaÎjŠÝø%ÁTýŸ„@»ß'…æd üWcJ¢ôÓ™¹Ë38¼Ý ´3Ò!Yg©Gvá‹°½E±ýÁ€K) ƯþÇ?þÚØaJâ»ÖÞV·ÖKÓs ï^qŽxeZݵDGz9¬ž&¾žh™SJ™ÚaŒÂ;¸à.Ø÷jmN¨œs)ªˆ¡[~­Íê.ÜÄþŽ'†Ó^õpŽ˜5Þ ýrïs¿ý28’Ecß$Yqýêû]Ãû|MÌ&ë`C#Äe˜ŒA_°Â¨„‘¦<ÖU÷Àô¤I¢]„,,R#®-ײ‡Ã{{qêó:»«f^Öý=M¬Gêµ>eµÓ¾V&ÄCÓË|ebx ëÅc´gÝ“´* «‘Ä}—P ¯¯„}Æ驶Õä°{â6‹äÔ³et.¨²t$»d!’ÈÔåŸê"ë9RaFõqšu_ MRa7v4È^f£U‡@ ;Ù$õ<Л ƒ¯ 6æ„ÁÂ4ó¸†.XbVšnÆåêp“¾æ‡Q™^ƒë¼öPƒ°uªì3VŒ³—[-‰ï¡C9¦‚kåË¿>6æüθ5ƒýŸ¡†Ì/Ø$#àHw!×™Óá9D“G͹ÑBKà!åy(»ŠÀy³Ý‚0ì—ì<ÉA]c˜:¨3 V»Î{A6ؼa‹ŸJ¯P¼2GÊt34ê Y«——,éQ0·©²}ËÛ;ˆÏ@ÃdPY˜kšÕTó\SU´<éø¿ -=¡/|zë&{ïE¶öjˆ7ÒNl/ûE˜u¶_À:ûñ”fmTn 5\D¤æ OÅdXÌ#lûSσ¤U¥Ý—ŽÍ´~Ãñwýwö‹*Ýßí\TKŠ‘èê±€„ežÀ÷n8´!©Ëῆ+’/1Ì Óèî£ÅXHã¥Ì;îu~}ø*ËÙ®)Egøk<Çy•†ÁIµäï½´X-ŽeÅm‡&=§íß@x(~ƒ©ÿí¶-•Oy‘ŒñeoýIÕçáE¿1»úÚ6‘Ú¡²F‰àëñ1Évb4¿‘ùK<×›­¥º€ûž­ÐÉù°80—Àzð†Ýç_b¯à ä'…¯]9òÚ¨êLÌ%n¨ÙÎ kwë4ü›>=ÆÄ}”£Ga±Ä@Èù*>ƒ­´ktÏ ÑìVb9m—‹¤†ì¥L¿e5i—…i›àêíÞU}EÅÿ6ë£20Ö°Ùíà­3µ£ˆ þÝ0 R -’žz¸¡ïô%†XÔº4D¡þu÷#Ú2ÈD6?3.â•~Ò„jFǀظË;jQIyÓàÀýþ×)螃\çFÈr£y46MÀZ3¹Häop-‡«ÙKÖx„Zmoﺀ۪0¼ë®¯ˆ<=PÁ;GÏ™ºê‰ÁG1w2œÕ7jÇS(ö)WöíÝŠiãœÅ ô;òn.‰«û âFÀBSô íã¿1£fç¤Aô.YÙÉWé;dl¤ÑëÒx¥A5ï8é_± õJ;Ø3ÆÙa'€<0îž*Na®4=*Ë5Ž ƒ·è›Mv‘nбZ5íhNS«§TMp¤l ÀÕß±¾BRH ´µõŸèTO ª0yµ¿láç-Ó]Ø«­[&’Y„y¡bõOÆ‚îñ’—éÁ›mé W«9Oå9lUT½„U;qí«ó7qœCð‘3SqœU#Ž[툽pɈ‘ f­Èø¥m†XD¥ÊÅzè–v.ïãéL¶ Ó?‹’ -´©ÙMÅÏÏfœ42f´´/9JnŠª‹±FGzÜ ¿ø‡%”¾|e-AÍz4BÈÞárp‚ÍΡèÑ D‘ý¨ìšWuˆ¡U37‰˜˜Œº“RÄ¡‘bùI‘Ê»ê¸ÃxàÈïÿx¨WÁÁ#;z:»¶÷KŒ¦Ø£ß7˜ÄÔÁ©M øîã_·Ä@Œ¢ñuÐÿÄùtñ_Ÿ-]pù¼=4K¥ H088m<’R7 xÓŽhGY Ù“11Çt\×öásv«PÊË$¬\d-X‡_0ÜÅ9fàO¢A@K r®R¹œ¹¿k+*o›æ2"ñWû1Âõ"õ¶“ŽVÀ™©T«³›þÙÛF+4Û×BršÙ€_;ý`{,#üw矉ãí\ãçŽH^=p„?² … -YúWðàºc®øž¤çÃû–Í<“^؈\=gÌÉ-uœQ9sß®éeè¿X5ŠÚ|ß&îȇïSsú­FrÌÓÆø1HQ^1¥‹1¾Ë¼Âc]ìi"^ºùüƒ‡€˜¤-ÇkP×€ÍHܾ€›+ ûaÇøCDBÁ.`IÜÆÉgRJ¿ñFSk3…XV -M³“5¿³t)µÓdd%G—VñBÈÊ*pd6üIð=%ß ¿×–“WìúÒ4<¾$lÐ)+°X·õè\V¡†ûc ½;§sáÛÛ"’ý´­¶Ö׊A‹:ÌÆ”2D -Yî6²a%ƒt)0­‘E K‹ù'­ØʶµfF~5ÍñF|ÅÀ$­”ƒ×…÷ŸA…³4ÜÃt·”R•2žÄŽj¶âüLÔMÃ^:c •LWt›ÊßæÞQ˜J!mªJL¤\Mµ4 Ô^Á×dÝéëÑB¢Úž-í]×sµ³ ([äW{¿6Ëkßeï"PÍiiåbÃärûI{Œ¥ 0æH1#Kl¢—™+ž’±óÉØ{é牑ÃÈÞ~šÉl±¨e¢O•jÌjt -ˆC7Æ›5|š$ö>å)Õºa…P7 pTõH¿*P‹gÓ+4É‚æg?Ó-_Ú,æ¹Bv ž¶‰²¯ÓмÉNTžýL¾ÌŽ$K¨$ЉÜùöì -ª­ &®ð?háöð¥,BÊ/J^k -ù™nþž`wHNPYîN@•3Âéž‚ñ±¶óµ°¹w)ÀŒ°ï¼§§Þ–r5mÿ¾£kÝjzö¥þaŠ×ggªU(Ü2±ûíJ3p !/îB€o½ËX‰¢÷¦wö3.Œk¡’Æþ¤—³ÅÿÓå–šŽ•bà=m¬iÓ—Öþs_N7Ìðv»;=$ÐíÑwÑÆLÏSîO[×µ-Šþ;E+ƒ^gVSÝ1>L½ŒxrA†š,Â6¥ œ;úª÷‹½^ ¼Z„r: k3 EÀh|LAQöy'>])Ü¿9Œ~Œ¢‰¯_U cp!I§ú§«Ò»D€: -%/ÄßÄ¡eÁäÛó|Ë!ô(AÞ‚i‹prß‹…É9¶•ßÛ±*iC©¯”Tw h˜qŸT«³â Ù0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ_ùc‹‹sˆ×t Úí?‚}¹ß´7-95†ãžç¬Ÿ¶©µÎM/®ÀåZà+üFCxw¹ö\#㺴úãDÝÉ«<ËÀa‚Ø=ÇVùÕ¾þË-°ã™—òdÔ½oe¥~”ÉÈ„š²é Ï£¬Í‘ÿRJ­rb±QźдÍUÒãiöè6È,YáåÇ?Þ?£ÊÒrÆ|l¿C¶oä¸g}¯î¡’ˆBþ±ôªhz­mÛä2qNyœúIØ¡¡(ó.‹($¼€AñæNÎ@SÄŸ +ìišu¸'.Ÿ•‚m³öC3…€Ž3Š‰ –!vÏf¦.:ïm‘ÈŒ‡Þ°<æÌßO¶Q™†Ñt ñ!w=hwß…ß²i£Àz¦f½óÅ=¢1‹¡† +³N(ºÆè-ÛCå :Éß’w .BÀ÷½ÆÙ béw0$[ŽŽ‰¹"P˜œU£~NY®*ž6¶4Ÿ¢À›±õôC>NïÇ^?˜0ë^~o¾&f¬Z9Œ-ò(*ÏŸÊVV9 +ƒ|J™ì7@ØsÏï.$‹DÊF“§‚YMÐi+M¿ÄÍ즒ÄDý¾÷¼SW[ò'1ç÷qy4­qZÃ;]6y·„É@FæÍ< +ØÑöV&±N3ÏÚn²‚]ÄDúb a[Àsÿ½üÊKõ kÔƒý†9ùèÐ$[F=e ñ,&Ȩî)uv–Ãñ1DØêVIj­a©Iç#«µ…™“ò +5Ík~ ­…QÎäa’MÃjFJ¡±L3úû†.0ÆlÅVemÙ;Œ Ynžâ±ª´y÷ú£Ry­´h¦$¾&Õ'¿õíàgYŽ‹x¤¼û Qi-°¾»“ o —´7âŇka¥c¢g92ÂX3ú£]²*Þ#5ÕÜsJã¬^îfX×’ëbû¤Aõ>ÿ!ÙÔÄ‘òkèõLa\­wŒèi\î¯pã² dÔ³JKWpº²©tè˜ö+þñ2£~-ÊOCá=±<”ߨìâ·7H'®†4ú‰­ FÎÓD‹ôSüÙ¤ñ”údŸÀ—4»iËsCœ°ÝD§Áò•è3Mû¤`ÿ=eOŸ³7éžmfû¨z~¹Ê6ÈH3‡6&ÚUÔèPÓæö² çÉÖ(5†òÛX.:|å[èH"É‚7‘Säyê¶Zþº?a§c´tS[ålÝùDA\‘t96‡6a—ú´ðn,2šàºA?Õ"ÙÃ:Ø6›×ÜÉß™7xH/5ùe—=èvúá ªŠeŠ³ðØãÝÑ¥sòÕ% *üWà]l ¸áþ(ê+zE»6:Ðl12 ,ª]Ì„,èš/§Ê鬙‚óèÏ#ÄüWý±Èþ•ÁàK œ0€F‰'Ë™³ÓŽ*ë›Ümö*çC|àÀjጆç[O(“„ˆE6çÅØÇ´ðPÙEéðK¨n£cù¾Ù}{«´Ð®b…V=ƒjðBŽHÐO˜%>W¢â|¦$ý,±ÞêÑã”[m6ÑÄ·«Ë"j¹¸ìô/¥X´S™^Zö*™$¢l~* IÈNN-þ\û¾6óJßD›4à‡¿:‘†ãMÀšbÀú¯ç¿/ýŠŽrŒ®. ©@ƒ +ÀC'SÒxÝÚË +¢p`Ò# ôº~w/'\è fñÃæŽÃ»›çbB¹™V,§ØË•K d‰îÁêPÅVãúÝÆZÈÜÁ°VQ0ˆMhÝøðe÷ëù›‘5§(˜ËöÁ¾~ð­b ª­¹ðÙÉQB +»7Òç:!ÂÑ©Í#œÛͧN ™á„TZA¯ƒ/ƒr”gYéÛtàÎE–°¢sø0¶H+Ë?v#]†áK îÛ}r{q!]B¿*Ì[⊮?ª&>e7"KZmI|‹6™¹K¸`¢SÆ÷®5Þºµje)×¼Ubˆ0ï@•õãK™$þjdµ}uÆ'Ð3—CÙ+>À-i† »8žv‹âÀìmZ#² ]!¾ë¸§ 0ÃBŸ¹ÖFŠç„¸»¶(îÂo¹ëâuòƒÍù±YØãŽI÷øÜö×m®*ØT¸Èå+`ÓUÎ#˜ƒŸºìCž­l¨5?A-Oomoü­Ö‚Ôx22¤ N¬ª®1ŽË£{ñ‡Ýáú<)>]¢M¢S£.À/üâeé BÓTYøŒç×A 9J‹q?+ìÌ! ¨)÷+7ý˜«bµHAú]ÑCšA¼Úg8¡ÐçuOÔ +ÄK~½¾]Å•ÆaØV8úëÃ'KxœÎ„¦Aqj³¬óo"ûÊ5áCk~!¬'“œrŠÍ=dpUÿ`·ÝV}ãÅolh0ðPÈðM‘"ɉä›j[öÓ*@ YØÀ'ñc²DO{ll +J¹5˜ðvæI¦ ÃBæ[ÛûcÁ*EÏZb¶«N3ß¾„9ó<¹"Aß×vxÍν¬ÕÝûÎ>UžBŒ¼¥Œs3 ªÁ ªð‘ë]ûÏ9Ë]o5±9êæØs,?ú߆€bînì½nŠs2{üÒB>Ñ;šÒqZ¿:/–Y9¬à3CoÖzn²÷ +?€äÞ“)2*¯u¼¾?G¶Sª9#F2‰°ú)4˜¾{…x>;ŒËõ¥¶à‹vô¡r¬†@†Çøz|B¼ÉrÍû¯»icê!†ÖÖ°à‘ØNôfgü"ÿƒ«` B‡êÖ«{Ô™møÛ-^‚ÐwôY~ÈÀ˜5 ÕËï²>lJ¶øpÔ“üEｿ3ú}™¼áöXS©a4нÆý]yCëœåøUA a·Õ¹:ÔÆ´(°À’˸Ž›†«ýlUõ;ð>|sª7?­/ÄÁÓxìfŽ’P–¨w.½Ž eêQšX˜Ð.Á@àéçÁÄ|Í\(±têqz4´Mmí°¥žÃf˜dÌS•‹í!Á¬{æÇ+̸‘÷ÃéÞ5´Î°0Jä£|ê¶Ha§–PJçfi1&|½G;ÀrGB~bnr–/`ôÖÍÆŠ^ûYS¸˜×VÚ4±ëD\=ÖÛ¿VJˆ£‰ìÃ}½e}ôH’îT¦!W‹™ñï(#¢d/œÆ@ w㺄X"‹Y6íà`õU-€ 'ˆê5rßü5狀Ÿaâu/ÿÝ.sñGcÏ9lïöøþÍw¡U>â¡OâT›róCér<•òIœÀDڙ΅„±jÈàx8[ÅÜ8K®zZ°Y{Üi>)}ùŽ²5LH%˜þ¼­qÍ­\c“+à‘í` 0ßhɧf‹^#?UÏ{:9Àµ¸ÞA‘'1‡ðd¯Ž. È^C—Oºó_þ+¼$&s ëì*å7éÁ©K+ƧJ55à^ÏÖùÑ?• ¿«½áWB,°Kc²íí¬-PŽÏ±Ę́k¬­w«úw“¥Ÿ\ª›_¹¤b­Äûê&\²ó1 C„¯£MEF‘Q§L©À&0X›Ë·L@l|û&`¸LÃZb¥%/²<ú*ÿË«µØ]L<È“ð5U»‚s|É€v¼Ú«Ô–ïC,ó£~‚„‘Hàa²æ _ݳF˜N(žÀ5N®|¿ E¨r·a•ËìsƒÎ¥Égá™±w¿™€¶ Ž?T ˜“d÷of$ÿVƒßÃemÔ[x‹;²N:m[hý^!¬½´2zk?Â*î²*¬-£QDÔŒ573ËëQ`yü:^{ï‘‹]¯î5Ý tTíÐPr¦¹ RÕ¯¥AxS¿9~§–V3XÃUXô*ú‰ï}vÙWÖµPý2º'¸54\͘¾ö½½ëÇkÛ#þ®Ÿå¡ñ{_ ‰Ý.=p½Ýí û–«öpÔ‰ñ¼„&£Q«ÎüÓq?$HøÇy.?çpîÚvø±»£Z â—½tbFdú‚ª§qæŒk( Œ³HÚ0—ü°/¥ˆ-ð;×z)¤!és¨|gÓLŽKbær×Ä?{à¡ {óìá¶@9eRÀ”îZŸÿýò°r¶Z¶2/ÕñÇjt¯ á»…9\cȸ0ëéL1Ϥ_K­vi™'TIçÆË•„ÿÞÂNÿ¢ï½«ˆ>_GÎõ!e$»Þ–fÌÂÍœt”ZõXviÖÂ,»‘º8?ƒ/Xˆ÷˜§§_ÝÄÎßH—†ûiü‡@0å3ø{‡å‚dÑyØŠÃõMI®9(–öÙÀñ2jàÓ)iŽé í¾Ùào*®Ÿ¾W\ŸH|F¸ “²7wͬ…-šUIòÛ€{†«v*ŸT$æ74Û9ø”¡4+A·JìÀŽ¨@ùhƒœÙš(Q’Ï]ÿäÆËMƒÌ¯ºÙ}”ØÛóÿů#ó¦ä™Ê Þ’IJs)œ³­5uɽºü(A¿Ô(tÌ_ÅPk‚é讈Z?ˆ–º²²Ô×R]à[=S$ˆŽÓÚ„Ä3&ù‡md÷>JÆí¢#ßc9¾éï,¢ñt Œ&vkPŽ¨Z‰c’€5˜²Ál]O&H‡Ø¿M¨‘Ý“£AàÌgãJ¨_s÷®:Hšœæö—½OÚÍÙ˲btÿ´uc˜$ÿRÒÌ™p²U»//}Íú;E±éûW=4±y WÖ¿!Û¢ÒEª`ñ“"ïEÓ–(s ¥ëF[‚šÅl‹.g륞d U +®™GéyÔ¢¬Ë ¶4Ø7„úhaÌÆ òþHþÿÒã³ìŸ2óKF^‰ËHÈ—-}“R þ°"¸”3ÎOã­TT¡+guŠTÊ45ÈÙŽ$^e2ï lK’÷gÒmu¸{‡Kð—ˆû·Ô¼¾ +kEý ”’ñb­§ƒþø~³?JÜfÏ)YݱzÏÄùzUèä­yß N¬Ÿ ïÈFU«¤Ê‘jf 6*göu‚7z‹¸¿>嚊mJ'8K¤Œz)dÌl»|¼5åÍÇ@¥Q–ÝÒb¾ð!Gõx~Ó.ÿ`ÈÄ%²®zCŠŠíD8÷|&á²R%Ó’™?"E4®ÃÕ’Ã\} +ÁjÀ% +èþG ŸÆ—úPÀAGtáÇÜ2 ñ„õØÈkJÉ(ý]eCˆ‚v‘BAüwŒÏ æà½÷w¯³ªÉ2+°×S<^ª‚†3L<#W€h= EÃi‡|¡/ËË2 ið”¡GÁÅF§pÆàyÕ…µÏ[x¨s>«Þ6Ñ¢Ú8š…öŒÂ>¿þLf½&@UÛ³£:"“ðm±<ì8þAÓÎ{2á¹·/2NÙSD¤9q‘& §¹8óL¨ò¸Ú=À}?uì<þ§™:ôÁÔë[å¤xÔ Ê¥b÷}ˆ‰‹¿ÑþhdWßÙµyäëD@ù÷i¬ +©é£JÿŽ;j€v«È¾/¬¤íRMÏà ãoz‡µ²,VloûÔX–jô­0Í1%|¬Ù¾„h×û¬{TJ:A^b*e”ŸG) á,•+‡´ÊXSšà7¨²ÔnfçÝÿÜÐ «öçuά ç¸æVbóÔ“yòCMD£}³®£»…è$Fþq‘ôÑ1“AZÑ»k}מTr®'ßÌM”´/dú­,cçi5ÓØÚÈ<3ᘠ+;Ó‘ˆÎÂœƒ—GEßàÛ"û›!]¯–òEé›ö›-ÈK,<ý9¯wE&ekQô³IÝ$wÙþépÕŠ1à Ñ(_Ï_×v®Fš£!W}?‹œ +.²ÂçÑ$UoŽ •û•ïÖuýYSî1¸¨þ³{°??à+³aóIÖÄ|õf¨½ý&Êæàÿ{ù¬ÒL‹UèÐÃGVí˜8y«$àÆ!Ò?nzôøÛnsG4µ•wÕ¥e¨[¬s"¨ká±sÝuŒÉ +ß.žo¨‚œÙÙãŒ×Œí¯§„þõ¼-ø uXÝñÕ`“1óö#0„Q{Å~-:—…ô½aj™8·wQx&RÏ£>'O Ý†r÷åº7#\~V/-CÞ ž¬‰5¨kè+žCý¦ÌbÕ¼Œöl„ŽØL¸²äª*„)¿îôIκó¢.¨;ër«…>÷F¢]Åp£çÅŠuˆyäiºÑ œžÊ–É#2¸éȬ@9æwµ©º—öªU: s”'34^p¼s¹. À˜`ƒ [jEeŠ7OF.Ú_Ø\Á”óV"UÛωÅ{ •´·™z¥ìT÷…šÊ…§“È nCd%Ê™¶ÇŠÐîÜ> HrúäÊ6u—¨~êH(ÅU ÐÓ°…ÖJÅ%Ó•VžÜ@5°±4]½”¬õë–¸Z·»)Ét>n3`SÔw‘"‡â—h¸"?Ý¢ö‡ê«f\SVÀVÝtbâpY /tï ~Æ31…‰oTÀðž1ê<ÌFx‹è^2w±­g øXe§|ÚØ˵°Ù3{>%âÅà·Ff_MoÏ<&kó +Ó9¿š¦½D_\¶kIí!”Ÿ’ë‡ô(;ÚfhÎ8í¶ØÎ!)v¶?F³-ï%ëGo5e +UŸb;c¹Ûú1ŠÊåRºÈm +Bp.Ô÷òôêè›ÞôÒ$1²ñ/Fs8T§%xÁãT9F +‚¨‡)lÚíDtüËîÅ õJVÏr ]tPØêvÝ´ET-W0y|¤bÎujJri•hþiçf•´Rîórݬ%z q¥²â¬±K~ηn¬ô;JtÛ¬FÇDˆüöëd°¥UŠ'>Ä}úùÜ°Y åÙÌ…pš‚ÝÁÀ¯yÈ’¹µ°§*[R€¶è@0‘ž™”/¸ž5EÒ°®ûÔzc[ .óÍ †ybÖúÇ戋…ÈÒœsµ°^oÈ4vZ³iü­?HúÔšÜ!÷€s¼ˆtl¤äª¾nK9Å—M ý—§iê]4ˆÈ­7ò|eE¸ÉW×ËáášçvoâØÙ—š¢=vüâ›°QHÄÁ˜„Z¬ˆç;ŵ$‡î×Ø^Ý;»´–úä*õiÅ :À"lõÖA`‚yËcû Ñ rNÓ@*Dð­mô(÷¬·R.–»Á<gÛL—Íü>¾¹àŒä>!†Ë9•TjŠ +Ú/`Ö#ŽÖå@ŒÓ¬8Ÿ ˜Þ â…£Œý—¾€’°Íç|«õ"6Heê¬S ®; àÞÍPÇoRû¢í„‚ :æ<‘×Ñ~»•—¾sákjÙjoTÕO+hI]6Ü¢o|ïõà[òT®;ž—Ë”ÐK_zˆj‘Õ¹>z¡ð:;FÓ°Vqú#,Ö[{Û8{*¥¾D‘I¸÷s·¦X5g¬à…ú)è#7pÝ\3õlþÙø¾¤t¯H¯Å~Ú*]°ˆ °GGŠž‰7¢â´U\ŽÞ5Ôoî‰+¬I#’çÄI«Ä1çÏÞ–’¹w ·¸2š%'é‰[â܎ίØXW>çQ­ålÌ–[«x]‘€Žq#)lå…9“èŒÄv¢)+ŒEÜW²#±¡R¹‰R4ø·…ÖwŶ÷Y¼¯< âLel_•ß›(ëÍoS‹»¤³3ËlÁ‹¶‡N +*ƒ`ó?uà`ʼnì*«Ô]”øžíxËU&]:hÏú¦y!Ï +¡¤gƒ7Rv9â7Ü~ìµ¢â">šÜüòZÕ­‹«m¾XCŒ j9£iT<¾¦á»ö¶Ô7rÐ×QCX q’ocO·|V MLæë³A3v’‘ZmfÜ]¢3q½<º›§Ã[¢bJ.ª‰­(`@Ý/ÿM+缋y{-¹]F6 ;÷>ý;šJ®JPiš7àqxÙñËùQ™ +¼Ï Æ$5£ÞÑyn ’L¤±÷:zwîÕTYƒœ@g®* +á—å`º%0t_ò†×ݧ³ôí‹ÒÕíÅÿ_ѧ¦ãuz¥ ‡ä'3‚«½¦>A§k´ì´yu¢ìüÀUV Fé]ÃÅþSÖRpy18r•*»@V¯"ãÙ¤¶ ŠDA’Æ¢Tým1êOÙMEŠh3þm6{_ò./jbiï'‰ÞÀ ýOvñBÅ|Îþ¢;g7~ÉE1mŒ"¡TÌbÊüSÇb— 9 ¿oC<ó"_ßqaC¿¼ÄŽ¶¶8ÎH¥®Æ[¦7<Ë@À\&[æJ¤Ð"[ŒSwYh;×ã'è¯ê«e·½ÉžÿŽ²äbR=)à†78×ÐíjASø½]¾/[ÿW“ÆÚñUÁ‚žrtNf6ñ&*€¥aÇO²caR¸x»9=>=Dq| $θhÁM§¡èñå’]æ#¾ýÂuè[^Qæë-kš D H]¨¹ô„ЃGJº$6ª‡½aÒ›]¹yÍFÿÔðSmoQUm–÷a=.½`̬H*ê µFöy¨SUÙF¢¾|ð™#˜¡™I8ç. 3h˜¦[Kp*»šÿ&}¹Â¦£Ž”ìuJû2ã1 Ï«mÓyˆÂ+¨¤|øMɦ‹É‰wIDá[Ç>`cPDMžù> £'/*PFŒ£ oö¢aŠUzhÐÉ°äUg‚¯þ(z. Ü̬ÃÓà # v?˜¾ÁumMßóniÛ„ÙÅî®g¥º‚ÍFESKÁšrª(ª\Ùv˜mü5@„G°ÂŽØ=ˆášç*úÛ<µ¸NËôÕ¢›uáBŒ¼RHù¶ñÇfi5‚ +DµVã 'N"ø7R¨¶¤ Åѧ<¸nGŸòp km ¹€ÚO〽ÊÄ*ª²;̓P¹OÄý\>ýŽ­«…žÞ«3³qßeî 8rŽ`ÑA~ÚFŸ•7µ‰U®‘Ü¥Þ²¾ãXÛÄÈz#„ªöóÜ:ˆ™³û±t¶vÙxÌ­½¯™ðD^ažDƒjnëæ6n¢D†>ëÙ%ýdÕQ6çªæGs.ßq8MÃ@YC¿3ž `Á´çiˆuУ"¼.Lò^¢>Êä ‰«3@6{âÌšµéy¾ÆïÎÌv0®?ÚÎ9–y™îÚg Ñ€¡"¬×f²=~3"ÒïVX1@¹0» ü:5Ÿ´a(ÓÅäg|¹z¾BLŽNÚ«³Öf^ì›Ïväù«Žƒ5=ä´YÖoTl¬€$ŠŸt†WLÈí²Î¨ŽŒÔ¼8«ÜæmÄ»/W”‚«ççt–ËéœØglÌf•ZÂ|ÿƒ1HV=uÆò,Ù?ïð¢ Ïà&¬8Vºæ¡ÏÍðªÝv4ÄK×B-¿Ðñkù$ :¼' ޙˑׂyÃ\¿—=?“?òØieðwH +MØbfÜ~'“Õ̓‰lé ÜûÒ'&eÂ8Xòðúª¼†±,ÐJ=ÕÔCœg’ÁOq\]W¹FLôÖi²¥ŽÕP¹ t +®å7ÕÆ°eVpL@­Þ®è=ÞŽõ˜Lÿû¨‘¾(Gá˜2 ²ƒ{Ö ¬~“¹Ë°‡©>Åþà ’¨!8ñ;ò½þG\ÔÄ(»VüqVùj/–«s–y×bê–?#]î®;mˆQ+Š¨žø••…í†4,:ÔL[ÿˬ‹8h|ÍrË$ú_æÊaºÑƒ|V¹ [ +y"‹=¶Äó ì†ÈÞºîLÔÏ·8ÐÃ8uI¥êr©$aQôW ’Ðñé–¡1®ý ñª"øA,¡X;¼D\’^Mð>K{ž¦*Õ1¾`¤iýÏuvŸªQE^B½Ýuˆ¸åh ¥z¸À`ÐÉéñX'%O92Yлù\ð$cí‡|'Ô ÿ³`a˜ùT¨™µi'D¹ºSvíy@Ø*ÊáËÆ›“ÛN<3urŠk"I+!oï¥ÐzyíèGo·<zˆ”Ou=”Ðä>W •Ì‚˽"ò¸ÚÜÃ.Fé}v'<dµä¦Èâïü ë ³¢¢íj"]„*+¼Ñ\ ‹9î +±ò +oJ-Jñ¾5¾l£ò@ò…m$ÚU:Ö~Zµ­ˆÝÜÙÀj d`` èô—T*èµh’6 Ó¡.›¥Ë‹¾ô¬ÃyìëKæ|,Q$¾pKyâäšÕÞü0á·ël-ìÚE/~é ŽTÁ–&vP”cþ]¹Ä²ÅLX|žºg½¢·ï»jFæmOÞÛ+“—¥Å‰Ö°Ó˜ø•‹KûHçôâÀ›ô¼é3ŠC 4ìâý§‡†ª)~àBg•ÀUk‘¨ß"ä©m/ŒÌíÛLF}RúòC`D¯˜­å ñˆÆÇ]-~fZÔxsû¦_ïß2¸¦ùu`C endstream endobj -176 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 531 0 R -/FirstChar 14 -/LastChar 122 -/Widths 532 0 R -/BaseFont /VOERAL+CMMI10 -/FontDescriptor 174 0 R ->> endobj -174 0 obj << +494 0 obj << +/Type /FontDescriptor +/FontName /IZMJER+CMBX10 +/Flags 4 +/FontBBox [-301 -250 1164 946] /Ascent 694 -/CapHeight 683 +/CapHeight 686 /Descent -194 -/FontName /VOERAL+CMMI10 -/ItalicAngle -14.04 -/StemV 72 -/XHeight 431 -/FontBBox [-32 -250 1048 750] -/Flags 4 -/CharSet (/delta/theta/omega/period/comma/greater/A/D/E/G/I/M/N/P/R/S/V/W/a/b/e/i/j/l/m/n/o/p/r/s/t/v/w/x/y/z) -/FontFile 175 0 R ->> endobj -532 0 obj -[444 0 0 0 469 0 0 0 0 0 0 0 0 0 0 0 0 0 0 622 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 278 0 0 778 0 0 750 0 0 828 738 0 786 0 440 0 0 0 970 803 0 642 0 759 613 0 0 583 944 0 0 0 0 0 0 0 0 0 529 429 0 0 466 0 0 0 345 412 0 298 878 600 485 503 0 451 469 361 0 485 716 572 490 465 ] -endobj -531 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 14/delta 15/.notdef 18/theta 19/.notdef 33/omega 34/.notdef 58/period/comma 60/.notdef 62/greater 63/.notdef 65/A 66/.notdef 68/D/E 70/.notdef 71/G 72/.notdef 73/I 74/.notdef 77/M/N 79/.notdef 80/P 81/.notdef 82/R/S 84/.notdef 86/V/W 88/.notdef 97/a/b 99/.notdef 101/e 102/.notdef 105/i/j 107/.notdef 108/l/m/n/o/p 113/.notdef 114/r/s/t 117/.notdef 118/v/w/x/y/z 123/.notdef] +/ItalicAngle 0 +/StemV 114 +/XHeight 444 +/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/R/S/U/a/b/c/d/e/eight/f/fi/five/four/g/hyphen/i/k/l/m/n/o/one/p/period/r/s/seven/six/t/three/two/u/v/w/zero) +/FontFile 493 0 R >> endobj -170 0 obj << -/Length1 1693 -/Length2 13827 -/Length3 532 -/Length 16052 +495 0 obj << +/Length1 1545 +/Length2 9023 +/Length3 0 +/Length 10568 >> stream -%!PS-AdobeFont-1.1: CMTI10 1.00B -%%CreationDate: 1992 Feb 19 19:56:16 +%!PS-AdobeFont-1.1: CMBX12 1.0 +%%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.00B) readonly def +/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMTI10) readonly def +/FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def +/Weight (Bold) readonly def +/ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /EAJXAT+CMTI10 def +/FontName /OBIUXM+CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 11 /ff put -dup 12 /fi put -dup 39 /quoteright put -dup 40 /parenleft put -dup 41 /parenright put -dup 44 /comma put -dup 45 /hyphen put -dup 46 /period put -dup 49 /one put -dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 56 /eight put -dup 57 /nine put -dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put @@ -9369,37 +5141,45 @@ dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put -dup 75 /K put dup 76 /L put dup 77 /M put +dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put -dup 84 /T put dup 85 /U put -dup 86 /V put -dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put +dup 56 /eight put dup 102 /f put +dup 12 /fi put +dup 53 /five put +dup 52 /four put dup 103 /g put dup 104 /h put +dup 45 /hyphen put dup 105 /i put -dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put +dup 49 /one put dup 112 /p put +dup 46 /period put dup 113 /q put +dup 39 /quoteright put dup 114 /r put dup 115 /s put +dup 55 /seven put +dup 54 /six put dup 116 /t put +dup 51 /three put +dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put @@ -9407,117 +5187,65 @@ dup 120 /x put dup 121 /y put dup 122 /z put readonly def -/FontBBox{-163 -250 1146 969}readonly def +/FontBBox{-53 -251 1139 750}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÕ™=ü 0)xfáÍ -1›kÙXž9Hÿ°´ç!.ÉvÖP™ØN 7§§qÃjÒj7!ì6CžìàÉ«T´w.]Ê‚ÐÔ¬Çô/´“ª£¿JÖìá†1]¾œýËèÓè0'Í:ú Ôf¨èÊqdÏU³2úÔ4‚tÔ¡Ë?@Ë^g+‚ Øþ0ùð[ðõµÌ -K–îT•B/ºU¾é¿ÙFM˜zÄÒ7Âú† .UÎ{7‚£KÂ.=ãUÙ¯ñžI ŽC¸^ì訹…ƒ$ÒO7Ûù—-tæìG„rzÀ œJ:ÓÚ"½ia~ -ÚõT"ò*Ê^MÍMùüч¥f·ûf0EM ÖÆÅ -z8uÆËøìwió*?ÁÀrºÞÉw”Ôé5(*5nZœÙ«Ø -Ä4*RƒäX§&’RôT»dR³žÕM3m ’ŽœÑ«&­ƒë ž.ÇP¢d8;]»F |H!µòÉ%Té ã[-¿Í˜€šŽÉü‘Þž †E|p¬°Vëù$MÀ¥»ÔUá]n1€1RÏP°¿} -dó¡‚ -í¼.{®µIþQŒ7™Æà‰µÕÖ^N-+C ßú#̲]•\MØ…1 -pk2 -²\t,o)•2TúTÚ®æÔw‡}¼ÒŽšµv°êqý `×;líSãgs3c-ðh®ðþ}ûW9;Ú¤9¦¤Ã–ø`2©€ êá${}è;;ämò‰…˜ÿ^l¦•1'C*–~OÔÝ`ÖäšXúUnó0‘xµ|§cÏɾì'iD½ê%W‰ïNÍáêCîÛ•Uô.ÝÏ9®R*ÂÜR?nìLÊâW’·ˆs/[µÌç趡¡Û†±ê8ˆ>Hêµ@#íÙ»”çx î¥w­ªžf«}†´ ažyòBÏRæ¬ ®C1|P|Û'êŠrÔèÙæ,˜ß°IÇŠÑU`ÎD£•½kUQe ]A©ÕmÃ\‚"Gm¸‰F”O½ƒ À)2rIuW‚\ñSøâWäš,'Ëv¾ÙÏdy]eqXH0#~èZ²9À…±|pÅžäPæO£HŠ¯au`öÎþ©C—Ñï©àbÇ鬅<Êç=ï?t8é!½Ô-~œC0¯VŸØY-™¤ð…¢aht×`õrxK[3ÍÏ,Øðf @Ñ=Ê]ëw˜G2C#ÜŽŒ»þƒd#QZ÷´^ÿ €â>~k†¤Ô!³ –î]lI½ô1”ÛöÄ“±h»ó÷K”*éQ9Aó–Lr íµÆ¢L¬X/’¾Ò‡'“Фô9׫Þô»á÷Þªáþ– <ü5ƒL -ؚ؞²EN_4, À5—éoÒ„v½%¸§ Êkj2àóÖ®àsÁ»&gëÂrÕ…ßdám|ƒWEOÈéÆšJ©ä!áAz¸â 5Q²{CA<¼°É>¹ÚŸrµƒ¶(.DÇ}ÿ`¢erÛÑ8ÞS!hÝ.íú=0 -XÄi“}w–B.ýúÓŒTI߸=fä~ŒÊ(Y&)ðGLig†»¥ú,`/^æ9¬ºæõ ™6¸…T -S1¿ŠÕ^WÖ6Oc—îú×ã _‘`6lÑ«K8\C/5ì¾–¶­_]P¸Ž®BÑîè¦2+µ¾#(¢, ’{j4 6â­ ¢>ßiØ'HâŽß¿{#Kºâ¸GÛs†%T{Åë;ÿƒ.™Hûž¡£!7H‚mÓ)€ª4*@r ¤ˆØŒ9¬`®ÃzpÔÜÓ™~´þ·(k²E{ %¡¤dKä^÷ 7)-ª må¸×twZऽ™«b²ëßOÓŽÑç29lP‹(¸LÉ5ÕóLÔæ1‹D´0ØgXðhGÏ€-ŠÃ*;c-4æ‰PÛÑF-í¬ËÖÕæ‘';äuÿ² àxã3 %Hâ#e#ñï¶ÙíÇö:¬ó·‰+]2»¨hÊÝ”“\0í”ÚyTˆ7?‰tömÆ 5”‰øXõ7 -qœ|HaXY‹'0d Œ‹ìJXø°†­H–'ñéMÁl‰A[l(,ºP9]âE,ÇÈ€vÑ?›)‹qs$åDkôª°=k·¼†Óþùà7r.®-ÔY)×):ƒd -Ó>µ2àÌqX˜fóô0|Bå•%êNß$ ãÅúÆ—§°mq¨2俳²qJyr2ø’ì¸ñ˜„Š‡´¥7\{|;±q’«4bUŸØ»Í?k¬’ï$¯có×\õUØ„©rx˜yOfÀˆ/ø,ÓQįå¯1ÂÚ:÷ÞOCµlòѲ’"õÇz”8sÑÿ€4ûl”£Q¡TÉS¶@ˆ0C„|®µU¶iøüz9,,„(ÿ¡î€×C`£4Ÿ$Iº±›þ5Ü4úS©°~ÇŠ½® ô„KßDªSÀ–l3Né¶Xàê dĨ5¼nEåI1ùÿÄJÍЛc(#3³õ„!Ï:Ú$Iàcxæ –4q‘4úÔ€¦íxŒÚæaCÿˆûqîC°okO`ï"OÇèy×åâŸ{AðêÊÓÖOƒh‰ixš¿¡Ráçš|N>ښͽ$zô5ncÿ6y¢ÃO㣜Q-Õ½ÚlÃ|Û/‡8q·¤£Ê›¹e™Õ•‡bÌ¿`€ËôVJ¿V[踒”g0qëºGÿ¹N€t!ü³&ý…¾›‡ˆ²®¶ÄyZÝ~öXëó•!#qV!ÿ!…ÙÅ@ÇÂTkê#ì´ê”7ÈÊl£î¯¿æ·ÌÙ¯®» ,“Éı¤·oV÷½\v\€˜§sc¯¦ªR ÌØÏ”œG’ÐôÑÿ–CÑkÄ^~¾øMÔ'U@µÝx˜2ŒËZ–/æ?bue–æÌ1°cõãAÒ¹Ø b^ô?Jé‘eÃ,%³ÂÉÕƆæÄ‘¶L}OÒ«Ž'ð– ÎB;¸úª?Þ²ƒ~ç€Øýuz%¾n$äÕò×ùäѯ¯°ƒ­&x\¯áÝ$~?PȦ©QG¬oOÁê…íÌM¬O)f+­ -þ®C‰3MÍ–y0ß~Ñ4Á.n—(j=oÑN¢…—2l¨)yìŽQg£Yðó×ûÂpOÕáñùÏð"£Æ¥®)%{èï„ÊK­XΖ] öÎÆ€bîò‘ßtÇ…äŠÂ‘óÈë’–iú –Z'Þ<8ü«-ÞÙý^¿™ŒG5ÃýÛJXtƒd…—Y•³È׿.qF75ÍWŸÐÚAË~†S†WÂ:Ë6ˆ%öPëÞ¤Îÿß>æªývüøÐ<}Êÿ>? d|…û€˜SÚ²ªØÕkªâHmƒâr˜¢´ÍAAq¯ƒpÀ3&êÚÊõ(¿kJf,ÈÿÌAj Îj䌯 dŠt‡ê6óeê`ŸÐ­ÞBûÊà¢r)s¸SžÏ™Ú»aŸd6µ° ­,QÓ ÕŽßwì€US“£UR8öÖþÚ?ˆÒvòp„:&X­¦×“9®¤zš$ -j#nzk3ùw…oaËñV Š}Z^4#¢4ëÐÛ*–w˜¨_Uh×oT:#8†`›~í¨ãÕÍä…qåB¯‡œ}êÒ9Ëò$ú&£3äE ‘–àPqãç×îJtL§gl­%„]Ð -Å\.éӞܨà÷Y:>ñâb¾×Ñ£Ꜩ–0ß¹´Âff«hÓßÊŠeÔ™žúîYPlÁïókÇ©F³¥°|Eˆ®8Ô–ÂûlkìG¢¯n•@kÀãdžĜ…$$eAð6OÙ>Èó&ôûÚØ=$8½džôÁ$°?û¼µDÒe7ßÒݦŸeâ´è9“.D3Tã ÏC#‰œc³å+Sã²e`—«H×Øï™4GjÊYüà”xqØ^8Ð$5z3”!K‚1Þ±iò¨k¾19n¸âƒÜ¿×˜¯–€Ý›eð)¡¨Þç`ÕÐRÞfæa½f¥º”~ÊÈýNýE·ºJ_Ši­ä6)æýÔ Î/ýØe®[¥V,fð,„/°3Y‚n„õ37€Eq ¨ï_žÏj·éž |š"„mÙŒ‹oIJÙ -îêfg!E}$3õ2Þ­¨ws8ºý€r¥¨a¥”ÖÿOç{ãµ.—IWM#(´ïÿPÇæý¹Ð¥½ÜÍ""™ÿÎ3bD>ÈÔ•¹ut±Z©ÇyI!?Ö|6áÇ KËå$èÐtÒmî†ÙLí:šŒÃÍiÊš„lÂåQ”¯ÖlZî*kYÏK3MÀfTˆ‘ÀùéSC^ÚJ?KµM”ÂlF´b'‡s -§ùpðJÔtVÃÝöOH´_ßÍŸ)þGy lŠNJß1¾¤DDÕú·§¯X@ß“`‹×†ýYV}Žuƒ¶®½ÓkY‹–ô£þŸb¶]3ƒ‡ÔpFE{~uÿh›vàvJu5àtýÿ?òó r:::cL…ËCW9•ezH.=gÕµSãšÊÒ(Á$Ìç¾oP‡ 7ÖÅ”¥Ï:íúÕ\™ì†ˆQ•»:&«2èçË£GaªfB 2¦ñ>kè -QºÃ ^Z‡òñ´â$Ž?üžá1Éz¢ëe‰lÈ0 àÚ|Ú‰>]µ~¯ce­}ûø"ò¾Yõôõ±IOVèƒpQ‹­¬Ýþ8È0G¡j&õÝqîÐ;k·rÛ?aLÿ 2w`'žÚEÂJ1†ïh îq -Ž±ÕPªô'5áÇ °Úшøº·}8äÔñtÒíŠ7ìã¤y}Ì´‡Mˆ»Kw™KÓÀ•ÏÛ^ÒR3—Mú(kŸv}8„®—oÏŠ¸Fªƒ?œ“‡g´i“t±¤JìÉØH¸ü:W˜¯ô -%b<1ã½è•Oz^D!{L%vÜv¢ OaÜ ÃP‰©d±ý‘¦¤V¯ ¾ ³è -dÔ|9 ,ô bfý>Ìe ŽŽB3»«‡4ê¸ ¢»5ÉŒi»E‚˜ð+mêŸÝÈ41iiÄ©ña~mŒÚíƒyŒ"ñœòÕ€1dv„E¿?ŒÉ†]DŸº‚~8ÕDÑjv3=T—1xìÎ8ùèÖ> -þo‰Éà¦[5qøx¿‘áI{ÞÌqî0¢\Ô“q~qI*žh|E~Ïw^UÏÒ:\#å4°±V”6æ# -;¡ä†‘¶`âáé‹*þË!²Ô¶ß+rg-ŒÓïH—% ÿu¯F-¹ñ›Õ$êO¸aW*.»=ǘ_Ñ|ÌŽm[BïK„ÉýC `?·u›@ßá•´n6jj!\”‘«™:-U2m›•(+b|Ÿ­ÏåJœÿ×o®‘Õ ?‚«e$5A#¯ÀˆÎ±©Ú-8'–ã@»'^àæŸxöý:ß(xj¾K­ Ù²)È8cà#eF)øDÑ[›× p>šñ<í4OýT¸‰}uuñr¯U»®¾šµ­>'Z;VÑP¢Ÿ‘'û—;ë4Η}ÿ?šM\#×BÀ¬âQLIudOÔ¢“ý#7—‚È4itó8H$—GÓðª¶ÇåËXÂ[°è6Bã ýÙ7v3f7ͨñ&|jjx§z«ÆýªAÆ,š(7^lþà»)S .ÉB®¥„*i!æÏ -ß B–ŽnØç1 ç½á¬kŸe;Ú$hÚÞî_¬µÚWý<Œß.—ã$úÿ€>ìª÷ˆfòÕØ!Äìòäv8¹Yh~Bg®Íà4ʺÜù$9ÆZyö:K;ùdý|ÉÀÓïD“HÜ¢Õ³Jì%L{YY¶Ä¥R“Ë'p·é§¸ŽJšPÕ€£@Ü®ÌfÅ*픸›R’"89¼Ô/¯Šó…ê‰å÷##o˜ÖŸZ}¦íT¢YUM¯vÃÒ–ŠôÀ¤í.§(Z®Ô›Lʔƽ¤4£ß ¡Ì“‡Q:MtÌëwÝsþIT1NP½¢š™o_°ÌþS©[/™íZT)þO‚¢ è'ðôï½Üoñ&ÎpŽsDC°+óÎÂüÿŠÜ4±n ÜóÙJÃjkéwáÁŒ‹V%û¼FfRBjCâ öS0ïàä¬pybYý¿=°!›•‰ö*£` éöOãuÖ¶éÓÎ’‚’-ã(ÆáBÄ ›ÈvwÈÌI`ùÿì¼â£:Ë×cîÎ>ئ>nòF]_·1O¯’¸Uå¸=={šAõÕô%Ó†f§wø®V6t…H0`³ÖÎH45• ¢ŠÒƒ]Ä -¶^%ŠO&·uç‹Ãl'žœ+@=M-{¶§’R.œº×Ëð!ž¥cµ|ÜIðqփ̓:4ÆÑMqªíÎôÕ¦7“…‚”î”.¡ãyª*±nwà˜^°>•' -Ô^Õ}JGâzÌë%«¹ ™)67ÿ€ÄgŠ÷¿†Aê`nÄ‘=-ÃäÍCÁÜÑûþØ”]Ú¾4ʸ`T€³3/0ˆSV¥¤¹¿-ñqÞ;‚¡†ks03‚㧯Z±ADéÖd-ìýÿwÚåÙuTUnÖ‚æ•bµ$Nš=ˆ›àüèK!2ÈÓÃe•›º¤è žÁ×ð\¬SfšdÎ6ò˜Aòæ+ן °¡)2wUgm'è?‡Ž§ÇUW¼:ü"¦,àÿÎI3ÕÂi®É#a`ð®ºÑ¯TE %½p<Ÿâj½…Nb‰FÈ1õEø^k¸.þ`¹•¥#–};A¥ºP©æº°É„âïË°ÿ‰J'ˆi â7?27Ôt}í¶.zˆâ³ÜÑëÙ~ÿ/‡åVÁ@‹%yɘAnÝ!àû9Šø~̨†½½£´jæ[ñçeUœ@]á}Õj¯ÉÌÖ?ØqÍÏIÂä=ˆ@B -=k7ÖÁ”5Bûñ\¾µA^‡uñzÚÿ¬È2ª•Su,iÞýÃèI× -?«Ã"ë4Rb]OPtÿÐ7™eÈN=£}Ê‘a7—#à {HXð>wBè}PŽ¼ fZ™6_A&ÈÐè3$Ü€QÎÿ'„ÔÀ Ö.á"+ŽyÝwƒÁÛ pĤ¥ÝwT!¹½PÇTVEXj ûp´õ¼2ña @Ù€IÐF’ÕJ滚ÅJáX>™l¯æ×t6›>4X¯ /Noç{龟â1B2Ôê‰LÓcø¾>1cÔ‡ÖÓ”çÜÄËÁPË0X3M€×O)¼M]ú€sÅ0ب«…êÆrŒ¸~ž‘Cj™ ÂØžídt€ušÏþq¸Gûƒvqâ›Læù€0Ú%„-;š•HUt[)RÄC"R]·ÊÛ®‘×!÷3°æ:ÕqÛ]­ŠLF$ x+‚MCÙì %×AŸÚa¾Òm>óCY˜ -6£D®ÀœÇ 5ˆ!#x­pyý: T¨¶¿N«ì6äaEf®¶0ÈÉ&Œj“D´&GœÔLyMèÞP -§ù~‹*0ªTèKÚVF‚µyÙbÑo"‰ÈÇÀŽ;µ.¥w)€ä‰¸pK”m¼\_F«òÁ¼©JDXŒ.[Üš["`lØ­Ž>þ@òHö7xzk*®]ãÈ{w;i3>Ž S´x^= Ø,õ^LÒê p…`r$XùWÝ{&¤Ó‹9½Õâ5Ì2¤twR!åž•tÐåú׺ïôXð™ÝFsî"„ÅB™{;)¦¿B ÇÒ£çtixæÚ˜˜ŸN­*™C³™5Ìù¨m Ó%¼ùÁga¥íéú¬ý¨!ßýl¶i —¥£{¥déyšÏ(i(jõ)­¢)-¸µ÷ÎÔý–y ÀÃ[« -‹ŽbúcÞTá}m£*0äò¬"!*ôRåÛ7‘,>´Ft-/&“¸ÿéÅôãe/Š]¹ÂGAà•m -~F”šø7Žâ&ÌÆÅ+sýÿrõÁÔPêVZœÆ 6Á['FK -·Ü˜šÃ‰®S#)½úSdßõHÖ»÷ 'cøešC=nÀá$jO¶€_e4WÂw˜ÓãHÑŠ'zð CH :œÅ›øT*Ð@–hA½g™¸ÚJ¤-ñ s×jc#OÈCk%H\Sê¿7f}Ž…n"0Ô…¨×%ÐtÊ(0áñY\Òk—Ь Yµ|eßGÍhR$ï„+A|ƒÜÌøÞ”BîO”Zm;Eo@B\ÞŠ --à8¹²äq x]§ÃHÀá´ù£KÀ&{¶®ú•¦M]_ë"ºÈ¡Œ9Ê!.˜;-À—ƒâJq°kú»¿^;‡qUÕØ 2ß㹿¨¤è‡WŒâ¨šuñ•Æþ¯øôlì-?Ôd®¥lOƒÚ›ºÍ꧛ڪÈ)SîƆM²X.1l]¥_öçˆÔ茥²ªKºüúd“Ó§òΖO®06¼jþHÏ-¢EîO/Â)Û)o? /þ$°r}Ä’Î×u€âd”Sz2:@“t@_¨0'þÞ÷D[ôÙ<³‡"a$?õŸžÉYÆÞ§í$ßO*•ûÞçNI7»J×ToŒu:Ùæ‘MØC -i¦ôJ¸Ö³ð;“ÕµFÍázÙ7wäùìÇ>>>ö³ø' ¸«U•­.RLÿâ2ÓGr7ã8¡ú"hâ?9ôo]Y·ÕÎ4ž¤¦Ü£¥ËsÌ’«-SÞÓÑãã°­q¦:®öÞYÄÍG| F*ø\þ4þHâ’ ùE(ñ‹Ñ*ЪžÐ°Êa";™+Ú“ŠâXX}çr“ù•ŠÝ,}·£ ;4½ÎÜ5Cš£Ñ»úLRs¬™_vˆ ÏöeN¦JyÖ2çÅ­Fb.Ìd©Õ~À£‡­Åë iWoX,Ͷ.¯”aNÔ ˆ×êvÌ{¢¾ó;;ãvi^^Dôì•[ˆä ;Ä ³]Vˆ.&[Ôÿ6Iùu£.Y&ËÔšj]ÈÜÇ ãEKãD·†ÄÏÖÞvÚs°P‡\e‘hp¼ûù÷·Kâwró–;ž•HÆÐr§"OÜ€(X_ƒsºC<]×Mþ7ó¤n³@ - -‚ 4ñw£›c¥‰`mØ9»¯BÂäñD UÃS[iV=!²ÙÙ ž„¿‘1j§SZMÛ?ˆ¬×åÉ?‹ðLÒé…²‡àçFÝâ´w¦)r$PTÆF`&ÿ¥%PDÿ“âÿ,VI5Áì嵨b”“¿ú"—>hA÷eÇ%ï; ,åfl`Ê6‹ãú:@ìQ2ë†.(="r 5ÛRy0Aô 5P`äÅŽ"h©9D%#"ΣžqøØ÷Øk]›14\Š×d>è~¼#O>›"µÛfõYhG<^¸¨wgôÚ–%w‰2ïäÒ"ÿæP:Mâ.ÞëB­\ÖÀ¤T•ë•ˆ€Ë"mVë¼ÈÓÕHF½4/‚G9ÒÆ[§ôÚk©šèf„¼rÓ5VÕ¶eZõp#=†YqÍÚÊ 'ühq(Dç:"ªmIÅÌn-²k«}2»½¤€Z‰ÎWèˆN¢jkõ«,¨Yi'á9×îpÝtuc¤[΄¬6¾¿ï‡HõPôA˜”ä:j1•6h|LL¢lé'/Å´‹îojÁ¡´±Œ ÑXû€HÓpu ²ÊäÑ8¦U6¥Š1küêЭ‡\¶&›x\|­}b enÿ´Ù§~f'ø0/¾ÉÅüÜb ~Ù©Ô¾uZõz—v'õ^—ZO±ö‡¶á­7 w)hŠs1‹§Àû½°7ñˆÈ—^zð£7ïwY†/šSÅE&µ‚¤ÒùwkNÖ†+_ÚÙ¿Vê‘×m['ÔæнK*®LÒyà……CÃ?-Ún¬€Ô©¿rŽCÌ@5›æ’YbéJ‹o{ÖÖÀ*eJ>ü£Þ³3N¼“žùÅ°ž«\ÅþámV²Æ«ÂKwuƒcyבI$înß–2¨°)NË?ÓI­½„””iª$vãKŽu³ßµ1á,ëLe½9¦6]=Iâ}ÓEªÕ  ½pûÚÈ×Ú<¢}$Ë_š1rl|™ CÛ^B¶Ét÷ÐqóY‹r¶CAV«è5Ú+0]Òhì¦á]’е¨s|;—)¤«;Ñ=y'q;oÛóQgÝb"UJ¤Ì ѾxJ¥§š‹¬’T<µ)ÜÕÄaûšh ²Æ®ÛÉ)²ß{´90,þ¦<윣C¢Ãļ>ÿÏÖ²¸¢GÛϯøá7Z¦HéÆ¿æG(f!˜8‡âåÎÔ€$6f<øžC!/ñÀ?¬îX5“°Oóæ¾)IÆ~´|¿¤aêÅße§QkžM23J¥ -·`ȃ&<2˜AL0Œ uîêÙª÷\†aÄËIÛ|àD%î@L{ÔTÊo›do\pͯÈõ…qÊ1hÛ v¨ô¾læDEa0Ì•àT¡HᎠ-ùÏhÒRb_~m¶Øá¿<+±äñ¹Ÿ4ØÜD(ùP÷ò§d$B•:rðèc0‡WMA('=%‘ÖFô·;í–b+¦â±ñ5ÁNY&ï%b…+VæP”»Ý´ãåöžË v8rÕ¦ÝûÝf…“•'@9x„…*¸l4¤ÿ‹ Z0”°ycî§Ñ ®ß -~çF¤uoòÖz&|Eä¸>!ó™ï؈Dty±F¬ÓçCìdß:r»È˼CÊ‚vz   ×DGÇ1΀ o—ë9€ž¼ï@i€w9*ší6zgç À…>²šiài-ZøİЄhß¼E-@] €{ãøºŠÒŠ™É›Ow …¿„€—,úŒfýmVÕ›éAûS·?ÓϧÚ;¾HíX¦¹>’¸Ôn9‡‘3‰̎蹄uÉ™$¼l(¨´ ¥@‹˜ÍÂ1¯©”dóàÁË!^ôºUZ³è¸ñÐ4½Šo¾6êÊîÚpì÷K]êÀj Ñ)_¢ÑZ6Ç-g&³w¢é5·°ú¬ ,OäÔÒ#÷Á šÉµ£•ÈŸþßwŒGêcÊ6’™2tÚÛÖNŸ>!,ü…«ãò™œzÍUMÇ"´—tfdÁ´q-ˆÖ̳©:²¸©@ýoªž@ å.äâO:^¼Žº)-JMEˆ¤Aé76°R~=áÖÇ+±¢gKýy¯L¼ð¦om‹²š³¨r`í -w=å¢äÿÛ1–¥é§¡ÒÂ΢G5úø7<·³ÒpÇó»« “F±ÊêyÐܸa@f¤Ø,éMqÂRÉuI ŽýDÌ%S˜SUá¢F¶Diö•Vñe—à…kYÌî&  ð%³x͈‰)¯ÍU RnFäG”M@¢ºÒ‘qPr1­% ÆœlQ@À¦ò´>—íË¡Mƒ nçd¾0 ®pÂj|ãüuP7pÔ,Qy(‘Añç y›øy=ÄÒ° '3|ß—b}¾L׺¬¤–®í‹È|д.¶uDRjs$óC¸ùR´©ÁÇ\ÓvHj5RDùÌ1²ÖÁÔ… ŸD`ËY”1Ì=¥þ°µa@†?N¾ÞküsÚð Xy–Š¶·)aû¯÷+‰OŒwð³#æi¼¥7W‰|³hqNT;¯|ÂR†ü:¶çÈ“v”†mæ¤'ãM–"Î%Ñav`\ ÏH–užì¤î¿w$Ú—íSI&¸?xÙ¦»oÍÆ£‘í*HË#O!‰ü3Ý´{«'R”n𬴘 7såîbÂÈ—ÉLkôžºU7_+ŶüD‚x}B¯œYÁÙ:Ækëý-)T FgÖ4Ä'¼‚¥ %”¢8aSÛÊÕk6BÃ#À¬ˆön;ÃŒÈV`"ÄC©+Ù ±øø+:ºlܺ„ £ájƒ~Û_2X©9‰qö6$³ê6ŽÐrzn5a½¡WÁbHvn>ÆPä1‘ï3†‚æjzpl8ÿÿwêó 3M!t2؃yÕ+"D;™b0ÅåQ½^LÉCZaïm¯vwL¯cX_ZX÷RÙÈ;xÆýøðþBvaÇêÃ0ïÆd‰mÚ‰ €™%˜Ùå@y™JTáÆ›—uþCò,Ýö•uvƒƒ˜¡Îf!ž>5ŲŸÛñ1MaùÞƒFÒzÍçu÷UÖÛO½uüñ? ¬ó’¡¥”‚>[œoP¿×GܦçñRyTÏÆ™q£K÷).(¸„”CÃ)±'÷÷ÿ%+׬i¶³‹ƒZ+EGÈ„ÏÎýNdÞõÌuë ׄž¢å”¥ÇFÒžg/‚´.Ûÿlg/øï*²xƒ§^Åžûœhö‡.s\Fì°{FøO£:!U³Á„V3óüjCé¬Y{0PGô.¥ßòE™™øEíÕE' ’9P¼ªÍ•²v (êÉïÆ6b8&÷«Î Ôåã.e\Ïô<ÃeþE¼µN'¡KZ?Æ#ª{›¥'ÄáÐU0Ç>aþs'.ËkòURrËs»cÿÉÖu>%U†ºˆa#§¨<¦xjª%Ç3>¾äͼC[1»öL ׈Fª3?ØPá³õ96üÎ? 0õñ748í¹mî!‡kd[k®Ü­ÕUi#¿G•"óñÎ8aR§ûÄûÓÚÖºÞ„Xg…äZÞ>õ«>\fÎXÜNΑĒð’´A Í ÊuI¼™€ÝÙN>e›9ÆŸ…è+¥ÏîÈ[èPî[M´!—õüBÝ)B! án9Ëpó›[ç®×¡"óA×¼ZïkØ’û²z$¢Q«vª0’ý-ƇÁ¥ ·Iú÷¬Ò ^å*c¿ëÜ/)!omÇ<Ó-il9â$Ÿ&È9Û’Aä ©à&…=…¸´äCçØ‹Vˆ\c»f‡‚ë‰Wù8PwG…… -{ÃN ªö‚$# ýVcU° @£­â,æ¼KµN¢æÄEÿžO€¶Žòçã/ÈëîFî¼UNwŒÿ}fò¶WÌšÜ9Jš—Ê£·~èfΦ|~QéÌŽGä}0‹«Gô:3î:¦W?<æÀdù0§``ê¿·€¿Çt§?s"¨ê mQ’™ùà*Y…´®#àâ#®¶"œÐ(Çpÿ¾7›)Xzyˆ‚õ`j*ÔRŽõé&×úÄ*³LÝ °:í²Ú=_A·n\0ª¤x-vÔbozÜ? v²*+ÞèûXbb×·O4¼)÷‹/Ï>ªôâUŸŽß¢t:ÒÙîOÓèæ:R8Úé x³Íô°.ß»dŠï7N[ÈÄŒ3V)¯uÜ©‡ úiÈ7;Q˜ÖÕž-„pú瀗å×H– -ƒìEè¯Ì¥±WRÑ'XxÄ-Š{ …iÅdF¦)ßô¾<ÂN3bÉßÓA:Mû+DF²tÈg8•óª2¦—¡ñ±;e Æ¢ÊèÀJ‡ÉõQ+—ÈtCüøéÉ÷îwY¨ ŒðRN˜üÄã^mâB²îJGÉÍà€³Ž£þ]%&níèY/×òø¯—Œä†…,Ù -“D7½ -7ƒoi‰Ì`Nžäõ zÌÀˆôF’LÜ^s\"Ù&”zNw:ïÝáAWù Àu~Ó;òW— Kj.NÏ#XlÍ¢, qrâп߶´rKáŒtnõŠ-g¯»RŒË†`iK{wÃú*U ýúà&×ùŠzRÍ‹ó³H\†ª¶ñÔ|Á]†Êkô¾½ ΠÝht‰äa©ÖXZ8°S.GJÁˆô»»Žâˆ`:¨‡tð)}N‚Á’)fÈÕú-?’†´i¦„UÖï&X¸Ÿ³¿÷w9ÃokÂ]ú±»Ô•g3ù{ÔÅ(ϳ‰ÆM3( Lî%#‡?4‘›\.£Æ{H ;?þx>é$ò`óðù(­EX\w­X<™æ%ÞZS¡WÈI[2òïý—:»$ï)´/Iï¨æ¥¤ài ’ -Ï-#ëpQÄ ÜÓ€YbNM•w¹G§ )ŸdËZ¸(Ã9$†eÜdŠó¼q ÌàŒcþÐÌ•‘Ѽ‹óÈ/î2ÿõÝdÍ…Û>ŽÓÀ ¶=õ¡bõ™£¥Êë•´DedÇ(=?B¹ßŒžúP «fŸ‰p«zÕ‰ÛÖêÒOöÎn­ Yí¥ÌŸï ´µ¹ÆƒøX/°ò½@v\•«qµ%š²oFÝçËÏ«õöµè 8ê"3øÞ=†žÞÁ›TLÑ¢5º ¢Â…Ä=™ÎÕ€|.áÅÿ¶¼•â>蜫"0K ]V>?ÉùDO Ç£zZ‹Cß6l«EypÅßfq¡Y¤zƒ÷÷™R8£á•àbn®QÜ¿þ.Vx1:#ë®0f?ç'$A‚…¸è¯'ÁÞro½©óôK*‚ØŸÁyM'óêe–6„®yG™LÂëi©ó#»î„5WÍòÅû¥ß3¯DkžuÝë¯N¥BÂ0’§¶KV¢Ø²®¸`¦ê.7;õæ½ -œ«“Ì"’R² pH1P.¸±úkm‡¥þ±Vš„çy´VÔÛ†{` „‰yV±V6žß_¦Ð¾£—ã5C£Ô*}Md`M“Ëi½Hºž…ˆ! :.›sbBø:½Vs$Š¬‹*Ê54Aÿ7ú–σë†.OmQØ«üñüj/fB–"Ñ; rreO}ê. 2rÍRá¯ëR± )îí(ïùú+ìÏ"¡[Úh-¨.ʤñzÞÒ=¥›hmÆøåBî€fKÕ(@D º€é ¦ oçÐlÔ:ôˆ~Ë%ãû£íëÁÜâAÔÊ7Rð€vTðòLç_qN§$ˆ0r3©PJh^è·gj¶Ê!™Î=ÓíÁ¬ßÑ­ ³Áktfä%nãÍÕ´ÑÁÀíØwxØü5ënÞ¨ÊCF›Æºú€‡tÅ領͌j ý­á#­ë‚†«wrÃ;é°±ŸÅ<ĸÅwµS›lÞïŸù¢­Ÿ¿ßãvD5Y!Y>pë~½a[rÒÝçã³äAXþ¶/Ý)G§÷qä x_G£¤ADÁxƒ]Ó߸tŒÝ.–ðÐÎ%Ë=g»ôãfL#uF©ÀÿOz†´O)SŒéÏq¸¤lŠ´ f§ZL©i‰ì¶ §²)jÒ(g£¹ÛÙ..¤gÈK$ž)ˆxW*¤äŽxµÊtá¡ãc÷àľ¬-×ñ·–æöÄ©ê²÷ç“Ï`,§ùL±/å^§1üvKw·öy¥iöˆ6[‡{{F²BH€ŽŠš¨/–Kö`bõ.Wj„NÛ‰Ÿ}ÙÒÀÌ´J•–ó:ØßvSïÌÆrí€d Ó‘W>¹ZÕ‰?ÛÌ»w¯­ÍkŸ9=ÙêØ„Êç¦ã¹ˆ”eb›({úD;Á3´¹/ıɓ+SCŸ²ìÛ)!˜½™ø£ËNg·qôõÞ%©ïÁ;óþªIÛzÕ­ÛŒÆl8fõ®ÑfaëŽ$P$u2j}QO&‹ílj‘|$G>Y:,l³êáÒ…B´T{”S™-@¶.L‡€E@ùZܶ¥p}\5fô/€…z†žvxa„­cx.e-.ŸJY¶tNj™Oê—MI -Yüg½4Ø#ÜR–8¼aÔ°ž¾:<•þÏËå´£‡f™I™Ê\9õ’¡¢ý 6¸1;^_ÚQìé^̵­júŽéF±zÛ_)qT\ˆìòT9ÆÁgåBWAÖ}|[`[&wÚÙ”ºZCœ¿Aí,÷“38§HiL0%ñwñ£…)ŸUm½¶âëôy¥X Ë‚9J€Í½dšJuŒKÄ×Aão eéϳò%[é³;„T›aÅHq -09È‚Ò"»-šIT*lªß¢N]pyó܇;7i½`󄚆RÁn˜¨Û@d»3à¶Á0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ_dÍV`÷Kî–y ãZúÌ÷±€]¨Šãu M™YŽ­üb[Üœ1[lòŒ›Ô'ó,t\™®¾pÚ®Ôž¤ZùO4ªG‰J7 iŠº½¤!U±¯&Ï·Ý¢¼h`ZNöÌ£ÖhKGÿµˆz;íà´ÓŽº¿ ˜ #1&ë¯(›)$ÿJ3K…ÙÖ…Eý­´™s±èjF¥¯ˆfÀ"P$Õå†-IÞµØìË•ÙBƒÅ +6=h¤qDVð<ã` EŠkÀ³ªE“NrraÆŒJGø ×~Lò{6ö¶ó¬IŽE6ùà¯U'õãÌy 0„gK>&)o>2\U]$XWŠ‰ç-1f£Å×@³«±'ÏB 1mùW‡= LðÛ%§5t¤Þ.O-]NŽ CTÏ4Û>&wÁ”vN­XÅ…ôžñCþŸßÙf å ›×¢¨r™¼1žf×¹VãC¡›“È–~äqŸ0 þXfðÖÚ^Å^$Ó·ï£%ÔG7dé›È±\ò¬­úlFcè0…]g<銷_‚Ÿ¢&«Wð{>}N|ãÓ·ë 05ŨÙú4H4ý¨ãÜžlGž>îš TÉ_¤cÑœé6àYŽ1— §»nUÏÕïr®Á-š–u$zq1k.â¡s+6'ž¤FË2»âç‚Íð‰.r¶q5…#3|uç)p“Õ¾Àc ÜN•r3ì ùåÊp<~“„˜s„?ÆaàÈG:m+å-뢅¹¡Ì^dÒ­¹æG)q„„Q¢EÝöª;‚%鬎F0°ÿ2Öyì'¬­…Æ9N¦÷#¶`îˆ=‹gh7éë¤ä+¨óeC:éðèŠ&3BÚ­øœ^y¹ia4eM‚ÁÛweî~ú+Àáݯ`Úûæé0—€¢µï>Ÿ¥&½GŽ%FJÆAÐý‘{-‰Ý„Ý`ÛÞ;êÑ‹«ø‚äáCy,.äÑ=¥ƒrSøW{gØ¢ð“aR«Uî @l™²y\[ 9Nöx”nÉ«ÆAÃû ‹ÖÄ­+Ãç!V­ô9îr‘Ä`$³dÐŽukÂi,#r—G§¥Žzk ð GMõ0]xjýKEužù÷Ž¤iI¾»7xÍG æñ­ ~xKÈBiŸêz‚Ð3ØÄiRXÈöx=¡°¿YCªF_‡£>—´w}­×)\N…¤k’p–êÞÅWÍ/TˆØ*ÈÕ ©epøóžp˜ èÈ2æ'èùû2° órdwC¥lyЃœ}¨}ììP‰qe³5%Sý´mªñ´‰„²âÕå8D²ÇÖÜz{*®UÅU{dàªíœêþ¯éº½,^ä·HÅ¿»n_N|2ú²òGÔ"þi'œ„…'äú»Ñ‹ö3Öd|”_ôܺÀ³œwrêÛç°êöyÎ…¿j„§¬·Àˈ…Ôa!gŒ0Ð?lE`I¤Íï¥*±!J­ŠöÞá‹ó3¶ÿMóµ[(˜N«Hõ×­ÝÇUh4×|†ì·ä[ç-*²_÷Ö2˜±cúÌN×#òâDL–D=»úEÊã?%ƒn9z”KtVޱђ¤Â,®_ç@¿í°Ô”9_±(0ZD…vß‚7²=¦¹KÉœQþÛã5€sˆ‚Q& 2ù+lŽFÞ~?Í“šˆ.÷ù5ÌPDГ½Wt¹%45+ÑO¾S¼ù ÚßõÙbefâR†Ö}1 šÃ-öš˦ß óF0;l²µÝ~3êuhÝåAÿuÛ.üÈ–ÄÕEû NÀ‚£üZÞQÚÈÀ5¯Ëùh™&*„]^òþïð“añ‡VÚ¹ŸfRÛÍB…=Ý ÞèÖŒ¤W£J¤>´9¸4=îô®†.£ôáh q`yYÀ~\P¬Ï *—ž=D®”³Òkr?\À29Qò› -IeæZ欈¼AzZÃŽ!6‡¢Ý9Nd…u$QÌ$Þ¡¡Âã »ùØÙ;Õ”|¶y«6³îõƒ³±ùÖR°Tbbw0<°6YØÎn/x¹’ûYÅã,Âr–é>;)lè©û3‰õÊ®I_r]!o}¿® œHº¿YŠ(³kHUÚ»6ÀM+sÚê8ÁUÀ‰Î¢^Q·ïëDð×BXKArÔ;â Œðc™ˆµ©c6c~iïr—uÆøg•:Ut°²Ä®æ|5þÆÕ=ölG›T5e q/}C’ËzJƒ3·³²FG´‡’|`´ø+ŧ$wîôƒÿ:6À œÿdÐá µqü|±Ãøm°ˆüYƒoå¤Dã#Òw|ê–jó”ª7mU©ÿEDš4 ‰Þ¼³ ÞÂÃejB vòâ< YB’oRBby49{¤ 6Ñ/¢•I]9G“Ç¥ C«ÛOœœ*ú$²mp—X²6 Œe¥í”6|W["V“…?6沩ßrEk#Â|o·ÞÎd"/jhÿüSQ誈Íé™ÅâÄ{D¿xäg,°U¡…š$)`«6Þ£#ÉÒñBw^º:¤*HŒfe*Ïkýâ‚g—C¿‚1žï%Ø Ìl²ëhêQ‹9°Si¸ 7„5»aZs…ð‡kÃÎÑÎ,»6üô°ò^÷ý ÙŸ’¸cÐmv@ n‡4dY+×õ¹hkŽJMaóîEé°ÄNeC+ömOHœ´¶ã~úãèiàbówÆ\¤6-Æ7×ï<ÀÕqêËÖ­öø˨{ž¬âÃ!‘¯ëTÏuV'¹^,ñ©~ìºBå@Úr¾gVr¼¨ì4wà(‰5ë ‡E²ˆ9dK~ˆZ,f´B ë:Ët!´ßÓf.JbißîvãLVünÈÇl %ýH eO¤‹¼xeK¡|÷DƒA{œâj¿Î~ž$'uè?ÎR€@„«`ûo–mUKtO%DF£`V¯eE›.0ß½#צ¼×-nw ñg½}‘\'·yüÆí½¨Çv†áð|›Ô‹¼1êKu€\ß'6ò½#Ì$³NO÷õ‚u¿ZÓœ¹w\w·Ã¢¾(µAïzò…;vB¼Ã×—I²†»GQ ¸Š ¡ã8Ź†ôKžD©„RfÄ~8£n&0 ç7û$¼4׎-šù1Òâ²WË È,,dêñWrJßS¾>º£Ÿ€è±ÁkÐoiÏDE–éÃ9Ñ‚« kTMÁd—?\À2›‡Ñ(bû¶ /ö› + aÔeqÁAÌ=7/‚¥ö‘Íï3z£+Añ:¤GâþטöE¬é‰9¿ ³Øãè+΀¾eËÖ5^N̘"ÝÞ37ªÒ6J:², +ù,L­ºÿ?Ms¸¬?zZÞnävºVÕU V6=×p£nÊYÒaÓǾž Ëy8öÆdQ±-a% Ìb.™'9¹»ÿþÿ‰]Ñâ4iŽ‹Ä„ºþ^¹Â}Š}4RoÕî»uKʇϚђÚ8ƒ4ÕÄ +ºœÙ½îE;)e”„,5ÕØŽ;4ü V‘Y?S99ølÚ¶e^ Îð^*³¯‰Ëƒæµ‹È$¹¡yý“ç)òuÄ)b ±_å›1Ñy&Œ‘ÝÙQ \p')—³—¸ý‚‰qC Ùæq…]u^Vµ— +ÊÈ餙‰Ü \NùæŽcÉ %ì§øñÜÏ7îº ßÒuà úºxÀÉ£É5(^÷ÓNG… |[ƒIWÈlê+í¦ûRá,£úL½ª8jLm’ |»éL°Í:ùˆA×å™\O<U!³me¿ïF%W>ñN=2À$n_} +‘q›Æ=¢ûLóÄ/N—Ûþùâ,šÌ¤uDÀGr½†ùl +|OÈ.‚úMzÜ;*FËþÔ%JŽM£›.á^Ñx§·[æŨøKñ"`hT}Q]ö’¯Â+(‘CvÍé!kN±Q³—i§ß„+c–Y¡|¯Užî=UQÝ™ ".@óV2C®Ë&µÖÁŸåãeq£R :%.õyùοkWôÚÌ_û~*Ü|íJÊcv‹‡õÇõ¹Â ËS>å/ŠKÕEÿH€µÆŸmêOÙd§, ˆÈ‘q¦Ìv ÜO¸Ì×ﮟå©[5¼§þágÑþPÆ%sƒ´£åj"dþÛÕRX{—ù³¡^ðhÑ”Ýt¦…ü/Õ2}ùePbï!bŠýÅ ÜÚüˆy¤ +ïû`ïè\1&’äü+Î^$Q ÄQ#ëðãÁ¶“ëÚL3ÓuÙêh)š1ÏF63ûþÆO=ÏÄO–ÏZ_Ó …`Ûéà€ªŒ1>Fd¢1búë¼ °q·‚cÎt~ž›e슩Û§òÁ·ÜÈJhBŸ&h›œô§Àt² ðCY”àe,HÆÙ‰›x4k’©EŠ8XØRÛmUc¥ÊMû%“ði>TXc€_°•ÌDJÞêœÆ1šæL¯wgUµ>¸Ö#²¡:÷ Ê3k‘èÝ6H%±\bÑ«‚!Þý9Î"?!ë¸sY£ë¡ë1œš.&„,Á%^ÀustpÔyÈòal€ÐÃFAýN‚¹M¦Vž¾h€SXæþú³VÂÏ…¬<, +'¦M«±™° QÅÁX³Ñ»ÇðRà…lHùdÉGVŒ¼E˜èÇs™ÙþYÖ¦µ%OE†ÌfÄÖÏÅ"¢õ=ã"o*3w)—Š«yuyé#P«áD‰V˜\_'wp4vwCºDÞòäÓq!‡9e´Ûÿ_9Ⱥµ^£ØQrÈžxÄlÌù±¾Žöþ +Ïp12Š¨Dsö„Èž–j§Ø”_!ÜX›Bsåd•=3ë'\3Ý>õŤ +VÁ§ðä×Ý#«OÝ04$t: }ü¶TsÔúÆ\{‘»ìTìQ§ÓeÁc$ {Ö9T”Ï÷±p+Õ˜^,¸ç¢`@º&ÖHíôqdñïû¡Ø» *·ÐÏdµ+ãHì{aÚ»28OçJ=TJŒöë[ +Kž:M°´xkNLoê‚žIxÆ‘JªX9\l!ávåöûfd=x¤®Ü·=øï¥ljw %î$¸Ñåµp¼¿HCmänXþ|]6”ù€CAÕî ñæºÖßÒíGü¨œ sD’|ŒÛÒs~ÃvmRNy·ž¼xbÒ ËôaÍrd];ôœ Žu8Àq`—"î‚ëʾüDää5ô´¾ªNݬF¥òèDs+à`ªêo³î.¸/žýϯm ]$—àdÔø6_%ûÁ^%jtsëC¼Ÿ‹~c–Ðüxizs;8 ¦H”û­¹;æñø=…)ogºñ“ÂÈà9¨^°>Ï@ó‹ƒÞz¢áQŸƒ{w5çî8Ü7í:©Eö—ö–>×5sï»û(‘‘ìÁ¢zÅ'\ò˜ý¤öUBut®và7ˆH,ÕÑmpBÅæ´±n8R#Ûiž[b¬?c àããÓëWqæ^ÏÀUA¢yãææZ³+ÛÖ (0ì[Ì™f—“pÖÈø䎜åsŸ/·šÖ™>Ñß3T@iðu+½@bæ¸$ÍÅííþõÇ{¦Ü+®‘äS"ë#û‚P&܈5i;îˆD'k „üš¤JŸ;m%_t=èc!:·ä¤éw@#û½›P`þÃÑÃz4Lf\|nD9’ôßb>aïk] +¾±9½ˆ“ˆHâ.Ÿž0°”°“õK¨¶™nÆ{·ŒÓBOUJÈ"íœ'ø”^þáÐ ) ¾}‡œZ¤SÝ|ûþ—µŒ [·è0“ç ±'?|Xú}Œ¶óÑ€àX! A濃FT ÜuqÕ©AÏ<ð­ÿsÜÓ–ÐÚœ'n/y`¾ѸT¤1Â…c1@ 1wé¦Ô_­Ðž=¦áŠÀÓ=BßßH~Û^¼Y«fa9Ãw^“º%ÿÓáâ +¼ÉÌ +Èñ6ïUkM¨Ó‘ +óþoqÂBæóE8’÷þ_Ò€äNê<(ø…Ï] +¤Áñ]2[_õ,kq_\‰ßÉ£*´â‚È º¯ÁöÄZ…?C ~âYâñOgyßbHýKÊpBøw‡¥ºóñ&¹1}]P×£\ë\@\‘.ñš/¨úse¸¦Jõÿ£åœ1üùÕR¤=³æô6 œ'ËH;d)âs‚öòƼD„¡\«êPÉÅÓnÆàSP w`~]²E w"“žŸ¡'SVá(]nnbMP1í@Xæ\$kAÚ{­°ã›aÇ~”‹yûGSí’š»Ï9 ˜Mó¼½?uX§Ú6ÊÖÛÞG%Z±&#h=q‡vw¹™ ÒÍnú››EŽëØB¬;…hñÌðû‰ë½cdF4éfÜñ;#o‹2ä sÈN|Ô5nr!h.íróÞ1RžÝM +¦O 7û¢ù6¿r‹c7­³×U„Õä@‹ä +ZúE¼]\ÏgiàiõiýWšp{UkH…!=ïQw".ÓdϤq½"˜&üÁÊû1a*¯…ó +ï3£ý2²ËÚ¦<ÍÏ|ëO æ]th5ì;ຫ÷³]á*©¸ãðwþÙaf®Ç¨ä +–3XÊ/nÀ§£¡°Áu˜bø¦p—žº;¤ëêj€9æL”9¢–òór”Ü¢|Jô×Æ®CmÕÙkí¨bœ«T˜VAÝ ©ñy<Ÿcæµn—>óÚ~so¹Ÿ’¦m=‘ T­ÑÁ4`L±³ æ‚)çýd¤#ÀÔ1áí ˤ¶~©vRÇí&Ž µ¥!•¬mõzã²ýÈçŸFún¿*3]ŸF5B]ǧq9[+˜[ž­ï–^m¤ˆN ™»Œ#e7eW!æ ¤¦)H¹Ñbû·ùóO÷ëÊÜT–˜¿‘ãqTîp›Ó@À|IŸÒ ]ܸÙì[Њ%|¾ ª€ŽFY)ïGØÔéŸqÆD&©¿ìú+^é÷Óáƒcwv¶J*ŽÙ’yÇ"x‡L{¢O›ŒØÆw$Ñïc.zyfÕfê‡×j¢:„G®;3îç×–œCað³ŸãhÛ$å2tQ+`wñ6¹ýÍT±¾5ÃÑóÔÝ«YÁ~$\¨öæùg‘0C¤ÛªT4zÅ;2Õ½î~§ãäÍ´ ;p36Mø¥Šä­¹Ìçx•J[ŠÖÓ'§'±›ýÇ’}µÔé+߇ÍÊ”Ê+ðÿ¯OÕÙ ¯GY)z ÛjƒüåEû%&ìï¸àbÒm<^s>cl43÷e.ÍoŒ„ Q%Ð8ý‘«¨ +UW…BßA[<Ã@X°ƒ~ÉRÔ„)oÿH^V¤á0¿®in-Gí.ì:¦¬a¸’¹ÌÇ¿nÞ¾kT’ »Ia_œ£fb€"¾J:8½}ÇAµ¥-…Í}„ON»m¾ØkË­WþÍœ?ÖJůÜU@„>wÝF#Ï(¼‘3gaÂ6Í÷šLŒ•þkk »9¹S²»-‰·’[Šø/s'¤•T¾Ï¨Cý«cÑ[¤Â3Ž µ÷\І=Ŧ¸QÄw—`%¦¢ë”Æ¿Ãû±HwÇt·«<éq°Y¥ã]&NBV±SËÌa¤ÇRcEÛˆþ&öw~‡â½$Ǥ„Ü o!¬ôÀW ÿüIeqày +Û)„SJÈ$Jœ–)˜Ð¸‰xÌëáLrˆ‡¿ôÞU°uŒ®$ +ä·òEyD½µ`DÕYÒÅe«A*toì1¹§‡[”ï^ŠÑžù‰†ÿÍ{¹‚Ö‰‹ð«ùâSûgDó} +‡ý=‚XQ–½£nðC÷€Ÿà_¶’C*;vþ¢SŒÐ­Òl¸guŽQÍrü-š!ÆZÝ-Z:±¦;]hâé÷1ùñzØGBHäuáѬ]ÇBHXe‡öý¯`mbÀw+e„`d’¶È ò®Ž Ì6©f1šwéÛoóä´¸ز&à«„c„‘;9,T9ÝÃÕ!¤þ¨zÌŠ'0ôëB†ç]HHÜÎ=…¶Eѽ¶kŠ–R\ªEuœ-ÌIók‡`ýeÔV!§L ƒ´w`yxÍvl:¿·yþâ%¡eH/x<\œR–hu¶ çÿXze?Þô¢cÆŠeñõ:úšGXâBKbF$|•uµžÍæq5~?J™y¿NŒ’KÝ»NŽùžP€`rçH½]êŽ÷T;„|4Ã0È âjÚPî¤yÕÖ…_z8ÆÀ= +«¶ÖUù,Üì²ë<›ÒïT vÚ9”ÿ…~W¸Â!5LwlÜþ ’Ñ4ËÓ–IÀš×3:W‰ÜŸ©?dš·eKV”N£ÈHtZmÉÐUDv1ˆæ1¢ž±_˜Š™ˆae°§ú’¯ï±[7¸üËX"`9/¢Êè +dªiMǾïú]™T,ì[Ь8vÆàáÏÍ…Ñc>FmBÁœñÒ¾ý"|Fy,8H†å„@À$xl¸ñ—_„ž>ˆš;döP7«‹Éï9G{z°JÂ~šøq”‰WàHÕ™U趕÷nN#8¼HWè‘WÁ‚Øövv!Z×,ø¢%‹U…oÊÄÌ}žNf%…½*#},.åó$ÀÆ”2R'Þ¸~q=ÃÆ ”sZL‹`å#>Ãy‰ý]Ùü¨™8ˆylW®Uµ»êçödω1ŒiÑî±x6xGÍg ¥ÛSߟ—6@!dÙc› +‹ÌïuÕvùØ®ñ’Rç櫪‘ñK§¾M³f÷•× X&yªy§°a”ÃmÚ²—ׇ=Ì±á Ž]I‘¢²Ó’àËPÁ.?»×#ð¿Vî Öè@c—4¥vÆ°%‹Þ¶÷atH‘ô›.~E2EeÇe}E÷ŒÑ0ó÷ñââ:'JIä¤;t$±©ãú13—gHÛÁjžeµ9Vw?«·$ïËã3ÁN£ +ô|8…Êò©Íºõó<ðëÜ1L>e²Ôq®eZÔ†ŸiÁ§ fâ6µ¯›?ˆ¿:ÒmÕG‹W4 +ÑAþbŽþM;Í1&F²—´±GÔ¾î:{ +¬²Ñõ°M÷ëûâ2‡U¼°Ô!«ëwš²ï%T÷ã*MüÒÁöï×´Ü ˆp‡µÇòf뙲'xË¢o²@N#gV‡áœ Ô•å<^૽î¶}Œ÷ûÌ ?AÚr ΰZ´1Oýæmñ¹%zl5ýÄÙÌum^]œ›:#{àOãlˆ‚†´|‘ùüF$´z²}ù2”°0ä;Ã]JÁv<ÁÑû?Ü¥ŽmDrãˆLbÎôÄ¿™4f"}Ž‹˜ÆŸœã÷%ìó²i—¨z(àRë¹Uøüù‚õ©Ùq%Ê÷ì×¢EäP©Ö§º.©cXI JáN7·Ó_B¾t›…n¦·ìžxñ©Àðuã»›Ó«1I³±œ7CjxOÊ }´ ª.n…GQíó¥¢¾-¡Ü[ú·Ev™ÃLÑÖZ.µ¼( Û›×ŒC0|8ó¾ÂH¦ X¶ÍůLÜÑO²œð3De¼ú¯cÐݳÁ¡*kYeȾ¦ºR[dIY‰cüq˸Õ­ïóN£ò±þ}6z{Jbí²OX"YQg¦åi‡¢ªhÞt6;›.q»ÄGeûŒØzÑF+*/ôžü}ZKŠÅŸ×çXYóSSø0ÔÏoÏÑb"5÷y£É‚ÕhEqö”{Äk'Hú?–ë¦uÓô«³ã¯RÖÎUd˜O 0¾Ó;}%w¡þ´êP8·ŠI$oë/?U¾‚TJÊob¬ aáí¾8žú…Çã~< Ýý¼˜ endstream -endobj -171 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 533 0 R -/FirstChar 11 -/LastChar 122 -/Widths 534 0 R -/BaseFont /EAJXAT+CMTI10 -/FontDescriptor 169 0 R ->> endobj -169 0 obj << +endobj +496 0 obj << +/Type /FontDescriptor +/FontName /OBIUXM+CMBX12 +/Flags 4 +/FontBBox [-53 -251 1139 750] /Ascent 694 -/CapHeight 683 +/CapHeight 686 /Descent -194 -/FontName /EAJXAT+CMTI10 -/ItalicAngle -14.04 -/StemV 68 -/XHeight 431 -/FontBBox [-163 -250 1146 969] -/Flags 4 -/CharSet (/ff/fi/quoteright/parenleft/parenright/comma/hyphen/period/one/two/three/four/five/eight/nine/colon/A/B/C/D/E/F/G/H/I/K/L/M/O/P/R/S/T/U/V/W/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z) -/FontFile 170 0 R ->> endobj -534 0 obj -[613 562 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 307 409 409 0 0 307 358 307 0 0 511 511 511 511 511 0 0 511 511 307 0 0 0 0 0 0 743 704 716 755 678 653 774 743 386 0 769 627 897 0 767 678 0 729 562 716 743 743 999 0 0 0 0 0 0 0 0 0 511 460 460 511 460 307 460 511 307 307 460 256 818 562 511 511 460 422 409 332 537 460 664 464 486 409 ] -endobj -533 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 11/ff/fi 13/.notdef 39/quoteright/parenleft/parenright 42/.notdef 44/comma/hyphen/period 47/.notdef 49/one/two/three/four/five 54/.notdef 56/eight/nine/colon 59/.notdef 65/A/B/C/D/E/F/G/H/I 74/.notdef 75/K/L/M 78/.notdef 79/O/P 81/.notdef 82/R/S/T/U/V/W 88/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef] +/ItalicAngle 0 +/StemV 109 +/XHeight 444 +/CharSet (/A/B/C/D/E/F/G/H/I/L/M/N/O/P/R/S/U/a/b/c/d/e/eight/f/fi/five/four/g/h/hyphen/i/k/l/m/n/o/one/p/period/q/quoteright/r/s/seven/six/t/three/two/u/v/w/x/y/z) +/FontFile 495 0 R >> endobj -128 0 obj << +497 0 obj << /Length1 1446 /Length2 8320 -/Length3 532 -/Length 10298 +/Length3 0 +/Length 9766 >> stream %!PS-AdobeFont-1.1: CMCSC10 1.0 @@ -9533,22 +5261,12 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /BMKJDJ+CMCSC10 def +/FontName /ZTPMDH+CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 39 /quoteright put -dup 40 /parenleft put -dup 45 /hyphen put -dup 49 /one put -dup 50 /two put -dup 52 /four put -dup 53 /five put -dup 54 /six put -dup 55 /seven put -dup 56 /eight put dup 65 /A put dup 66 /B put dup 67 /C put @@ -9569,19 +5287,29 @@ dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put +dup 56 /eight put dup 102 /f put +dup 53 /five put +dup 52 /four put dup 103 /g put dup 104 /h put +dup 45 /hyphen put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put +dup 49 /one put dup 112 /p put +dup 40 /parenleft put +dup 39 /quoteright put dup 114 /r put dup 115 /s put +dup 55 /seven put +dup 54 /six put dup 116 /t put +dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put @@ -9626,214 +5354,394 @@ o \J]Bî‰å\KVÏ^!GIÁ”ü¿æDá& „qn¾Ä[˜ñŒýñý½® ýýjytùõ>,ê‰ÍE€Å‘ýFj«ƒ '©ÄȾ¥î™Ÿx¥Ø”'…SEAˆê@ê»b¥øÒkì1ÅÚ~¡Ó¾ `ðmº›ò–IJÿX¤(škxæÉQŸÛ9ö]”íÛ¹úññЧzkWQ¬ªs‘ž>éK˜]g%}µÊ¨rx²¤L3©m­¸˜p`ìC~Ú^T{%Ú¶mB›ß¹#äOÚ¨ÿ.lÏ2!T/¯ ^Z7NE fGÚ…ç"¸òå%%CÖýwrxècóèC¼é­¡J„ýÃ$à>î ¦=*‘ô~(¹˜vs|ÉÛ'›Ôýýð7ìV°05÷ˆºüü‘À"¢¾~f¤U¥ s:¶·^Á‰I¶¥?cHNc ?rImdQÞÔg?‹ÍökJãÅEÄœ?*š++ˆúÌóy ªìàШ*ž4ô°lÊQ¼ª7¹R4òóœ¹HÈRG5£Ry´4Û÷+þ²`£¡ãTe{©owâz¥Yï‹TxØö.pç‡Ïƒ‰ž°¼7'Óø ƒo—h©æ%éÇþŒ…¾_ïßv¸y(w€òÈ,Fo؈Èà†»G±­¾)Y}7èelr궃°W´wFûSO oL,ùÙl¶Pû4ÞjXx‰iÙÒE¨ hm®}ñnt äÊõ½Ÿ°œò€;ðE–ÜSøú…-[YÅpSÖ9o£Wî ÆöVîNœ?仓Îfƒ­g‘”oûHzƒ„*xÁ^ [{¤±™,°¦áR÷Æ¡Þ)Ü'æàd*bîôãK´±1€¼œ´¤¸‹ÃË‚£š&8>…:hÂïøïh¯áPè€Ö¬›{»¼ªlgèQ¡øè«Ée¤uL¾¯i»Fˆœî9Æ–ærôb#I›. œØ $×ò©í¾~8¬~fuCV÷ªS2Öí,}¿*Û“´-+ôÊÿÌà æ³W&íþ[%ÚïýõòÙe×oC'•¾ïb5ÃÉp[c*áÇÙ—æÅth.ž¼0’B¾™Êd¨ÖÌPþ&lo™ýìüng™DßÖºÝÎÁ÷ÊäÌ?rȲ¬h çųœtÀÉ+´‘#ÖÅXfôGô=1ë‘{•eðÓ[þü†®~gø¸ržï0Pº)õà¤âzîÊ.í Nl»²½è]^ÂìwB’}EœøR{YçœÎMy”6§Ì«‹Ï*ÞY¤´7‘ž~—¬’/.¨K÷vê©è[Â.¬™û4pÂÂ`w¤yÑyþŽ±Ò@Ðô²+4ŸŠàŸc¹ã¥w´-ÓŽJă£Yv Tq£ÅÒ³ü•áÿ¬QŠå>5ò@Ú÷§£;P¦FU~&Õb<ÂEÄTô¼lóÔ`[9'C[\D¥¡Ç5„ÄÁ‚¸î©^•9˜_Ñ1< ±¡à'vˆ†Ã”£è¾}¯žÀ ¬M©0ªw$q‹)ï·Ëíy1ä"ã4~]¯JŒ;ò½jÁlgQàcŒù‘Â:žnéc@).äú ¦)Õ|õ‰´®†XýÝIî¨7œÍÌ’bnLÆkhìÅ{“p\ñz« Neì’%KtQ3¨F«ª{<&š·óÇpŸîçløÂ3!_§'Ç\Êð1ÙÇ ‰CLXPI}4ÐBŠlÀ¶|]Ê–{å1©è\•ÇeP0=·°À˜å]b3¢¹ÐN^áãr~Tž¨e~Cb9à³RC6ùÈ?óZš>ª ² m·CÔê«Úè÷½9[ú⺹͙p6âaëÎwð‹Ž£lÇW!f–o¾èÕ¯ïGçÊÝ Þ•n9‹-,ŒsÂÚ½[ÐÇvsë¼"=æÉ®án»•Qî"kÎpP B¯Š‰Rñ«ï™‹²e™%€ªD?´ãÊANU{Ñ0ó[œÇ¥™®ø3vÂë~ʾ–Âã»M\Ë3{Pæ7‡†{ôAßÝïDZˆù‹Â /•åóZ+Ã!?eSwžTÅ}sÚ¤Õ; æ¾gY9¬è˜Å$~â» Â2qÊøN¼Ý4XçäC[-bÍ.Ù÷ª…ï)ïý&óÁà}BÑ<²_ThÙMcÿ5¦Äu ³MàLr‘|ñ“ŽgûöFðÍ/‘Ž¼2X¯f–_î{‰’[¥GRu8èùdK÷ŽŒÈ:Æï5qWBõ·V- óÒ¼mv,HIÇw©Å9xIƒø}F(Ýç$ó!!AHÅ~п|@ŠêT„Í+¹ü‡Ú½7šºk’Cü)uBi/µo¶ás;â@½j˜ƈ1¯›÷q½•éL6À)m÷.ì8ô¹ Ãî ´H‹uHl„‘aCd*¿n|Sˆ{†\zqèØ•{™aø2,)9ÁJ)ÉVë@^ž¸>NùðºäáÀâ?"1É{uGÆÿlüë<E[;ŸÌ7øìµþ/É\i­c…gÞ"Q‚QÁňž  ©LßæƒFÓEêøè-„„ø.;¶bQãð©À-kƾå[’"ÛB ±ÁäÌ6¯Žg‡Ÿ1J‡°àšÌèñ€Þöç-Ý%”ø„¬ qœhòΔ[Pc³*lmÝãVíAᤠ“híÞ^  '³‹Žçb ‰®u8©âH.#þŽWÚO¼ µLÙ&‰ -çJ2iG5²¼'¶|°KÉ;Ûùìš±.F‹ )µ«»ˆj±ŽWAªfKt[œ0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +çJ2iG5²¼'¶|°KÉ;Ûùìš±.F‹ )µ«»ˆj±ŽWAªfKt[œ endstream endobj -129 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 535 0 R -/FirstChar 39 -/LastChar 121 -/Widths 536 0 R -/BaseFont /BMKJDJ+CMCSC10 -/FontDescriptor 127 0 R ->> endobj -127 0 obj << +498 0 obj << +/Type /FontDescriptor +/FontName /ZTPMDH+CMCSC10 +/Flags 4 +/FontBBox [14 -250 1077 750] /Ascent 514 /CapHeight 683 -/Descent 0 -/FontName /BMKJDJ+CMCSC10 -/ItalicAngle 0 -/StemV 72 +/Descent 0 +/ItalicAngle 0 +/StemV 72 +/XHeight 431 +/CharSet (/A/B/C/D/E/G/I/L/M/N/O/P/R/S/U/a/b/c/d/e/eight/f/five/four/g/h/hyphen/i/k/l/m/n/o/one/p/parenleft/quoteright/r/s/seven/six/t/two/u/v/w/y) +/FontFile 497 0 R +>> endobj +499 0 obj << +/Length1 935 +/Length2 2339 +/Length3 0 +/Length 3274 +>> +stream +%!PS-AdobeFont-1.1: CMEX10 1.00 +%%CreationDate: 1992 Jul 23 21:22:48 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /QZSJAN+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 110 /braceleftBig put +dup 26 /braceleftbigg put +dup 111 /bracerightBig put +dup 0 /parenleftbig put +dup 1 /parenrightbig put +dup 112 /radicalbig put +dup 88 /summationdisplay put +dup 80 /summationtext put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\õ¸ÊƧ¾µÐ"våÿ¯*áÞo$1”Ð|¬Ã#ó`ˆ¡ݧ’ó2Y†ý°«ßÈŽK@瘉!ÕQìgëÊDÀVWðÜ‘>{0¥óá3{i‡þ¼Eù‰ÈÜmÀ­W~?ÐÕB ®(Ç4ñ0Á3´„"¾Ô†9¢·NLòçâJ™óGàô9LæN¬µIWn‰NRê¾Y[ÉdmŒ+«IfN•|=‰ÄÇcÕèßú¬G5‚ÊàyJ©i,dRhŠt§¦§­ ¸©x<#^Áê!V&³1‚qEÞ1[nÁ³Ø¶{3#÷aêôÂ#»!LLk-(PAÐh1ŸIƒvØïºYˆK£1Œ[ÉV„òàYÀѲ¤Y*óa¸¬F®nH¼ ˆŽD‡hƒPé­PtîHH'ä¬ÃŒ¼=³(ÝÕ³A¯šf(º8J—‹˜H:cüÄXÐã¼æýƒ~ °Û˜zkc·F8üŸ!¥ŒhGž…"VpלÝå¬ wõ©”Êp _ñùÆ>ýà#5ðJ ر*àfvÃbª£•Íï +Ià3YeòûA˜I—™ÎÌȪ]%RdxLÓ +>‚•ˆŽû +Ý׺ÄZîîÍÿzG¨ŽiØLžW&Á¬i£K_ èîNߟJÞ‡h $ØÕ·>ðN­E—|¨­sÔÝEÞf£¸%†L5X€Ý& È–Ñ«†’YtŽ˜öqN$&žÕó(4Fd:ùñÎgÛ/]>§~ç4Ò¾Ö#ùsæ„ ­,<&fÝMÑÁÃ/‚c…å_ ÉHãuK{HƒÝ«û€RV·Ô—ôÓÙ-ÇR?J-" sèmk¸Û<3C"†©8&Ž vÙâ§ø$âq¼iÇB·Â³^ «;]5“8ìåf(!êœ(vo3švã Ø)W•]¤gn§ÓlÙ¾:j©tÏl+r÷ŒA”Á¼Ò¨¨ÁЩ‡¾N?€KF•òXød“qu€h ‚ì¬Ç]¯ò)yHcƒ"Q—ëS}D9É9AWÌ*”œJ®Å¼%·O¹™ðOÊÛÉŠ_v}ÊéKby é'²/\S!ÀÄ>G÷9¬)4:ЖãW¯¤ˆwuЮèz ­~sr»Ý ~)FáVã7rn_ã²¾h¼f±˜¯<¥Êž ÑÓ#ÓxEÙ,®uaÈøõç)~fŸ®#GÇùñÍÍ`ÞšÛ¥uÂi ˆÅßs”ƒ%ÛÂåΈ)Õû ÄP4ˆöÄZ؉8 +A _gPsB1uUÿ±÷8íIÏúuÐT† +Å…Ûþ_=½ +—-Øèz7ÔIœ¯"þ ‚=sy·´$%‡&sÅ«Ž =ôa±‚ò3-… æ•:%‘¾qqÀßiéù±_¦Ö¸ÐÛ¸™¸¤ +> wŸœ·æßL¬ÇDKâ×{gö& +4²N%pî.¯óh‹‡ìó7‰ãMHSF`ÐYv9Î>±m.(²çd®Fn˜ oè 53MT +«<çÃST Iµ¼<ÀW&à¹cúI>ðgàÞ »À Ë +§ÁCÄA‰ÛkmSù:…d_ŠQ=]MxY5œpÛÊöQÀâ…«wu)«rWØ)-nÒ[$‹q¸¡tóšR;¯ø…~æMè¤Ü‡´V Z¯Æ—kS…’uŽàMì(Õ+Ð<û0îž¹­Ìí—Z7_UïÉ>Ö÷_èul¼q$UƒŸê(³÷h(2:Sù2Â;ïÍÌÊGáoÿµÄ~9Õšç³}uVãÖ-«Ù^Ÿ­ÀÇ%äP vUöXKb…|«%–4ñ&‹‡¶ª¯ aŸ_œ0Tï—Ãù¢wñ}GßÀLPžÒR3ø­=Vgy K'òøCEÄCݽ½HÛV îÂxñEÁv}›Â=soÇ\{¡ëÚ¾Ž"™×c>QœF@òµ(í ÄþYð:©Üûe&ˆl`°ZÈ+I«ülrà^™Ë–¸N®€ë”G ÜЗDòasðô5õ1ŠÓ£ÿ»ÚÚì¦É ?–D}|éç^ÅME>¨®B˜R™ÊÈ’ö÷ýãq§ `4°ØI"h±¡oˆ=Ëy†`]W·«Ûð”Ž1`ÑžÕ{±t»rÒ§Äà‚ –’¨ôtŸv ›« +¤zFí9)[?h|)b•gÉä3Œ½×.&ìæŸïBºj: X3;™àáÓG¯÷k„š(´ƒB,ûÖvç +endstream +endobj +500 0 obj << +/Type /FontDescriptor +/FontName /QZSJAN+CMEX10 +/Flags 4 +/FontBBox [-24 -2960 1454 772] +/Ascent 40 +/CapHeight 0 +/Descent -600 +/ItalicAngle 0 +/StemV 47 +/XHeight 431 +/CharSet (/braceleftBig/braceleftbigg/bracerightBig/parenleftbig/parenrightbig/radicalbig/summationdisplay/summationtext) +/FontFile 499 0 R +>> endobj +501 0 obj << +/Length1 1281 +/Length2 8108 +/Length3 0 +/Length 9389 +>> +stream +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /QSIFYW+CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 68 /D put +dup 69 /E put +dup 71 /G put +dup 73 /I put +dup 77 /M put +dup 78 /N put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 86 /V put +dup 87 /W put +dup 97 /a put +dup 98 /b put +dup 59 /comma put +dup 14 /delta put +dup 101 /e put +dup 62 /greater put +dup 105 /i put +dup 106 /j put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 33 /omega put +dup 112 /p put +dup 58 /period put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 18 /theta put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– +]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÕ™=ü 0)xfáÍ +1›kÙXž9JS:6ÔV ™ =!™X>¹¸KMîãÑ)9ã!™ ÒI‚}–HWIUöª¡c©l=G¥e°ÂZ¿m>nÁ‡ä°Q‚k°Ð2=”1p·•%R`ùý%ò$ô]ûûÞ÷ÿ‹¿ïc{!®W+8›?v(+ë)Ì0ÓˆÇ!Yah“çtA?HÞ @‹ÆmÎ?á|¹øM X9Õ€Ö¨ˆ#Ù2 +é:ùm— ,MZ+²¸Ç’\Ex9YÄn<á¢ðêÄ¿‹›2^FC[Þ`¼T×+ȬµÀ£D¬‡]ǸFF£$¸oØãB!>;A\äT hŽÙÁÒxìh½|5úù«:6Òü;åÏ–UÇ·í§6~åƒkŽ.ìT*{8î¾K¬`yÐ8¬³ÇÉ'—dT|-Q—k«©K©†myñ9 •ª9°ð1 |½ôA¸ÅfŸr ¯(Kõ*)Æ%_ʬñtPû¢`.rY?¼¿Ânrnä®ù{v2¼O_5;\gþÒ>§R¤¥{ïñ×4‰_ +: áØã9pEz–~ÿ„öØGu E¸Ì[Ùn窙ÝÉài9ヽ¤u#=X­&>¿¯Â~J~П°ƒUöêtå0°t1Cò¨qs-bØ5±ŸÒÇýð„Õ 4AšÆG˧÷OE1Ü»Ú"®ê?»»@~ +ÌR½Æ ¢”ÌO“ë‹öÔ>›¨XÕO8‘ŠÈ' IVÕ‘ðTnPü¯¦ÛÐ ‘#õìÔ«3³ÛL®3z‰ŽÙ›oH9@ÉuDøˆêðËë JÀsÐf*¨+ ­5èx/…Jöl ÀþñÍÑdc!¹=2~SØŒ è%ú•ªW½qœìJ¨&¹ªY\ƒœFbÕ.”'JbÉ¢“>úôBžå؉úùp‡,ý#€¦ËõåÚ  AjDBWÜ›3mT~ø9,ÙOg–j†»§”®›²„”_¨”b]’eZ9ààUuhÄäsŒÙ‹1λ2ñ¹Ãåv6ܪ%j(„MÚ¹aã›,Ä{yˆ—‚[,zå¨ìøç0lÕH ¡®á«YÇÄR¸ßÙoi„¯NZ»%Ã^ï£;fçFm˽8Ÿþ=ž%”VÍôÝÐxÿZõê$&é­dnÊà=ÏÂ5)3±‰ž#o(ßÿl )`¬j1Br“O8@â1'B~ܬ…ãs¹±¥.zYžÉ,/@(‡;ÉFþºÖ]s{¯Rú³Þ¬h¨È²»Õ7œ*“q®l•¨t ’â3.9@¦WhŠÌÙÔÇ zß—ï¡ñ$Š~¼)Ip†À›1HlÂŒfû²h,Ñóôý®<`=¤<‹d‚ð7;‡`~]ñ­_Ì-­´ïƒfÏ8äÁò¡EƒÌãlI×?…|%¹ñ¯©ÒÉ(m ‘r,ߢÅTþ„kyÒÔÐ]ø£áÀ$ú-{=*fP wéЇ¬oÛða¾Ïi­Òs&`^Æp~|Œë†ìµ9·ð ÇBâ†Ü”W +À7WRÃßÜâ=Ò 1”ƒCÓØŽñÜa<Ó+©cçñÑ}6Jó_õ•¼â`#ÉHÖ°Ö¼¿IM Ç„5Ááj¦øvÒÐDKÍ3†ãÞFш]¡†¿äE6&R¶†-svìgÚßÈ;RÂŒNæT-Sºu>ã `Jp{P· ¤mÍ7™„±zBÓU9·úYÈcZ yÎÖ2”u›ÝP&ú¥¬Ü`x ¦"¨ Oµïžv÷<©óEpê’†£”óoJ-/Ag",Θ³Ó•Ð'¥Y¾ÆEú0jb*7ÍÀ%~Ò)ÁØ嚟ûj]çQ ïÓøæ‚»ö/Ú‚}ûóâ+]nÍWÖvuSX{ ¾²0‚A¼K¿Ýùo«,%|´„Y Å4À¡_Ä–­tøQ=¶A›ÿÏõå‰ ÇR mksþŠ!6[œQjО„†'.©|X‚ºY‡øÝi÷w’d°'h<Óæzx[¿¨éÆ™2×&†Œ=ùÆDÌí àY¼;aüâr?üÈ¡ƒij«•qà¡«âqŸç¥’B“3äG맨Såõ’5ú^T +\ܸ.„: þóVäh(o¹~:P·XÙž³ Ç4dHldPÀ²ç 'Ô [Á¾p¤sà¿Ó÷Ö^¢ Ì<À?°k¡µ3*D cÃ"(‘ {MÞ¼_ïG;@δÇ7µ|ŠEa¶±Ù<Ù† Fš±Ñ¢yÏži¢‰‚NºÍ”ýŠ"´ m_Rñ,iä¡CXÎÃìëI‰Xù¹&ÃÛVÓ{IJä®& 2úæœqw·Ü±ëª I·Ó—þ2¢# +¬†Þö—wQ‚€6dLÃΕ¶Ä¬‹ôº«ãCÌL—3¤ôŸB\y%mL_š£F9βæU·µ‰Æ$34«d…”ÚsØÖ‚Ž¶†ò\†½›É4ër;Ô‹f •ÂCE™›)g5Í&&pâ¦Ê d"Cˆ´Úüªb±¢ne.†:”¬Pû½Ý®2ŠÎ Ÿ4d:˜L!"_HÊæq)ú*´VÔð—ôG‡?¡‹úXóÕ24–}ç¯w»ç¶=‘‡}RŽ$ž¤?»FÅýˆšU€Þ!nôqi:`^‘ÉÚgýƒ˜u®ÏYq«i~ú+\î8 ²Ø;3 àMŸƒÉÎÐV:=v˜…È3’r–cóÝk]ò2¬2JLè½!&.“ç(±I€rÝNá@6Œ§{Ô‘ÔKßžXt –LÄœ|v|>+ï®âü„ñR¥jZµ‘a·ÉÙnLŒ/OcC æ…(ª*¢+‹ÖÚ‹ËÖYÅzÍÔaT|ød¬1Åeì4‹‘té“P|±ä”øª¤E©;å0ª ³ŒNs(àãžÈÌìZ¦è‚¸!*²)ZVx ²£ôT'A¸FµÐKCÁE°Î;2ôSþ-°¸P*ÅüçkWÒ¶ ɧtÿYMK[œk¨(GÓ £Ñ–ÏeäN”#•`EH6RÌt6RÑHÞàî–"óJ’å¾6°¥n$UÛ-MÆbMá­ð…üzX3ɲŽ‰Rqö©f’êÒ[¥|_èµúþTý°{]„øÓ‚ãÎÈ~˜Æ‡ý3Š93ÈÒS(ÉÑÙÑü6¥«és•Ãžîæï²kçȈ Ä.ø’8fø¶r3392Î:"s¶b[à-le$b,’äC3Žs˜£O¤"¬’«wœ-h`îwåE§¹Ã¯û|ÌŒ|½.Æ äÈü/œÌ›íÞ‚"ßš:5%jY€Uš‘Ï<¢îD“ìŠð;Kr´½_jaàa°ˆ—0R>ן |•wvª)Hvà·ÍZ>ÈY~›£1›ØN#^²§Ì’&XxÒæ®t¤(º÷ARÛKuÜo®ŸáÀ áÇRTø¼ˆ2SÂð“²i[K'£‡tLÀ)H¸›iK#¨é~ú–(kÃg' 0·ñ1Œ$…z›l½ºi±Â%•í=«¬Õa9È{³ÆL7ø”u˾9ƒ´·ÏyˆÇCL5æ=sSv¾sQñ‡¥³à\4鑪€ã?×ýomý÷Š™3á0We¼“‡‡Ä¥'Th}»-}Ÿ膽iýošÛÎ2¡Gåïä6ƒÈš‹Rç ¢ÊPm{êÚ˜ãä<¦¶ÜcrïÔÍ)ž“ÇùùÖ¬ùÚ"•ý¨®Û ås-Ë#«ÇÇ'Px „¦Éq$Ù±°|{¬Ò—‰š7Yë†Y¾WÑŽÐÖeš/‡óßCõå{‚à:œç*_ÕÀÔ%a6#¬åÓæ²÷à”çÒÍ´^Nt2úp`Bú¶D+ò(ß +ñH +X¤*W"ñYÚåæ)–Õ*ÛÆãpñ1°Î¢‡ˆmE«(µ™ì^PÔÝ1iýXeãʸuK̼¬¡C‹ö—\ÿ–@Ûí­A6£*“ÀUªéýe_ð6ÉÁ\U”bJ'µ_á |ŒÍÝ%¾OìçZ5†Ý[ œ «*u÷‡v{âB,3'åGs¾øDu«kAÁh)¾_ЗVÝ2ëçÖ;ÜѾ©¾¼C¦D[Z}òz†et²`Q¥nqŽ?à¢ÝC˜9ê à>¸pÈeb÷XÅ@iÀH?Þé•pY b\é½/b©ø#‚,‹áhA@kóÿùoÏg>¯®6ŸžŠ—"¥~›Ö°JI? DԀ߰àœýÄjŒŠãY7c€r‘µMÃ)8¹¨tGf¶QET'JˆåÙqš}üñ¨¤î¢qe_EW>:VJ¤¹ï,é²öÉT*ªÊVWÆv/ô^m7¥©_}ȾonPlY?J½O_t±5dñ¢ª¢J™ .õÅþl5©%‰(—`w,,išŸw‹ BWc[Ω¾˜¦œCZÐóv>÷3 +QUûF1’\€+þ’é³iÛJ¼„xÉ…ß°Âå:!€jçð©nU¶æ2ó":¶V$´®8H¹Tbéjš/ëm­×Á‡+(è¹¹pˆZf9gWo?ôY˲ëWh+j}Ág¼ÖóµgƒÉZŸ¾@ú¶MfýÕB?—s nʹ5sè¢GæZ†ÉâDïÉ¥«ÅÀŒ@^\§½H&ÐZã$2óG-4¾à¼º{2ý$Œ/ƒnÝÍÁžJ (ãMº$%ÅB>±ñáû¾¦_ÞøÙU#|¥Ø™©½€E›©gàÇžGÒѨç›áífC#¶ó=3à‚úw涪EئƴøÃñSQÝÃy«Vq×ý¨ÿò9ðG ÑäÊ$üêÿž¸„;ôöEcÆ/*š±’7Œ±á$jôãJõXA-†c+±EÒ$Ñÿ³Gý¼TSgCý‹Œi#ÎaÄ'à—ÈqÚô-ÊÇ~ÛxÓoîF€s³4h *¸eúñ´e½ƒ˜O·Óiî´8Eí¢V:´pC/ÝÏþ=×?£d>·áHd* méßäŸÎt„È&ðMr=õ=á¹|ˆÑ2$á>ë©Ájã7ì_¾v0·h7ôíú»+mXº€ ©A"Ý@F^±yi+™µ;6–!~žñÝ’XëIkDe2OrÁlþ‘¶BYB/ܬïN¼Þ¯®eð:W•U&ªÑß„Ê+ü7nQâeH®C%Ÿ…ÂÝL=švþ§òܼæ~ç‚ò š·›r`Т9¿<àyu9ÝäMŶ¯ÙÖ“±2ÅÕÛ9(1ë8HO¼Ç6붭$m•^'«Cî`ÊIV/ ‚™1ÎTÔ¹T5y^F„™ƒ­MŒ„ĵRªu¿ÊÌVN:Ο§åÇ66Cð®éR·aŸÃjo$XÔEuRÀìl/¸{~ª§±ÁN`Ø,j](‘Ÿåµ¡ +JU¯GlóC½üÖÒÝh f8tç.Š¿æ»—`/Mº´#˜Ä8/;¯Tüuçò9´JŠ…ÍsÌöñט£x´Š?…Ãÿ¢øaÎjŠÝø%ÁTýŸ„@»ß'…æd üWcJ¢ôÓ™¹Ë38¼Ý ´3Ò!Yg©Gvá‹°½E±ýÁ€K) ƯþÇ?þÚØaJâ»ÖÞV·ÖKÓs ï^qŽxeZݵDGz9¬ž&¾žh™SJ™ÚaŒÂ;¸à.Ø÷jmN¨œs)ªˆ¡[~­Íê.ÜÄþŽ'†Ó^õpŽ˜5Þ ýrïs¿ý28’Ecß$Yqýêû]Ãû|MÌ&ë`C#Äe˜ŒA_°Â¨„‘¦<ÖU÷Àô¤I¢]„,,R#®-ײ‡Ã{{qêó:»«f^Öý=M¬Gêµ>eµÓ¾V&ÄCÓË|ebx ëÅc´gÝ“´* «‘Ä}—P ¯¯„}Æ驶Õä°{â6‹äÔ³et.¨²t$»d!’ÈÔåŸê"ë9RaFõqšu_ MRa7v4È^f£U‡@ ;Ù$õ<Л ƒ¯ 6æ„ÁÂ4ó¸†.XbVšnÆåêp“¾æ‡Q™^ƒë¼öPƒ°uªì3VŒ³—[-‰ï¡C9¦‚kåË¿>6æüθ5ƒýŸ¡†Ì/Ø$#àHw!×™Óá9D“G͹ÑBKà!åy(»ŠÀy³Ý‚0ì—ì<ÉA]c˜:¨3 V»Î{A6ؼa‹ŸJ¯P¼2GÊt34ê Y«——,éQ0·©²}ËÛ;ˆÏ@ÃdPY˜kšÕTó\SU´<éø¿ +=¡/|zë&{ïE¶öjˆ7ÒNl/ûE˜u¶_À:ûñ”fmTn 5\D¤æ OÅdXÌ#lûSσ¤U¥Ý—ŽÍ´~Ãñwýwö‹*Ýßí\TKŠ‘èê±€„ežÀ÷n8´!©Ëῆ+’/1Ì Óèî£ÅXHã¥Ì;îu~}ø*ËÙ®)Egøk<Çy•†ÁIµäï½´X-ŽeÅm‡&=§íß@x(~ƒ©ÿí¶-•Oy‘ŒñeoýIÕçáE¿1»úÚ6‘Ú¡²F‰àëñ1Évb4¿‘ùK<×›­¥º€ûž­ÐÉù°80—Àzð†Ýç_b¯à ä'…¯]9òÚ¨êLÌ%n¨ÙÎ kwë4ü›>=ÆÄ}”£Ga±Ä@Èù*>ƒ­´ktÏ ÑìVb9m—‹¤†ì¥L¿e5i—…i›àêíÞU}EÅÿ6ë£20Ö°Ùíà­3µ£ˆ þÝ0 R +’žz¸¡ïô%†XÔº4D¡þu÷#Ú2ÈD6?3.â•~Ò„jFǀظË;jQIyÓàÀýþ×)螃\çFÈr£y46MÀZ3¹Häop-‡«ÙKÖx„Zmoﺀ۪0¼ë®¯ˆ<=PÁ;GÏ™ºê‰ÁG1w2œÕ7jÇS(ö)WöíÝŠiãœÅ ô;òn.‰«û âFÀBSô íã¿1£fç¤Aô.YÙÉWé;dl¤ÑëÒx¥A5ï8é_± õJ;Ø3ÆÙa'€<0îž*Na®4=*Ë5Ž ƒ·è›Mv‘nбZ5íhNS«§TMp¤l ÀÕß±¾BRH ´µõŸèTO ª0yµ¿láç-Ó]Ø«­[&’Y„y¡bõOÆ‚îñ’—éÁ›mé W«9Oå9lUT½„U;qí«ó7qœCð‘3SqœU#Ž[툽pɈ‘ f­Èø¥m†XD¥ÊÅzè–v.ïãéL¶ Ó?‹’ +´©ÙMÅÏÏfœ42f´´/9JnŠª‹±FGzÜ ¿ø‡%”¾|e-AÍz4BÈÞárp‚ÍΡèÑ D‘ý¨ìšWuˆ¡U37‰˜˜Œº“RÄ¡‘bùI‘Ê»ê¸ÃxàÈïÿx¨WÁÁ#;z:»¶÷KŒ¦Ø£ß7˜ÄÔÁ©M øîã_·Ä@Œ¢ñuÐÿÄùtñ_Ÿ-]pù¼=4K¥ H088m<’R7 xÓŽhGY Ù“11Çt\×öásv«PÊË$¬\d-X‡_0ÜÅ9fàO¢A@K r®R¹œ¹¿k+*o›æ2"ñWû1Âõ"õ¶“ŽVÀ™©T«³›þÙÛF+4Û×BršÙ€_;ý`{,#üw矉ãí\ãçŽH^=p„?² … +YúWðàºc®øž¤çÃû–Í<“^؈\=gÌÉ-uœQ9sß®éeè¿X5ŠÚ|ß&îȇïSsú­FrÌÓÆø1HQ^1¥‹1¾Ë¼Âc]ìi"^ºùüƒ‡€˜¤-ÇkP×€ÍHܾ€›+ ûaÇøCDBÁ.`IÜÆÉgRJ¿ñFSk3…XV +M³“5¿³t)µÓdd%G—VñBÈÊ*pd6üIð=%ß ¿×–“WìúÒ4<¾$lÐ)+°X·õè\V¡†ûc ½;§sáÛÛ"’ý´­¶Ö׊A‹:ÌÆ”2D +Yî6²a%ƒt)0­‘E K‹ù'­ØʶµfF~5ÍñF|ÅÀ$­”ƒ×…÷ŸA…³4ÜÃt·”R•2žÄŽj¶âüLÔMÃ^:c •LWt›ÊßæÞQ˜J!mªJL¤\Mµ4 Ô^Á×dÝéëÑB¢Úž-í]×sµ³ ([äW{¿6Ëkßeï"PÍiiåbÃärûI{Œ¥ 0æH1#Kl¢—™+ž’±óÉØ{é牑ÃÈÞ~šÉl±¨e¢O•jÌjt +ˆC7Æ›5|š$ö>å)Õºa…P7 pTõH¿*P‹gÓ+4É‚æg?Ó-_Ú,æ¹Bv ž¶‰²¯ÓмÉNTžýL¾ÌŽ$K¨$ЉÜùöì +ª­ &®ð?háöð¥,BÊ/J^k +ù™nþž`wHNPYîN@•3Âéž‚ñ±¶óµ°¹w)ÀŒ°ï¼§§Þ–r5mÿ¾£kÝjzö¥þaŠ×ggªU(Ü2±ûíJ3p !/îB€o½ËX‰¢÷¦wö3.Œk¡’Æþ¤—³ÅÿÓå–šŽ•bà=m¬iÓ—Öþs_N7Ìðv»;=$ÐíÑwÑÆLÏSîO[×µ-Šþ;E+ƒ^gVSÝ1>L½ŒxrA†š,Â6¥ œ;úª÷‹½^ ¼Z„r: k3 EÀh|LAQöy'>])Ü¿9Œ~Œ¢‰¯_U cp!I§ú§«Ò»D€: +%/ÄßÄ¡eÁäÛó|Ë!ô(AÞ‚i‹prß‹…É9¶•ßÛ±*iC©¯”Tw h˜qŸT«³â Ù +endstream +endobj +502 0 obj << +/Type /FontDescriptor +/FontName /QSIFYW+CMMI10 +/Flags 4 +/FontBBox [-32 -250 1048 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 72 +/XHeight 431 +/CharSet (/A/D/E/G/I/M/N/P/R/S/V/W/a/b/comma/delta/e/greater/i/j/l/m/n/o/omega/p/period/r/s/t/theta/v/w/x/y/z) +/FontFile 501 0 R +>> endobj +503 0 obj << +/Length1 777 +/Length2 1473 +/Length3 0 +/Length 2250 +>> +stream +%!PS-AdobeFont-1.1: CMMI6 1.100 +%%CreationDate: 1996 Jul 23 07:53:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /OFGSEC+CMMI6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 67 /C put +dup 14 /delta put +dup 105 /i put +readonly def +/FontBBox{11 -250 1241 750}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– +]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÖ¨ð[G¯•ï(©ÅaÛܘÄ|õRPé6n¶ý=: ªbãÕÙ9s2m4{~ÜC‘ÉßD…¸ü˜Ô%Åx’Ýð4,¡C v•ƒjÖû-ÄÁ?x”vä„ynhQ¯`¦?°ÞfÕ\ñ +Ö[“BËhnVGXÉadÿ§±èÇ&óÇ»D»Òƒš¤gWGßaá0¥^)|¥ð*?ùZòõHqr@w©8~'‡š–I­_o3P¬¢f4½Î!ìÐãYåê^afRoëà 0 Ÿ½Á¼/›bïîăEª˜øЪT·¤€çBfQ†\ŽDNÛyŒ~ +öå§íˆeaÕ‰‹R†a}8ÒÎÉU‰Z ySráºq'tû©±5Òàã\ÿ~…¹å;ª (Ï?¯^ËAK®Þ”fñ¸êöÇ:*mÈVoö2˜ø¬õ)õA]«­³foþLÓ˜t\7¸g3&Ü5é#eªŒ5qeÿ];¨unwï¨E«ÿâ9È,}éïî#WºD‹=«Ö^ä'Ìžß›]J›q],Tˆm–« þ|Í>=V¾ÈDÕZ*Z±†ˆ4×£Ù†§âDó˜‚%Ý6öV½6ðá>Îñ" Ó¡[¼%Rëq2t5—·h]òQS2TšyIA@»Ò©cÖ'é÷ |œþ3Ý1ÎOd~ +ÉZTò³_Ãhï]ßá“Åâŵ÷¾ù +à^×µGºS76×ã1Ñz'ˆã²C½UHÕè g¡ G(µ¿ ô‚?â’W ûf±%™[*&¿TÀ”è&¿€õ":|6éóÊAæ $< UßD‰Ô5 >Ó +endstream +endobj +504 0 obj << +/Type /FontDescriptor +/FontName /OFGSEC+CMMI6 +/Flags 4 +/FontBBox [11 -250 1241 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 85 /XHeight 431 -/FontBBox [14 -250 1077 750] -/Flags 4 -/CharSet (/quoteright/parenleft/hyphen/one/two/four/five/six/seven/eight/A/B/C/D/E/G/I/L/M/N/O/P/R/S/U/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/r/s/t/u/v/w/y) -/FontFile 128 0 R +/CharSet (/C/delta/i) +/FontFile 503 0 R >> endobj -536 0 obj -[319 436 0 0 0 0 378 0 0 0 553 553 0 553 553 553 553 553 0 0 0 0 0 0 0 0 814 771 786 829 742 0 851 0 406 0 0 683 989 814 844 742 0 800 611 0 814 0 0 0 0 0 0 0 0 0 0 0 613 580 591 624 558 536 641 613 302 0 636 513 747 613 636 558 0 602 458 591 613 613 836 0 613 ] +505 0 obj << +/Length1 803 +/Length2 1857 +/Length3 0 +/Length 2660 +>> +stream +%!PS-AdobeFont-1.1: CMMI7 1.100 +%%CreationDate: 1996 Jul 23 07:53:53 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CFAIUE+CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 84 /T put +dup 101 /e put +dup 108 /l put +dup 110 /n put +dup 118 /v put +readonly def +/FontBBox{0 -250 1171 750}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– +]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸM×v9ß2¤Ö#:œ¯i±QßÓ?À–.¬n>¿¸­%j”zGm >Nj›S]Éñ¾Ñ)Å7uÕÖ‡‡¥Œ“ŸÕÚU±•¹QhÈ4)½-‡‚×p#êz£™É{8YãаGP¸9 ññ¼)Ü"¼­PìÆ£Æ3ГzYèYåZùõgp_P÷C߬CÄçÜ”DÎþC'šý<|”(‰£Ròÿ€l/ø³ëIÕxªXÏüMYz©”í„»è²ntÔŸlõAv·)|Ú*iQ€P3|ºTxë˜LÝ" ®ÙʃÃ?¼ÈAwõ·pŸÆÒ‹:rï÷)ˆÁ6,ç›Nœ{?åˆé‚J¼oÑA剳‘Js¤(0T9†$ø“Õ¶Ã'§î'0ÞÞj—°œ%&Æ4öLŸ„wÍQcK¦HüpöYÉ ÀBÀÖ¶ŒÑß6Ö$ób¸ZXÖZŽmýX>ù§šB# µ9Žëxôµ¨šÒ¥à6IUJ½eG#˜ÿ݆>@P1o(ýß‹UøÖc˜Cо¤"‰ø[ØD‰´.ÇÅ)Ó>çè;@Ly›ŽŒˆ—‡ÍÅÍ—¿ˆ`50/¬—+Rª1›¯&e7ØH¿ê?ž¡Û6Ÿy÷@Vxžó™!+Ô ãÈSkä,ŒÆ×ýÎM8Ú±kp/ ñh(”Ç!:ÿÔŸÃH'5˜…²II,LIlí9°®ª#ozð)”‹ç®bÿúz“¼¡¡&õÚ2eöŠpDQ/‹T‘UÝ^ riFÅQdþ‹'@8¾„—¸ÑNL5‰`ññëNC§‡ø®Amÿ·îô3ÂIÒQûþ™AJ¼Ùqla_YÐ&¢ÆíP„èmj‹Naz!vœ¥×4à°÷%.™ª™Ý§„Çèã\Ö–ŒÝb`Û+#·ð`‹\ܠḄ¦FÒr=„Z +¬ŠšLç2-·Ãàêq; ]˜Æ¼®±n²l›²•,ÅLt4‹žœä–-`_ÛM¾ùÁ–yç檭õÁ +RBéÙŠ€1äjùý¼•GO._í=] Viæ°šlê@¦øÒå%fÀé½…YB1ëq4MèÅkºÛ—¥í$_’ÔêN>÷à‚B0¢}á\äSZh«–?sÈ€¯‚O“ËwJªXmQ¦6ž½²8›XN3A?¶Œ¾Â(Y}ND§$R{óÕ¿‚&è¦ ÝÕ\ËÔìëñ€šù\á‘z½Þº¿ˆmå—±*¶P äk«ð¯-‡ì£°‹›è´BÀF‘ *Íñ♹8ÊcýšlmÎþot‘÷g³J‚(OƒóÑlj^– Øðü~^&¹Y´üç0ìÜTI\žÍ1¬'6ÆØ“Bcx˜3|'ÅÞ]PxªTi\ú[¼`¼ßýß»,·Ï}Ìy*•ãÚ1PAÄ@H³1}c >­¾¦Iä|N¶_ŸDÅåkغãš^ï©~+($ÑïÙ65)øœ¾qAŒahˆÒJƒÒ¾ùU“¸Ð(Á¬qísš3F•ªjÃékXµìÖõ[;Õ8vâ;;ñ¨$=Nž™Ynú… \XÖ=ˆ(iv/…Á·Qg¦“¼_,\ðüç-÷]C 3­ÓˆG;¨öV-¾ˆòÑÚî|yn^ç4ÆÒÏ@Édx¬¬]Ö*Ú~Ð.|8îÿùÌD?,©ÕÀõ㋽ö»5¾©ØçÁÑ`aøû” +endstream endobj -535 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 39/quoteright/parenleft 41/.notdef 45/hyphen 46/.notdef 49/one/two 51/.notdef 52/four/five/six/seven/eight 57/.notdef 65/A/B/C/D/E 70/.notdef 71/G 72/.notdef 73/I 74/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S 84/.notdef 85/U 86/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef 121/y 122/.notdef] +506 0 obj << +/Type /FontDescriptor +/FontName /CFAIUE+CMMI7 +/Flags 4 +/FontBBox [0 -250 1171 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 81 +/XHeight 431 +/CharSet (/T/e/l/n/v) +/FontFile 505 0 R >> endobj -125 0 obj << -/Length1 1483 -/Length2 9915 -/Length3 532 -/Length 11930 +507 0 obj << +/Length1 994 +/Length2 4891 +/Length3 0 +/Length 5885 >> stream -%!PS-AdobeFont-1.1: CMBX10 1.00B -%%CreationDate: 1992 Feb 19 19:54:06 +%!PS-AdobeFont-1.1: CMMI8 1.100 +%%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.00B) readonly def +/version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMBX10) readonly def +/FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /EXZABF+CMBX10 def +/FontName /VCFHMD+CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 12 /fi put -dup 45 /hyphen put -dup 46 /period put -dup 48 /zero put -dup 49 /one put -dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 54 /six put -dup 55 /seven put -dup 56 /eight put dup 65 /A put -dup 66 /B put dup 67 /C put -dup 68 /D put dup 69 /E put -dup 70 /F put -dup 71 /G put dup 72 /H put -dup 73 /I put -dup 75 /K put dup 76 /L put -dup 77 /M put -dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 103 /g put +dup 84 /T put +dup 14 /delta put dup 105 /i put -dup 107 /k put +dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put -dup 111 /o put -dup 112 /p put dup 114 /r put dup 115 /s put -dup 116 /t put -dup 117 /u put -dup 118 /v put -dup 119 /w put readonly def -/FontBBox{-301 -250 1164 946}readonly def +/FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ_ùc‹‹sˆ×t Úí?‚}¹ß´7-95†ãžç¬Ÿ¶©µÎM/®ÀåZà+üFCxw¹ö\#㺴úãDÝÉ«<ËÀa‚Ø=ÇVùÕ¾þË-°ã™—òdÔ½oe¥~”ÉÈ„š²é Ï£¬Í‘ÿRJ­rb±QźдÍUÒãiöè6È,YáåÇ?Þ?£ÊÒrÆ|l¿C¶oä¸g}¯î¡’ˆBþ±ôªhz­mÛä2qNyœúIØ¡¡(ó.‹($¼€AñæNÎ@SÄŸ -ìišu¸'.Ÿ•‚m³öC3…€Ž3Š‰ –!vÏf¦.:ïm‘ÈŒ‡Þ°<æÌßO¶Q™†Ñt ñ!w=hwß…ß²i£Àz¦f½óÅ=¢1‹¡† -³N(ºÆè-ÛCå :Éß’w .BÀ÷½ÆÙ béw0$[ŽŽ‰¹"P˜œU£~NY®*ž6¶4Ÿ¢À›±õôC>NïÇ^?˜0ë^~o¾&f¬Z9Œ-ò(*ÏŸÊVV9 -ƒ|J™ì7@ØsÏï.$‹DÊF“§‚YMÐi+M¿ÄÍ즒ÄDý¾÷¼SW[ò'1ç÷qy4­qZÃ;]6y·„É@FæÍ< -ØÑöV&±N3ÏÚn²‚]ÄDúb a[Àsÿ½üÊKõ kÔƒý†9ùèÐ$[F=e ñ,&Ȩî)uv–Ãñ1DØêVIj­a©Iç#«µ…™“ò -5Ík~ ­…QÎäa’MÃjFJ¡±L3úû†.0ÆlÅVemÙ;Œ Ynžâ±ª´y÷ú£Ry­´h¦$¾&Õ'¿õíàgYŽ‹x¤¼û Qi-°¾»“ o —´7âŇka¥c¢g92ÂX3ú£]²*Þ#5ÕÜsJã¬^îfX×’ëbû¤Aõ>ÿ!ÙÔÄ‘òkèõLa\­wŒèi\î¯pã² dÔ³JKWpº²©tè˜ö+þñ2£~-ÊOCá=±<”ߨìâ·7H'®†4ú‰­ FÎÓD‹ôSüÙ¤ñ”údŸÀ—4»iËsCœ°ÝD§Áò•è3Mû¤`ÿ=eOŸ³7éžmfû¨z~¹Ê6ÈH3‡6&ÚUÔèPÓæö² çÉÖ(5†òÛX.:|å[èH"É‚7‘Säyê¶Zþº?a§c´tS[ålÝùDA\‘t96‡6a—ú´ðn,2šàºA?Õ"ÙÃ:Ø6›×ÜÉß™7xH/5ùe—=èvúá ªŠeŠ³ðØãÝÑ¥sòÕ% *üWà]l ¸áþ(ê+zE»6:Ðl12 ,ª]Ì„,èš/§Ê鬙‚óèÏ#ÄüWý±Èþ•ÁàK œ0€F‰'Ë™³ÓŽ*ë›Ümö*çC|àÀjጆç[O(“„ˆE6çÅØÇ´ðPÙEéðK¨n£cù¾Ù}{«´Ð®b…V=ƒjðBŽHÐO˜%>W¢â|¦$ý,±ÞêÑã”[m6ÑÄ·«Ë"j¹¸ìô/¥X´S™^Zö*™$¢l~* IÈNN-þ\û¾6óJßD›4à‡¿:‘†ãMÀšbÀú¯ç¿/ýŠŽrŒ®. ©@ƒ -ÀC'SÒxÝÚË -¢p`Ò# ôº~w/'\è fñÃæŽÃ»›çbB¹™V,§ØË•K d‰îÁêPÅVãúÝÆZÈÜÁ°VQ0ˆMhÝøðe÷ëù›‘5§(˜ËöÁ¾~ð­b ª­¹ðÙÉQB -»7Òç:!ÂÑ©Í#œÛͧN ™á„TZA¯ƒ/ƒr”gYéÛtàÎE–°¢sø0¶H+Ë?v#]†áK îÛ}r{q!]B¿*Ì[⊮?ª&>e7"KZmI|‹6™¹K¸`¢SÆ÷®5Þºµje)×¼Ubˆ0ï@•õãK™$þjdµ}uÆ'Ð3—CÙ+>À-i† »8žv‹âÀìmZ#² ]!¾ë¸§ 0ÃBŸ¹ÖFŠç„¸»¶(îÂo¹ëâuòƒÍù±YØãŽI÷øÜö×m®*ØT¸Èå+`ÓUÎ#˜ƒŸºìCž­l¨5?A-Oomoü­Ö‚Ôx22¤ N¬ª®1ŽË£{ñ‡Ýáú<)>]¢M¢S£.À/üâeé BÓTYøŒç×A 9J‹q?+ìÌ! ¨)÷+7ý˜«bµHAú]ÑCšA¼Úg8¡ÐçuOÔ -ÄK~½¾]Å•ÆaØV8úëÃ'KxœÎ„¦Aqj³¬óo"ûÊ5áCk~!¬'“œrŠÍ=dpUÿ`·ÝV}ãÅolh0ðPÈðM‘"ɉä›j[öÓ*@ YØÀ'ñc²DO{ll -J¹5˜ðvæI¦ ÃBæ[ÛûcÁ*EÏZb¶«N3ß¾„9ó<¹"Aß×vxÍν¬ÕÝûÎ>UžBŒ¼¥Œs3 ªÁ ªð‘ë]ûÏ9Ë]o5±9êæØs,?ú߆€bînì½nŠs2{üÒB>Ñ;šÒqZ¿:/–Y9¬à3CoÖzn²÷ -?€äÞ“)2*¯u¼¾?G¶Sª9#F2‰°ú)4˜¾{…x>;ŒËõ¥¶à‹vô¡r¬†@†Çøz|B¼ÉrÍû¯»icê!†ÖÖ°à‘ØNôfgü"ÿƒ«` B‡êÖ«{Ô™møÛ-^‚ÐwôY~ÈÀ˜5 ÕËï²>lJ¶øpÔ“üEｿ3ú}™¼áöXS©a4нÆý]yCëœåøUA a·Õ¹:ÔÆ´(°À’˸Ž›†«ýlUõ;ð>|sª7?­/ÄÁÓxìfŽ’P–¨w.½Ž eêQšX˜Ð.Á@àéçÁÄ|Í\(±têqz4´Mmí°¥žÃf˜dÌS•‹í!Á¬{æÇ+̸‘÷ÃéÞ5´Î°0Jä£|ê¶Ha§–PJçfi1&|½G;ÀrGB~bnr–/`ôÖÍÆŠ^ûYS¸˜×VÚ4±ëD\=ÖÛ¿VJˆ£‰ìÃ}½e}ôH’îT¦!W‹™ñï(#¢d/œÆ@ w㺄X"‹Y6íà`õU-€ 'ˆê5rßü5狀Ÿaâu/ÿÝ.sñGcÏ9lïöøþÍw¡U>â¡OâT›róCér<•òIœÀDڙ΅„±jÈàx8[ÅÜ8K®zZ°Y{Üi>)}ùŽ²5LH%˜þ¼­qÍ­\c“+à‘í` 0ßhɧf‹^#?UÏ{:9Àµ¸ÞA‘'1‡ðd¯Ž. È^C—Oºó_þ+¼$&s ëì*å7éÁ©K+ƧJ55à^ÏÖùÑ?• ¿«½áWB,°Kc²íí¬-PŽÏ±Ę́k¬­w«úw“¥Ÿ\ª›_¹¤b­Äûê&\²ó1 C„¯£MEF‘Q§L©À&0X›Ë·L@l|û&`¸LÃZb¥%/²<ú*ÿË«µØ]L<È“ð5U»‚s|É€v¼Ú«Ô–ïC,ó£~‚„‘Hàa²æ _ݳF˜N(žÀ5N®|¿ E¨r·a•ËìsƒÎ¥Égá™±w¿™€¶ Ž?T ˜“d÷of$ÿVƒßÃemÔ[x‹;²N:m[hý^!¬½´2zk?Â*î²*¬-£QDÔŒ573ËëQ`yü:^{ï‘‹]¯î5Ý tTíÐPr¦¹ RÕ¯¥AxS¿9~§–V3XÃUXô*ú‰ï}vÙWÖµPý2º'¸54\͘¾ö½½ëÇkÛ#þ®Ÿå¡ñ{_ ‰Ý.=p½Ýí û–«öpÔ‰ñ¼„&£Q«ÎüÓq?$HøÇy.?çpîÚvø±»£Z â—½tbFdú‚ª§qæŒk( Œ³HÚ0—ü°/¥ˆ-ð;×z)¤!és¨|gÓLŽKbær×Ä?{à¡ {óìá¶@9eRÀ”îZŸÿýò°r¶Z¶2/ÕñÇjt¯ á»…9\cȸ0ëéL1Ϥ_K­vi™'TIçÆË•„ÿÞÂNÿ¢ï½«ˆ>_GÎõ!e$»Þ–fÌÂÍœt”ZõXviÖÂ,»‘º8?ƒ/Xˆ÷˜§§_ÝÄÎßH—†ûiü‡@0å3ø{‡å‚dÑyØŠÃõMI®9(–öÙÀñ2jàÓ)iŽé í¾Ùào*®Ÿ¾W\ŸH|F¸ “²7wͬ…-šUIòÛ€{†«v*ŸT$æ74Û9ø”¡4+A·JìÀŽ¨@ùhƒœÙš(Q’Ï]ÿäÆËMƒÌ¯ºÙ}”ØÛóÿů#ó¦ä™Ê Þ’IJs)œ³­5uɽºü(A¿Ô(tÌ_ÅPk‚é讈Z?ˆ–º²²Ô×R]à[=S$ˆŽÓÚ„Ä3&ù‡md÷>JÆí¢#ßc9¾éï,¢ñt Œ&vkPŽ¨Z‰c’€5˜²Ál]O&H‡Ø¿M¨‘Ý“£AàÌgãJ¨_s÷®:Hšœæö—½OÚÍÙ˲btÿ´uc˜$ÿRÒÌ™p²U»//}Íú;E±éûW=4±y WÖ¿!Û¢ÒEª`ñ“"ïEÓ–(s ¥ëF[‚šÅl‹.g륞d U -®™GéyÔ¢¬Ë ¶4Ø7„úhaÌÆ òþHþÿÒã³ìŸ2óKF^‰ËHÈ—-}“R þ°"¸”3ÎOã­TT¡+guŠTÊ45ÈÙŽ$^e2ï lK’÷gÒmu¸{‡Kð—ˆû·Ô¼¾ -kEý ”’ñb­§ƒþø~³?JÜfÏ)YݱzÏÄùzUèä­yß N¬Ÿ ïÈFU«¤Ê‘jf 6*göu‚7z‹¸¿>嚊mJ'8K¤Œz)dÌl»|¼5åÍÇ@¥Q–ÝÒb¾ð!Gõx~Ó.ÿ`ÈÄ%²®zCŠŠíD8÷|&á²R%Ó’™?"E4®ÃÕ’Ã\} -ÁjÀ% -èþG ŸÆ—úPÀAGtáÇÜ2 ñ„õØÈkJÉ(ý]eCˆ‚v‘BAüwŒÏ æà½÷w¯³ªÉ2+°×S<^ª‚†3L<#W€h= EÃi‡|¡/ËË2 ið”¡GÁÅF§pÆàyÕ…µÏ[x¨s>«Þ6Ñ¢Ú8š…öŒÂ>¿þLf½&@UÛ³£:"“ðm±<ì8þAÓÎ{2á¹·/2NÙSD¤9q‘& §¹8óL¨ò¸Ú=À}?uì<þ§™:ôÁÔë[å¤xÔ Ê¥b÷}ˆ‰‹¿ÑþhdWßÙµyäëD@ù÷i¬ -©é£JÿŽ;j€v«È¾/¬¤íRMÏà ãoz‡µ²,VloûÔX–jô­0Í1%|¬Ù¾„h×û¬{TJ:A^b*e”ŸG) á,•+‡´ÊXSšà7¨²ÔnfçÝÿÜÐ «öçuά ç¸æVbóÔ“yòCMD£}³®£»…è$Fþq‘ôÑ1“AZÑ»k}מTr®'ßÌM”´/dú­,cçi5ÓØÚÈ<3ᘠ-;Ó‘ˆÎÂœƒ—GEßàÛ"û›!]¯–òEé›ö›-ÈK,<ý9¯wE&ekQô³IÝ$wÙþépÕŠ1à Ñ(_Ï_×v®Fš£!W}?‹œ -.²ÂçÑ$UoŽ •û•ïÖuýYSî1¸¨þ³{°??à+³aóIÖÄ|õf¨½ý&Êæàÿ{ù¬ÒL‹UèÐÃGVí˜8y«$àÆ!Ò?nzôøÛnsG4µ•wÕ¥e¨[¬s"¨ká±sÝuŒÉ -ß.žo¨‚œÙÙãŒ×Œí¯§„þõ¼-ø uXÝñÕ`“1óö#0„Q{Å~-:—…ô½aj™8·wQx&RÏ£>'O Ý†r÷åº7#\~V/-CÞ ž¬‰5¨kè+žCý¦ÌbÕ¼Œöl„ŽØL¸²äª*„)¿îôIκó¢.¨;ër«…>÷F¢]Åp£çÅŠuˆyäiºÑ œžÊ–É#2¸éȬ@9æwµ©º—öªU: s”'34^p¼s¹. À˜`ƒ [jEeŠ7OF.Ú_Ø\Á”óV"UÛωÅ{ •´·™z¥ìT÷…šÊ…§“È nCd%Ê™¶ÇŠÐîÜ> HrúäÊ6u—¨~êH(ÅU ÐÓ°…ÖJÅ%Ó•VžÜ@5°±4]½”¬õë–¸Z·»)Ét>n3`SÔw‘"‡â—h¸"?Ý¢ö‡ê«f\SVÀVÝtbâpY /tï ~Æ31…‰oTÀðž1ê<ÌFx‹è^2w±­g øXe§|ÚØ˵°Ù3{>%âÅà·Ff_MoÏ<&kó -Ó9¿š¦½D_\¶kIí!”Ÿ’ë‡ô(;ÚfhÎ8í¶ØÎ!)v¶?F³-ï%ëGo5e -UŸb;c¹Ûú1ŠÊåRºÈm -Bp.Ô÷òôêè›ÞôÒ$1²ñ/Fs8T§%xÁãT9F -‚¨‡)lÚíDtüËîÅ õJVÏr ]tPØêvÝ´ET-W0y|¤bÎujJri•hþiçf•´Rîórݬ%z q¥²â¬±K~ηn¬ô;JtÛ¬FÇDˆüöëd°¥UŠ'>Ä}úùÜ°Y åÙÌ…pš‚ÝÁÀ¯yÈ’¹µ°§*[R€¶è@0‘ž™”/¸ž5EÒ°®ûÔzc[ .óÍ †ybÖúÇ戋…ÈÒœsµ°^oÈ4vZ³iü­?HúÔšÜ!÷€s¼ˆtl¤äª¾nK9Å—M ý—§iê]4ˆÈ­7ò|eE¸ÉW×ËáášçvoâØÙ—š¢=vüâ›°QHÄÁ˜„Z¬ˆç;ŵ$‡î×Ø^Ý;»´–úä*õiÅ :À"lõÖA`‚yËcû Ñ rNÓ@*Dð­mô(÷¬·R.–»Á<gÛL—Íü>¾¹àŒä>!†Ë9•TjŠ -Ú/`Ö#ŽÖå@ŒÓ¬8Ÿ ˜Þ â…£Œý—¾€’°Íç|«õ"6Heê¬S ®; àÞÍPÇoRû¢í„‚ :æ<‘×Ñ~»•—¾sákjÙjoTÕO+hI]6Ü¢o|ïõà[òT®;ž—Ë”ÐK_zˆj‘Õ¹>z¡ð:;FÓ°Vqú#,Ö[{Û8{*¥¾D‘I¸÷s·¦X5g¬à…ú)è#7pÝ\3õlþÙø¾¤t¯H¯Å~Ú*]°ˆ °GGŠž‰7¢â´U\ŽÞ5Ôoî‰+¬I#’çÄI«Ä1çÏÞ–’¹w ·¸2š%'é‰[â܎ίØXW>çQ­ålÌ–[«x]‘€Žq#)lå…9“èŒÄv¢)+ŒEÜW²#±¡R¹‰R4ø·…ÖwŶ÷Y¼¯< âLel_•ß›(ëÍoS‹»¤³3ËlÁ‹¶‡N -*ƒ`ó?uà`ʼnì*«Ô]”øžíxËU&]:hÏú¦y!Ï -¡¤gƒ7Rv9â7Ü~ìµ¢â">šÜüòZÕ­‹«m¾XCŒ j9£iT<¾¦á»ö¶Ô7rÐ×QCX q’ocO·|V MLæë³A3v’‘ZmfÜ]¢3q½<º›§Ã[¢bJ.ª‰­(`@Ý/ÿM+缋y{-¹]F6 ;÷>ý;šJ®JPiš7àqxÙñËùQ™ -¼Ï Æ$5£ÞÑyn ’L¤±÷:zwîÕTYƒœ@g®* -á—å`º%0t_ò†×ݧ³ôí‹ÒÕíÅÿ_ѧ¦ãuz¥ ‡ä'3‚«½¦>A§k´ì´yu¢ìüÀUV Fé]ÃÅþSÖRpy18r•*»@V¯"ãÙ¤¶ ŠDA’Æ¢Tým1êOÙMEŠh3þm6{_ò./jbiï'‰ÞÀ ýOvñBÅ|Îþ¢;g7~ÉE1mŒ"¡TÌbÊüSÇb— 9 ¿oC<ó"_ßqaC¿¼ÄŽ¶¶8ÎH¥®Æ[¦7<Ë@À\&[æJ¤Ð"[ŒSwYh;×ã'è¯ê«e·½ÉžÿŽ²äbR=)à†78×ÐíjASø½]¾/[ÿW“ÆÚñUÁ‚žrtNf6ñ&*€¥aÇO²caR¸x»9=>=Dq| $θhÁM§¡èñå’]æ#¾ýÂuè[^Qæë-kš D H]¨¹ô„ЃGJº$6ª‡½aÒ›]¹yÍFÿÔðSmoQUm–÷a=.½`̬H*ê µFöy¨SUÙF¢¾|ð™#˜¡™I8ç. 3h˜¦[Kp*»šÿ&}¹Â¦£Ž”ìuJû2ã1 Ï«mÓyˆÂ+¨¤|øMɦ‹É‰wIDá[Ç>`cPDMžù> £'/*PFŒ£ oö¢aŠUzhÐÉ°äUg‚¯þ(z. Ü̬ÃÓà # v?˜¾ÁumMßóniÛ„ÙÅî®g¥º‚ÍFESKÁšrª(ª\Ùv˜mü5@„G°ÂŽØ=ˆášç*úÛ<µ¸NËôÕ¢›uáBŒ¼RHù¶ñÇfi5‚ -DµVã 'N"ø7R¨¶¤ Åѧ<¸nGŸòp km ¹€ÚO〽ÊÄ*ª²;̓P¹OÄý\>ýŽ­«…žÞ«3³qßeî 8rŽ`ÑA~ÚFŸ•7µ‰U®‘Ü¥Þ²¾ãXÛÄÈz#„ªöóÜ:ˆ™³û±t¶vÙxÌ­½¯™ðD^ažDƒjnëæ6n¢D†>ëÙ%ýdÕQ6çªæGs.ßq8MÃ@YC¿3ž `Á´çiˆuУ"¼.Lò^¢>Êä ‰«3@6{âÌšµéy¾ÆïÎÌv0®?ÚÎ9–y™îÚg Ñ€¡"¬×f²=~3"ÒïVX1@¹0» ü:5Ÿ´a(ÓÅäg|¹z¾BLŽNÚ«³Öf^ì›Ïväù«Žƒ5=ä´YÖoTl¬€$ŠŸt†WLÈí²Î¨ŽŒÔ¼8«ÜæmÄ»/W”‚«ççt–ËéœØglÌf•ZÂ|ÿƒ1HV=uÆò,Ù?ïð¢ Ïà&¬8Vºæ¡ÏÍðªÝv4ÄK×B-¿Ðñkù$ :¼' ޙˑׂyÃ\¿—=?“?òØieðwH -MØbfÜ~'“Õ̓‰lé ÜûÒ'&eÂ8Xòðúª¼†±,ÐJ=ÕÔCœg’ÁOq\]W¹FLôÖi²¥ŽÕP¹ t -®å7ÕÆ°eVpL@­Þ®è=ÞŽõ˜Lÿû¨‘¾(Gá˜2 ²ƒ{Ö ¬~“¹Ë°‡©>Åþà ’¨!8ñ;ò½þG\ÔÄ(»VüqVùj/–«s–y×bê–?#]î®;mˆQ+Š¨žø••…í†4,:ÔL[ÿˬ‹8h|ÍrË$ú_æÊaºÑƒ|V¹ [ -y"‹=¶Äó ì†ÈÞºîLÔÏ·8ÐÃ8uI¥êr©$aQôW ’Ðñé–¡1®ý ñª"øA,¡X;¼D\’^Mð>K{ž¦*Õ1¾`¤iýÏuvŸªQE^B½Ýuˆ¸åh ¥z¸À`ÐÉéñX'%O92Yлù\ð$cí‡|'Ô ÿ³`a˜ùT¨™µi'D¹ºSvíy@Ø*ÊáËÆ›“ÛN<3urŠk"I+!oï¥ÐzyíèGo·<zˆ”Ou=”Ðä>W •Ì‚˽"ò¸ÚÜÃ.Fé}v'<dµä¦Èâïü ë ³¢¢íj"]„*+¼Ñ\ ‹9î -±ò -oJ-Jñ¾5¾l£ò@ò…m$ÚU:Ö~Zµ­ˆÝÜÙÀj d`` èô—T*èµh’6 Ó¡.›¥Ë‹¾ô¬ÃyìëKæ|,Q$¾pKyâäšÕÞü0á·ël-ìÚE/~é ŽTÁ–&vP”cþ]¹Ä²ÅLX|žºg½¢·ï»jFæmOÞÛ+“—¥Å‰Ö°Ó˜ø•‹KûHçôâÀ›ô¼é3ŠC 4ìâý§‡†ª)~àBg•ÀUk‘¨ß"ä©m/ŒÌíÛLF}RúòC`D¯˜­å ñˆÆÇ]-~fZÔxsû¦_ïß2¸¦ùu`C0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– +]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÖ¨ð[G¯•ï(©ÅaÛܘÄ|õRPé6n¶ý=: ªbãÕÙ9s2m4{~ÜC‘ÉßD…¸ü˜Ô%Åx’Ý÷Sd,Õ&©jÎÚA x"±ÐŸ—”æmѬ,+;ÆþÅboB|Õ®œTÇ÷bÃoI³Âåæ*ûVÜî‡DZ©BÁJæÑþ©ÏŸª2a{YŒå‡ï0Qâ(÷/e@­™§AòGÆ€挄éÑп™ª]w}ˆ§ÓÎÒêgô®a輕çÚ8.‚ݲ° ÝcS,tã¾^ÅU ¼»j³‚†×q.’o†–ƒr¸!N›]@Ájß +ýGÄ“75uÆÊ‘ämˆÞ$æ‚ÞÄKWêŠøNWÔVF2PØ,KPË» 6™2aƒóÔbw;S³ÉæÛBÖ³ö{‚ Õu&D“C½ùúÏhN¾ã›e^±½L2Ib^ÇžY6þ2Ùò"CSò¤l5Xï!ok²£º÷R¾ì6ÄD UjïìôTº|»§S{ËëÂG3:‰‰6A…|Ùõžº °£ÙºJ 3•3kLÚK¦EnMpúÙ½«·òq¼lHÙßZo®xV ވ˘U§>ŽU©Ïó^îo°\WáóŽbY<&~…~S'_ZÁþ `¤žgקZW(U7ÛTg°4{{Ór§»ˆ ÷çsÄ^=ç²ò£Pé0ëœê¨Ð@õ._ßÌ^×–c]ÀDÉd0“š‹«ƒXžä,¡a÷<øä5Âݦ°u0ÅoHdêxÇwÄâÂôE}…g»í£/ú÷ è(Š ™ã¼:.‚ÙÈ€€Vj™{E§~$>>o !4;_Àú¸Hd¨[+öªhÜ)DÒn…çï«ï¨Ïý“ÀâH:B§øhV¿aK›õ’ 1ñºéxg LÔ”}w“¡ÑÂå“Zõ¿êŠ“Ú»›ÌµFê1GR !0n@0›nWJìTîwèïÅʳÅ'B-âÜM;xøùðëZ¤ŠO½ åYXÀÊ%55ðÖ’›qŽÂzÈ#ŽÝ!4=ÄôÏpËãÈ•4S¾Ý€„Õ2£öú2º/Ò‹jÙœÎÏÚftÁñ<ǨQ–ס»µÁÐ 6vû»»y²ø¬´˜eÑ8죵…CíJUÌx± ©ÏÕÍâ[‹Ĥ"\oM•I‘[KKŸ!t@WdT7’(Ä?Ÿù+¿¿O'³•É}«Ä“¢€"}Sí"ƒF€Åšsˆ³6ndïâaT4M!¿Ÿ…RVîÔeDg=ã}¢¦2´¬òžw;,§ŽÃEC^&?­ž~Î܉NGÝFï‹íøš–ù²Ge`&¶D(®ƒ¬N:=|•$ZÃäÀR1­n—¿†²ÈPÀÌ»À= °?¼¬_ÌxÙGoÒº¹à‡¯ VìmZC*X0…1>}Ãê\g`lИÜÍ6Ë`Ø]ð\;¨ +NÝ/ã˜$pjZVÆŠ^áØY>¨‹º>¥ü†—Ž,Û.'aòš0:_…ÁÃ8z瘱åβyr u¸Ñê¥t^žñ +›cb+¯Ð å1%b>а€§“h“-X?”®}°ú¦†ÃÿÌsk‘=p³n¼°Hãât(êóz.»éö Ç¥há4®í’Ž7r߇í’€—É=‹±=B;¥-½ ànsGË\7”1ß÷Ä\L Õ“«› µAÞ¸¡zŒo%ÉílÏJ³W@!ÊŸý;ø• À4r¨àM22|Ø`%*Ù:c˜¤'¾ ùËNùö¶f;UÏoÛkÛÌJ[ Š]-ñ‰º[ªLÉÃlΔûŠÏA:x» ÝEÃ1žè'BèÉ–ˆô`@Ýœ¿ +ëóqÑk3A"l=ñ^üþ§yןë}AŠdt´úÛÎù6j%¼Kƒü¤`‰t"Oâ¾k$ëc’I˜fU7;(G‘ €“F©×RòD@$t)|Le{U)ŠÙé½qŒÖGp‡V#Ä}ú¸—¿ïf2óÙ Þþ×m1Ó“¢ÑÓÆõ"‘qSU[(BæúÓl./µ}ôl'/Pþð(œ¨g8^`µ!¹æÁ™ˆ”´¥íWb´³>¹î“%$W£¶Ñ‹·AhW2ytƒ½ÈßÙjªº¨[Îkøµ¶B4ÖÍg¯ã¢ó•ÍwL¬y‡.Š‚I¡KlgÛ &ФÂÿ„bïˆõ›J Un±&žÏ}$ ’M@ÃìXlŒD²sk›†f×B›™> œ$L:B£±y\Æu‹¶7œ²”’] lThpÌš0G1ë‚T>_“æ<©S’5ÅÅŠ ¶b*¯ÌuIÛÈÆÈÉëVWÉ—‹U¯=A=×<ú¬IcÌðU_1Új{Ÿ”Ç0-z„ i‚&¢Ën;ùÙù:öƒûèRÀßEÓŸ;yÞ°Xº Û©h¹(šðh•&ƯÞW^ª[°`éÑèË¿ßq¢u·H[ÖXôµÓ?Æ硺¢¸Ò‰ µÄ&ª¤ëï;VqÍxÛ‰ ¥Q÷ +ªÇoç -.¤÷Å8iŒÇ5Ž~°{‹­øÝôäÜŸ½àãÂÝ“S›§p½ôói5ni*nêç@Õ*™g3ø¡ÂÒ(S`¨¬Ä"Ömÿ–|H»¦J ɽ­»Væ¯%ïébZžjA ²xM§äë—ËD¤LðâLaR(`,06ûÇƆôÉ·W‹Ç_ñUo¾ÅøJlÀüó/ÞGÉT6? ©©ù‡²xdR`qÚ ´x]…͵êHƒ¶(Ä §Q»@¼$LT•ãg9±åx+1û͵Æìlò:õÄÙ™ÞT¸XIGü;ìp 6)m¯n’¨äÉ·b¬D«úÔ)éú|ÕoìÛ +=פQ‡`°ŽZ™¥·¹k ²Þ«}ù^4}dç‘O.+1ÀoÍãð2’ô!WÒR…ÉÅt[¦ŸºÄ¢(bvÞ!®‹r{V¿.Åqa'Á¯åºŒŸxL +dÅi).[Võ;‘'c1:{å¾6@Ä]PZ×,Vciß6•å]´«(ÏfÚ9îÁq¶ÀŽÚ™¦,oÒ²ç‡ °BJ« exéù°@²©ãèþ¹èÿË©#Gïr ú¤èÑk¢œP8Lg/õðÓ·!¸<Š]ÛÕ"Êbò®X_ <ÎÈu°7÷‡÷²’ØœëÍ߇\Ál.ƒ&÷D“ÃÐ/uGîûŽN³,´ã(E¢ÞzR9Z>ÂÓ}ïÔƒqbäW„çÉŸ"ÏŸ@†0Þê‹Æy-γ¡#ô3j?¯$Ùùî<Çqôÿ¨•œoŠPj.9älMü¼ŠL‚Çq¤³¤åŠ6;Û&?±E´D)‰Û! çÑ]¹Mliå«£¼çÁ‹dgYJ +‚£}Ö=¢ÀlºÝ÷ ì¼æ}ùñ÷”á?ȃʗ¥‘hfÞrüæàÓɽXüDcÊ¡“ŒÈfEØÚŒÆw±moh)füpD†!hÝÁ‡ü¸DÒìâë÷¤‘PLµ&zY¸¾˜[ö9XõGËÞ FÝ ozµ¶ŸvƒäÏ.²ïW~j>Y´:6aéts½ØNrü»oÀ÷h8H`’2à›‹s~ƒ)Š×Óƒ½yooí2>¡Ò>†ÂYQðµóœW–u>;öÿÀ-Ùœ<ä,ïE3rÅÚý/gº.Š¼§ÖÃ#RÏ/ÃÆÅÀffÁ1㸺|zMæT!øDÔz—Ùü/x‡*úà)²;bkZkµá±ÒŽ1økLQŸ\œ“ ý°5µìÝ’ÃÉå/X¹Ð»WÒõ–ÝíbŒ~îE‚Ê.Câ6äµòcWS‰‚ñ©|Lµߦž "èãæ¢cž,¤/Tá2ɺSÙzóì¼=Œþ~ÌžgÑ+f)9A’XŠäÕ(3×™FY²9Óê[€'ÖvÍÀӒÄ„ÁÇ7k’5™z>›-ã¶ÕGh=UE¯Q#Ǹ“LñΞ÷–Þ< 9¸c@<Þ´‡mdkF²t¼TÐTá iŠ­w¤Xó-4á^;qK¹L}ºèï®IB¶¹÷R†Ä& HÔxç1ÙÐNwö ÈîÏò¨þv̸³¡§ËH>úi,œÐÕN~I’G£Å-PC½D•¦‹ endstream endobj -126 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 537 0 R -/FirstChar 12 -/LastChar 119 -/Widths 538 0 R -/BaseFont /EXZABF+CMBX10 -/FontDescriptor 124 0 R ->> endobj -124 0 obj << +508 0 obj << +/Type /FontDescriptor +/FontName /VCFHMD+CMMI8 +/Flags 4 +/FontBBox [-24 -250 1110 750] /Ascent 694 -/CapHeight 686 +/CapHeight 683 /Descent -194 -/FontName /EXZABF+CMBX10 -/ItalicAngle 0 -/StemV 114 -/XHeight 444 -/FontBBox [-301 -250 1164 946] -/Flags 4 -/CharSet (/fi/hyphen/period/zero/one/two/three/four/five/six/seven/eight/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/R/S/U/a/b/c/d/e/f/g/i/k/l/m/n/o/p/r/s/t/u/v/w) -/FontFile 125 0 R ->> endobj -538 0 obj -[639 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 383 319 0 575 575 575 575 575 575 575 575 575 0 0 0 0 0 0 0 0 869 818 831 882 756 724 904 900 436 0 901 692 1092 900 864 786 0 862 639 0 885 0 0 0 0 0 0 0 0 0 0 0 559 639 511 639 527 351 575 0 319 0 607 319 958 639 575 639 0 474 454 447 639 607 831 ] -endobj -537 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 12/fi 13/.notdef 45/hyphen/period 47/.notdef 48/zero/one/two/three/four/five/six/seven/eight 57/.notdef 65/A/B/C/D/E/F/G/H/I 74/.notdef 75/K/L/M/N/O/P 81/.notdef 82/R/S 84/.notdef 85/U 86/.notdef 97/a/b/c/d/e/f/g 104/.notdef 105/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef] +/ItalicAngle -14 +/StemV 78 +/XHeight 431 +/CharSet (/A/C/E/H/L/O/P/R/S/T/delta/i/j/l/m/n/r/s) +/FontFile 507 0 R >> endobj -122 0 obj << +509 0 obj << /Length1 2159 /Length2 15471 -/Length3 532 -/Length 18162 +/Length3 0 +/Length 17630 >> stream %!PS-AdobeFont-1.1: CMR10 1.00B @@ -9849,41 +5757,12 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /ARBLRW+CMR10 def +/FontName /WOSUPX+CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 11 /ff put -dup 12 /fi put -dup 13 /fl put -dup 14 /ffi put -dup 20 /caron put -dup 33 /exclam put -dup 34 /quotedblright put -dup 39 /quoteright put -dup 40 /parenleft put -dup 41 /parenright put -dup 43 /plus put -dup 44 /comma put -dup 45 /hyphen put -dup 46 /period put -dup 47 /slash put -dup 48 /zero put -dup 49 /one put -dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 54 /six put -dup 55 /seven put -dup 56 /eight put -dup 57 /nine put -dup 58 /colon put -dup 59 /semicolon put -dup 61 /equal put -dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put @@ -9908,40 +5787,69 @@ dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put -dup 91 /bracketleft put -dup 92 /quotedblleft put -dup 93 /bracketright put -dup 96 /quoteleft put dup 97 /a put dup 98 /b put +dup 91 /bracketleft put +dup 93 /bracketright put dup 99 /c put +dup 20 /caron put +dup 58 /colon put +dup 44 /comma put dup 100 /d put +dup 127 /dieresis put dup 101 /e put +dup 56 /eight put +dup 124 /emdash put +dup 123 /endash put +dup 61 /equal put +dup 33 /exclam put dup 102 /f put +dup 11 /ff put +dup 14 /ffi put +dup 12 /fi put +dup 53 /five put +dup 13 /fl put +dup 52 /four put dup 103 /g put dup 104 /h put +dup 45 /hyphen put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put +dup 57 /nine put dup 111 /o put +dup 49 /one put dup 112 /p put +dup 40 /parenleft put +dup 41 /parenright put +dup 46 /period put +dup 43 /plus put dup 113 /q put +dup 63 /question put +dup 92 /quotedblleft put +dup 34 /quotedblright put +dup 96 /quoteleft put +dup 39 /quoteright put dup 114 /r put dup 115 /s put +dup 59 /semicolon put +dup 55 /seven put +dup 54 /six put +dup 47 /slash put dup 116 /t put +dup 51 /three put +dup 126 /tilde put +dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put -dup 123 /endash put -dup 124 /emdash put -dup 126 /tilde put -dup 127 /dieresis put +dup 48 /zero put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end @@ -10013,199 +5921,602 @@ K, ©åîY$°ã%³ñ¹²cÐÉyo$tZî­z{pÖI¸@ÀóyÏ ¢Ê|DEfzöBÒñÌ—Œæ†j$è…:;Ð^¤¦Ã¥°¯qpÜʵ®é¿:â/@`4£§”rìJv‚S×fK9ˆKh˜å­ÞWeų^PîMq›þµ…¶¬F;×{ÝôzzÀÚŒo›NZÜ–Ù¦nK«XÌëž v»ñÉ~|…æ?G=×à+î×MëÎY5,ylsY¿(„>QQ‡ö½Þ0%$ù‘““¶ù³“ » /b—ÿ+Œ¶g±ËJöáŸqï3ª¶­nk[@[Ê8–üäç- ¿}2ôÕÑü}œŠ¢†©‹aN½ä·¬AÎ!eCuVY‘JohÉwp…nS[…¦™#hk㤜ÍßQèÌÁYo Ä–c+:³ P{Ð,žúÜÒ龋<31KÖ; -û“:‚~À‚·I™p+X•Rh‡ž•dJšècQ|ÒÇ0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +û“:‚~À‚·I™p+X•Rh‡ž•dJšècQ|ÒÇ +endstream +endobj +510 0 obj << +/Type /FontDescriptor +/FontName /WOSUPX+CMR10 +/Flags 4 +/FontBBox [-251 -250 1009 969] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle 0 +/StemV 69 +/XHeight 431 +/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/X/Y/a/b/bracketleft/bracketright/c/caron/colon/comma/d/dieresis/e/eight/emdash/endash/equal/exclam/f/ff/ffi/fi/five/fl/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/question/quotedblleft/quotedblright/quoteleft/quoteright/r/s/semicolon/seven/six/slash/t/three/tilde/two/u/v/w/x/y/z/zero) +/FontFile 509 0 R +>> endobj +511 0 obj << +/Length1 1336 +/Length2 6946 +/Length3 0 +/Length 8282 +>> +stream +%!PS-AdobeFont-1.1: CMR12 1.0 +%%CreationDate: 1991 Aug 20 16:38:05 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /KBJWDR+CMR12 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 67 /C put +dup 73 /I put +dup 74 /J put +dup 78 /N put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 97 /a put +dup 99 /c put +dup 58 /colon put +dup 44 /comma put +dup 100 /d put +dup 101 /e put +dup 56 /eight put +dup 102 /f put +dup 103 /g put +dup 45 /hyphen put +dup 105 /i put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 49 /one put +dup 112 /p put +dup 46 /period put +dup 92 /quotedblleft put +dup 34 /quotedblright put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 50 /two put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 121 /y put +dup 48 /zero put +readonly def +/FontBBox{-34 -251 988 750}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\ôéÒ@[œÕ6]nÎÕ×hÖmlha‹ŒH+4Œ£Ž›¹ºüú­œ/?Ð3¶&˜nÔ=œ“a6E¸#’ÕÊá|´~.‚ÜÔ…Ë Lw2.²æ§sÜNYÁ ¢Ú»›÷.,òVÝnµNìºX«Ù3µ|裠Ñk(Q×IOs mõ;Üf»ø–µ‡ß–C1}_a Ù˜Io#Ýà0÷²wÝ™\‹œ®œ™ŠÄáPÍü,fí’ë´Ì *ªŒábG¡3ZÓ2Ú©PÒ•§8L3ÿrê£[‰vnc_EÄÀh­~èg9°|¹M)ÿ }Yÿ™aÑ•©HãØ|1‚’•¥m!‡[A˜z¡XpPÃÇNCU»7òUÖ²7ΖòTg÷¡ž…x_ôh”œÌyòø®WÕ÷›¹ÅÏ^í]˜W¹–}›–ÍÏsÕÖ_÷Zú»fs@ºâdYr ÈŸÑsy&vJ“Ðx´ë)Œ‡Öî¢Ý±®ˆÅ~ÏïKqä +4•Ü5h¨LÉ#q§‰:4pPý¦ì÷?gÒ |GJS†nœˆæ^i2º‡§6†ê°“‰øM˜ Ęz0í”.²° ¿õ¼Ç ôâvÃ3›1¶ê»°xCj »7}0a¢ ¹‡–¸`~ì¼i”Eê¨fÃŽí}O>ÛÊ&*ö¤g¯Ï¿60ÉCúL͘Šsc÷·^¯X0°IF +3yˆñP¹.˜žwPŨ=óv…H?†Ñôtxˆ??jKv¥ª‰èñcšÝJ’ ÞŠO(WfÀn¨Yc›’ÌÍÊõ›+¸ÕˆÊuMW¿÷kS˜Mô“p“ªïy2¢šLûa }gH,H×ùèA ­ngV¶U4çŸÑNòN6ð9î<¯Šo±\îV·¡‹\;ùÊ­àÀåT!6é¨oÜïd"‰œ±Ç.JCȦŽ<^"ɶ2±¤î§4¿8ÓÏ[;OªÔD$Ã×ÐŒµÑ§¢o/0ìÀ¹OýxõPÉ®^[­ÌVZÍ)£8¡I:¹±u{Ñ÷$¬ÛxRlþ4sñÈ''ö DñœaqÑûpBÏÅFW|>í_ÜtaLúBûß&ÍÅŠPp®9ÒLŽŠù–\Ó‡ÔÞ_FÁ£X¦…nY`2–œ²n6C5A„Bk@r©uŸW¥Px +…ÕŠš=ŽY4\æ‰'Ë7BÐÀÀÉÓÒ'ÁL`ûÒÔ²k¿ Ú‹X݇ΡdøÜ;’³ÑÏêu›Îõ+µ7  Ò¯SJ´k¦! ú•¶ÈË+ ¡úNò±ª÷ë0ó‚ÈÚ"FQê–¨Ö†‹Â©T»ìqÙ\Ü?¿ø2î˜4ÆA(ПSKߎèüŸÂæf‹’Ì-æp–E®MnÏá¤Ø™zÀHc"¢Ë€êtn@Üîyq+^Œà¹Ò÷>[JóýgX6W'×8épä­El/¯7d9Ûz…/šü1ã•3«×ÁÛcÕ¥ôgœ×Rt³šŽ>Ð"RóU΂@œ÷Gå&Œ}kÊqû9eô×#r%oª§ +äyÑ +Ú +iÚj‰$y™E¿oè‰â¥û6uH1ž’W/܆y©¬7s¾u,/R>^Yâ3›¦H¶·èù=çæ“jß=Jî'@Rf„Cþ‘>Ì®rÐÂX'Ñ´_Yb‡w@ÿׇ1ûY‹ÑíÊ žEe{¦I‹|"/në,rÅ#§µl%‚eŠ½“Udþ¦Ÿ$·qQíúóÞC×ýÃ]Ä¿™®d‚äaÛksëÄ’>>ñŒ²è +goê¢]ž¹ ;u¡]z¹þ_(óÚëüýÍ8Ñ‘lŒ\Ìu 6 I‘ª Ï ¥¸­p§>5?øfш+Ëê“2•0H/^s°’Ëá“oÐÖ^AïÊLÐ ±KëØ…ïmÈ6lR»|ÒU_ÊWÝF¥0š¥*hXq„×ë pi~ÑôöRðXå2oW;7“ÊâÛžGɨ" ÇÿmïCf®p Á _o6¢æçÊÞ¹lvfªÏ9êèj®à=^¯÷gÿLVû›²D¼3Up¥¥AÈžº¶?>†n\Ê%ºgFa46U9G>NÑþF0«iÒùqÁ£Ž£±îŒ,ìÔ½Ú”i¥a·çù¡°Óº/&ËÑÚÆÂ÷Éà3~§è×|"W§Šßýhm†O°€´%#aôûðR­Å}üUƒ•Ú=[¯u[»1úBºf/¢ÛÑÀ9Á^}bM ¤]¨Ð׈³Ç&%ù¬Þz5q·÷½@¿Bó¢*éÒêüLJwƒ ˜¶±ýÀqG†àŠð vœo{[†Ë¦›£wäöÞ6©Ýb蜔êBêîÝ~Yh€ˆÑýwG‡û¢É%×HËùúqMÙ¶i'ÈÂr6ïü A©Gä™ôp‘s_Ŷ“¯ŠZH¯¤’—(pÄiBÐÙSÑ|ä×pÐq›ñÀÈQ¾dìUl«Â!«öØ:-4À—Ë«Ïp”r&ìüæz•ª¼âê±ðGx Çšñ]˜¢2™ ¤~DÝ>¸ÚïuÏ·´¬kÏɵÇdþëj/ZžX%K”ûÍO7£Ì¾ˆ›—Ç%[OMɹûñÌ£jÄÀš“V´3Œ;œQéÍæxÄI]|UÑ×h¯;=ZzÝÀFÚ ödû+t.E¡–…ì®{/ÊíØUhìyœZQ½E–˜ÆÖù»g©-è’\Ùš’àW=¦lƒÈQü±—´0!xÞFqÞ#¡"‘5\ucS0G•‰ðÐè_˜„t_²;5'ñrð“XW„Ìp[÷:m'ÖûYÎá/ GKFf§Y8pÈ›ÔÃ;0W)u'eI­.síió0:¿šE†Qšº‘Åa€amŒÖg#Ú~\8¦rmµàV…%‘«ƒ"R@î*ÕúòZ »‡“°ˆ·àʯDah+EbG°›ÝWPœ.E›ãNÌüz·tX¡©O_änuÕk†Uø ¨ZiÆH(Ÿa¶\-c¯w8<›ý ‹ìçcÎlW(üÎ¥^óR! ÂQÌî|ø¦†p/]5rÆU8ôýeÄ|qW«Öñ17 X/?á;“Oüÿ2U5Šµ'°¶’OŽP¤Šj·ùªìd[8|ès¯õµÒ¡ü+0G}9‡ZôzÉG¼3"¾Ö½Sß7¢3òõyGÉnk¹œn0ktcf4–~ŒvU †417rnØá"V·}Fª™ZÎ+Ñ[vn˜îBÒŒâ3Õ¿l*Q×$ 1̯JA¿”¦¤úfæÿãUœI]ó +P\é7p“=Ráñ´Ñ´Ûòß[GìTyÛÒº´@ìà6¸2 aZCÉ‚C›…¥üLâJëð×}gîZõîì»ÎËÆbä‹Bz‡î=òó.méQŠs°;­WahËpÞ +[”XR +™Ý +Ò~g:I‚ðdtŸc_ocïÉ»€ÁACz*Ž…÷7ü>‡ ÑFiÔ¨ÂMH·ƒ8> +Gb«ò@Z(I‡²†=èbã@I^š€Ê5¬Òì˜q:âGQ(^•GÛ´ûhG•ò‚gÌJzä*¾Çk-úŠ@p°ûUc „ØФù`JK‡àdÁà¼K;'Žiìà‡çf€Y1«óø++Ne Cg¾f–«dãP«Œ-„©ˆ[-é¯CÚ›0ÛøC$·xŠŸ¸ê‹á¼'Þ5zõh°wn —XI#Mw)}þ1 +n² _c+WqIZ7 aY´È²/ã°Ë—Bõp^ ­b*å€Óù—ŒÂ«<(ÅPýÒ`Þ´DÞYÕ'âtcß5 ø›CœNKO½+”nãWð™ ýqàin´$CúÕù·íÒÒèáNÆS Óf<; qçTb’Ç…¯Ž@­ âtèMÄ\nê°˜7œ&%j‡àZé¶@µaiÕsØãH@TBÜM#ëQ벓=‡*ΆŽdõ …ëþû.=Ó8ŒxGM—àÓá(ag›Eë«d »Î}[¦wýƒµX䃯OšÚ— Ö’ìÙÂ`ŒÊ¼¾Šzj.üüøwÚRèÀtì“ɇ²<0Låá_ºeIx`Î|ÇD\¹ôÍnÅ9w&sayÎt˜LÏš\›Vêìzš¥Hw*ª£Ó¿éTnÆ$ÒÄf&D9 ´£d‘ÐQ{‡8;ÃÉ ¢À^7‚KðŽìú‰ú¤à=r=óEI†)6š"ÙèòœE>êpäF$ᆵÍö±ÀÄ4âÙ ò¸±&hŸSªÇ|þ)39n¨¤ùí9¡pxÌC-—…É+“Èr—×·%·]j©ÇiÈ;]ô.„¯:«’¦ÝêŬºW)²«N ¾¡ »t¾;OöŽ5ú¯¼lápÜWô‰W´ÈìvQc¯Èwlw6‹!b5>ÒS¡uÚÚ@|öbóf’C— N9Š‘7QÆ‹økeòºiáHœì ®.ãp¬rL«ûMc jtb`W +•¨Y +1ömW£Ïí¨ÖÂôÄ€²×€ÝçzÙV܉Š¬ áKƒÍBë]åX‡È6ifþ»Êµmó‘@,yv‹× ü¡Ø¥ œèEõU¯ÒåÊ"¹Ê/¹oªmŸ¬Ðs Û„äÝíxë¿)Þ´„ ž¶­¦¿ò—OsIñÙÙ@ºVXvùÝÙ¶ð;UjÀéY-q–²7›} +>Šo-BÑ©aüØ¥`ýuB¢¬Ï£ÓºÅH +í§c íÖ² ²ýÐÁf~î©âyF;Ý“^ì>Jqª#ĪÙ฾”Llš†_0ö|ÈPÊ*FcÍÖÖ>žrÀ†Ü¿]ô ä@KŸ¦çhõs|ß”q‡©‰„Ï·»Ã]óŽ8LyÀ6To¤•r±,d¹KÇ@::G|3Ȇ™b}¿2^ÖÎ`Á9Á ÂF·Y@&êóO°^™Qú<;XÔðûNƒ ¸ò€ƒ—iLoÄ×[®såãŽÊö!ä;¤-d©ƒýòp¸\¹ûÑàuœ]±Ö_­‘PeÆÎ}ƒË¯R0“#ôÊúcøÛZSûK¾ ªdOeZWˆáJ·ýÊ"3÷|=ì3“à  +&Ä1ÉG°y_“ƒ/Ç•,b¾á'‡†ÈËböŸÎ蜖¯‡¢æœædç|³%yG3ÏB5*)…]°’Ö¦¿dò[) L{¹lµƒÑ FRÖç·táu¤§Jiß2¿›¶YvtÌúÕNœ$,·fÒïó×ÏÁ6v·ß‘TyCqý/±‹ž™.öúÑ„‘–¿„û…¹‡z:•$EYŽÈŸÆœ.Ý1¯#£ÀÖàe5W÷öÂõ0ÖVw?EX^Èž -Ö?íu3ƒL„ 8ºà"‚+0æPÍ÷ðÊÙ&P¤w\¼ÜV xr=« o–>5¢X¿Ÿ"JÑkF^Ö£k}õ]Û–&-[$íâÒößûž =õXØÌÀÒ*L9¢Íá'¶wÿ0³í= ¿N«¼ÚûߦÒñò;;˜JÞ"h¬ÄÀÈ:fPCb G7]|ð/‡kwûÙ›îÅeó³æº²uˆ¦Êâv¼GÏy®Ï?„@ñ¥Û¨![h\üPds2ººÃBÊÏ®ŒB g¹gæ;ìVá­:…a +žQ¬3¶d¬¦M+Ó §ƒ;yÊ1‚ƒu–öþœª¿è0c-†¼êB¤èÜŠ¯<ü9,ÓDÂwö\°øî'æ<\®”ô>ÏÆδ¸ 6yªb;-÷<.òØ.áÖ‡-œòÖ ÿ±J˜Š6„r³4S{¾ätƒH7· +V,_Ê[4ΑnnÄV¨€|ÉBy#ÉßÅ" btw•(º?FJW„ƒg ’+!§/ïzÛäW„ÍÄB< S d"õ4 +¥“ŸO@²Ž¥„ÚööçXºÖ z´ › Ò·ëv5V-éò’$¼Åå¶ +z"‰þ"c±‘°ÿ«Hòrƒ˜·÷µ]A­Ï`Á,.¬mô• +† È2í`¢*I£V[’õÌ·]:zóêÅÝ–+‡çƒ¹öP^ß"ÁCô¬:>›.¶ŠÄ7ˆÂ¤Z€ îÖß–À;Zø­FŒÈMŽÓ;àa–p$66á(Ïù› +|44=6ñ¿½¤Ù*Ñx ¯RòJjÀim¢OŽ´ß Ë™¹ô +Àl~{f© {áƒ=«Æ$;òŸŸ«v˜k6Ä.»¤œ÷lUÜù…KsJûY‡0ŒDƒrCÚ¸„+¼g׬Z{ü2Í9Æmim«€>ùÏÏa°õ'9nlÛ½Ú)E +Ñ[•®“Ô¢¾>Æýž—¿µ,MÈÇ\ŒËè‚~`­Ù’®WÔœm½Lúµ— +Ž?-,1ª‘Ëïrr×Ü$½xsÅï^±ÜóSÀŸÖ©8'É¿Ï{-ŸV +ºÈĹÅôžj’ahc0½e)?s1ÌÕE`G¡ÖÑ«HXêÛ0¼õÉaÊ~ .wQjµK¤üÉ›²¿öÔK<%–ìæzœ2&«§-Þ ÿ+Í`†R… 2¥§CG|?«ûË¥Š‚ÚC>#¯ÝI¯ÊúSE¶rÒ,UÛóŠæ‡MüNisQQ€~þ|¬—e]Ý$uÝǀƒ@4ª{MkßÏ(]ð>wˆ˜c¡^5@¿Ò_¹¨¹aˆÔ`Y³ŠÿYÈÃþ„S01nÚ£AÆhÆo‹9JÔŠÏÚÁ*#4ÖÏ0XÁVõsö 7ðQø=`”æTŒ£gE*ð/¤Q¢\µJ߶9K_է܊ˉÔÒÿO¾µµõ:Ø¡úÐKœâu‹¡ +ÜOÍG]˜(iñ_ŠóÇÙ¥šAm!C’³³¨ƒðm5ôV¾YíÁ„ŽOùiÃWïÆQ ð/ÄV€T@_cä ëÖˆYAÌå¾a[JÑ®ðËFnª6­ ͈ 'óú ÍcÂë`O“îóñU³¡¿'4£Ï(Q.&±{:-ÁüHaw°÷—c›1mÊUë$0Ï1ô*ö·àÌÏÎãÞŸã;¼¾±Uõ[wq¡o¬u NsõùçekzY2”´ÆŸ+Á·xÞ¬ †•¼@æü¯î èLøD ¸c /+ÈǨbíLÓ!â$Ôzƒ;’V[@±%½ÂTµ2×½£rXƒüNÀ…²Ð *¯?/‚̬ur 쬄–ß­ˆié4¦íßþpžÒ§M ÁÿËóPS‡=fèúó3ôj(läÛ\nåÉ:ÊÔ9WÍ}Z4|éFÓÊú³<8A¹ý—]€÷ cXÊ6#k·¤ò÷¦^¤vo¼Yø^kÌç(Û,Ué]gÙ|më½â¥"ËtBó?xÙ¦Ž-ãõ*„]¶¡Ž°Œïr,Ýmÿj_$Ã÷!4@Ñ}X®+Œ|÷žÌAJáAFw(Û¢FaÊÅû +çmYìAyµ­ô"Öfp‹»eŸö‹r–Êdå T㈮ G¬Ðï°ÚÍæ„ø³¢Ëó=ÞÕ.&ƒ­ƒTK7AˆütMPšÚ¿[z{ŸPâ‚4˜°r¯Ûªh<Ê|ÙÌa ÝŒ’4Õ1ßò­;Õ0„©)!U{–¥ìߤF¥á»"«SQŽP–:­ÊI›Kƒ‡‡0Ú—–$¨—…Âvǵ"µ/b¿° }/\®­+tFFÙö”±ÛËþ_n{OpÊ‚7”IÙa‹:1/µè9DäýZdË~ +èî$׫óbõr§XVir(阾Ӟ·êJm< +ˆþ‡¢™41Æ´Û_ßp†àµJ  +SØgpAò¬µ‹‰4°TÇçÖ˜¸ü=q Øèþ&œ³AE¼*™±™~J‚-„€'ºîšh#Ro‚k :ô¢\G³)€ÃzØ–e ¸vTYù/·L¯Rrw—D)è_{±äæ yô‘Êåø^ #Ô@Nee#a¨;Ðà7ä¾{¬¬@E\ËÔ¸ ìò\¼Ô߇6°¨²Ü£ûGIÀ:e£ w^ºÊo1¼¡-Z °lHÄ3• £|ûlîµÞMªi.TE¹î-ÑÛ§[ljfðÏäc¿³èA”KèdÒUÙãÁæ‚df `Ž•Šq…®Ì¸ùLŸÊôøp`¹h‚ôÝCÉoæ +endstream +endobj +512 0 obj << +/Type /FontDescriptor +/FontName /KBJWDR+CMR12 +/Flags 4 +/FontBBox [-34 -251 988 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle 0 +/StemV 65 +/XHeight 431 +/CharSet (/A/C/I/J/N/R/S/T/U/V/a/c/colon/comma/d/e/eight/f/g/hyphen/i/l/m/n/o/one/p/period/quotedblleft/quotedblright/r/s/t/two/u/v/w/y/zero) +/FontFile 511 0 R +>> endobj +513 0 obj << +/Length1 752 +/Length2 1167 +/Length3 0 +/Length 1919 +>> +stream +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /TQVOAL+CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 43 /plus put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\õ¸Ê»ŸülÃñé®2ò4ë`þ}ãI•±¬ÿRBŽ¢ ŽÔýsã“\ëÔ­pÀˆzEÈG®ÞA‘ÌÛ‹a4_Ðpý0ÄóuØAÝEG)¢Q³ö®|ˆ‚8B‚ýÖ*èîþÞdGWjú'¤‚©Ê×0Viäx²†ò#(ò®„ï=äœ@'q¢IªÁúT5i +(Ñ´t†`È ?á¿E<øG¢KO„d¦<ê섪"ý^t„~Bkh•}Ñõ +_2…áùXñÇðâoî|c™Ž¡2‹É„WÈ FÒÂü4bI¦dìû¢ÎP6Χ5ŸÊÀö†Ã»'îúEÕH÷½LæbjOƒÆŸé:S$:x6/0ŽÌ€Ý Iá7Íɬºã’‚âjzMŒ›•ò'½¢¢¯©ÚëóPC€²¢ÏŸë.š?³½>€ŸÆ)4‡§E^³¸yÒ´½F”+±$8–&G"ËYl?e½Y¹jt±+²šT¯I2! nþXKÀt`‰Ë±~h„]{> Qîäaãiσ\¾mFÇU#GŽvh2uöÙnÃ8½­WÕ;Rõ4¬ŸàEjÑ1‚B4²b¬ «¤;bëÚ9y[®lþ—V:Pªáñ•ˆ‡9òg`†©\šJ~ óO>%V‰0­ø ݬ;cJÔºjYr¤t’6Ïy«¤ql4˜QoÙ«~ØôoÁ†‹_=6xßqªw,ñ÷Ý",kñŽðÏ·§oÆÑ +Ó#ÁvI«7_ ÏÍfz°”âÇË!yÄ(3)Éä5ç¤*к Y³øb#a€³M?ÎØ3G%wºÍG*LÕÇ4}. f0ôFópË)¨@Cÿ™”Þê—,W š”€Ú'˜’Ó §—'—]8Ñ7¦Go´}yÈ-IõÞ‚Î%³Ðú ;ÂdŒÝ»í·‡ýƒyåï%‰•I«+³-tŒ7šóÊˬ'Åä$· ì;›9ð†ûWJ]µ.ôIùuŒò®Zò8CôpÛ-ÿ–ç$X‰ ÊÓ½„TÔÖ¶c+÷…DßEA1ñâ_oKC5³à—Ýö@Æâ‡Ç{®¡ !^þqñ‘ü¹©î‚RˆBÖ­ÍdºŠpÿ’ï=Ìþ‚?E‹‡­ „Á¶™OS°97õ­òºkøîúÖò,+³Ä©Iö^+͆S# +ia®s”1 +'_¥ÝÔm Ã'©ädº,ÁÒ]XÒé{&ßíØ41ú¼Y9HY‡_\½*2Õ|$Êg}å/MØ#ž9§]ržîZRaà^3cs!7烬y¡D6ÅÇ$1/Ñnh¨ +endstream +endobj +514 0 obj << +/Type /FontDescriptor +/FontName /TQVOAL+CMR7 +/Flags 4 +/FontBBox [-27 -250 1122 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle 0 +/StemV 79 +/XHeight 431 +/CharSet (/one/plus) +/FontFile 513 0 R +>> endobj +515 0 obj << +/Length1 786 +/Length2 1479 +/Length3 0 +/Length 2265 +>> +stream +%!PS-AdobeFont-1.1: CMR8 1.0 +%%CreationDate: 1991 Aug 20 16:39:40 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CGCFOU+CMR8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 61 /equal put +dup 49 /one put +dup 50 /two put +dup 48 /zero put +readonly def +/FontBBox{-36 -250 1070 750}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\ôéÒ@[œÕ6]nÎÕ×hÖmlha‹ŒH+4Œ£Ž›¹ºüú­œ/?Ð3¶&˜nÔ=œ“a6E¸#’ÕÊá|´~.‚ÜÔ…Ë¡w,ä"»rƒ­g[eH§êi¨ƒìª>žÎu†ÖÏ +ŒÕWÇåת>©~ºÓ–Ñ¿ÏJmdv‡Aíê +[û¿4|ܾ.×V–z¶ÛÄ_¢£1. F¥ýf« |Xÿîĸ9^Rw] +ü×ÛŠ³31S\D¤ËKZÍW`– äP”Š^êÝ3ê ’eÛŽÈ Í8`2?Òl;ˆÈŠ!eXxh +Dfú@=$»—*I¸BÁ€äÒXÉÔ!ÐWx-b1ƒ £™³ÅòòÝC; p™À}½âhÐÿíQi¼Ð=H²ðX­bØgŒbmÇ£óR,™º–>ù_ŠÑ¸°ÓQ! +äÂÅZØž¶Ar“]< £˜óîîÃQ–jt8ï?îB,mN3v լǵ+í˜Kú­6ï t‹Ð{äAJc—Q%ÒrúØ?væÿø60¾RmXsŤ+pú‘Ǹiñ:þUësõ‚ƒ‡“¸Ì)káÜÏPýWË\~Ú;’í” 7 T“.ÅN ¹„ü¤«}.¡‚¼ñ&:¢D°~ÀêzŸpŸ0C„Ë_§HòO­šzCÔêBy½AOve1k`ÃG|f2¾þ8—µŒ'j0&®òuk6sw,› I´Ù5¨&{oƒ¶®¤ÚÄõ³P}p2ªd +«ãC¤é½ÏAœ§!8ˆ²Zô⓪ÎÙ¦½ÇŽaÚBLeÌ…÷b¾±ls†ëLK›1B¹f/HÏ[UÜD&Ÿ—V{˜FB16³¥h¹X"·lñÍLÐÆMÅTÌ.„?³pSêþ˜Z˜Ïž@‡«+½/kb/t9{ä¾ú ÌQ£ 2l6TµåHµý[æ¿ý .ñ*”‰!9† ¦wm€ð·ÃéŽ4‘†Šk%glÝqðÛ×ÏQOc±[l~bï›â'ëDÌø‹‹_Ý¡^b—`ýê & O–°[écN™ÒåDObÂkº×frîɉH·ÙÈ®»·ÉË¡l½üY]zÓù&Q¶=PÌ~’ôélMârþéO¿å„9yÓh¼å7OonôXl«i—'w —¨h.uésƒ-4ý{´Žè +9âcÃO `+Þ÷‚§¼ñ‚Ëm†ãø.f›)K¾›ZÒœÑ/©ÝªÈ«M»f?ŒPG,|óϹ®q-ƒ³™‰÷Z‡¦ÈÏy#nžábòly@Jn¸zÅ2¢œGÉE]=̤Ž+&@ë<Ñ~ÆÄãõ³h'ßu Í&¾÷ÅBÐ3+*/hì¬:,•ÃñuvÞ½¹GƒCîb-øÈ÷Ĉí–izzÿeŽ«ÞõÔ =–‘•ÚôË»ài¬¿ºKŠ¢á_±ëxÌÆæjx¡Ð%¼­ZUí«L¹ˆà1ú„(Sܦe]/™­^åáìÀÇ ÙÃamaÏ[Š‘±a²`û¾ÙTQ)|F¨½ÍÇ‹•êú+•ìÏmCð›[êPß+¨<Âý!ˆw ÉfR”< àIFVpGž‘æjgÿn•œ¹ rÎ-îìbì¥béGÛ±l\¯hë|—è±í•ÓXÌ#;øˆhPjnð<*§ZÍMGœK²à8ÿõp~ƒ­> endobj +517 0 obj << +/Length1 1016 +/Length2 2355 +/Length3 0 +/Length 3371 +>> +stream +%!PS-AdobeFont-1.1: CMSY10 1.0 +%%CreationDate: 1991 Aug 15 07:20:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /WYYAGH+CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 60 /Rfractur put +dup 110 /backslash put +dup 106 /bar put +dup 102 /braceleft put +dup 103 /braceright put +dup 15 /bullet put +dup 50 /element put +dup 21 /greaterequal put +dup 0 /minus put +dup 54 /negationslash put +dup 26 /propersubset put +dup 27 /propersuperset put +dup 91 /union put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª/ ùÈ­éÙÀX¸~›id}S5žQ!gt¤ê¡âµŽÃkÑJc;•r´NŒ^ô¢¬µŠ ¦X€5¿.ØSyƒŠ– þ+'êIÃqV˜œ…â:¿r㚉#,Ùô#È ždèBZ£¾÷ÞÖ *R’*"7Ù¨ÝyÝçÓò¸—Ç=cîÍÚLIPsFŠ'Ñf> bôaöä +]fvÑÑ+QæAÁÔèâwdüOŒ¿[xìˆ"‡%ñÄS¦xõŠ~{×ÊpÒˆë¡õ|O +¿BÅÝÐÄÇâ/€G¾LÈã3hûÈ+N–g0Þ3²æ¸ËjäU±¯1‡ÿè¥~ø¦akœ·”Dìzq§»=÷U}.K¶˜Y碌à ֻ1?ÔÙCùŸ NÌŠ2Muµö–¸hŽë/åí4ÌÖÐG¤ã€m |Q]· +OaFþÁåÞ‹Åp4ò|ð¹ä¿dÒŠ=“fH1y¤äw&a%sA­Ï*¾ç'ËÞÇV¶jÓ_߶ã{ݬ¦ƒpæ@ã$lð÷¤c”¥+^4±á®P *óÏÕ$•²¾hš0P¤TŠpÓÿÏêÚ|Œ/‡‰dWÕVº£ÝQs&Å¥=*ÚìJa¾Bª´rÀ,°'‰£@jüe<ÃB½D! JÕ„Ü¥ÅYž·\?VVzÑ|½­ã!à£jIÒß5‘$ }+Ã>És$ß<}.Ìï)æ&:2&O‹Äò>mKOÔ‡1Aò5…Pã@© +xÔÅ@ØCõ¬ƒÛ1+,g­ØAªSpF¨Âñð+†ÿ: "[Ç .@€qÓ5t,GJ.ÔT'";ðÅ@_é,°Ã›Ù×·eã$<Æ8™•rÎP5• +=$AYÎ`-§‚C1$—ÉŒ› ¬èt©\jÑKŽÐ\D‘Ùµjé¥Ì?.™çB¨,ÆžVJÂZü(9ÂHêÜ¢³»FÂœY5› y…ÖÞSý)—“ÚÉs2¯‘0Ú¾‚œÉ61<œã&¬Cˆ.o¡øºŽÐc9€ýîWÄ”–dÞ\?G=€ÀV&’ôXŽ?Ye4ŸKw.e „º/›Ÿ ¦ +шC!Öý«î¶ ª¼Ž§—%¦ÎåvyúÈ|Ë–Rë¸ëÑâë©ötÆÜ/I¿EVÍà5AlÑ·XÊ!Í-íÀøëvEê šQðÀ6”„æNûh›†-´#iÄwGЀÑO§·JÎ}¶ÊùÊÚò™¨‘K¶ÛMéM¸P©¹Š‰VâUè2Ë8¿Fܶ]³Ü—ÒLÉj4mãpñ#Íx‹vlSŠQo]›#Õ#Í3ñ žw£Â¤kêÒÞɉQX|:©¦–RœíÄþ$´îÌ69¯ã ám¾lw=#,Z éIÝ3ZF«++Í–²¯+"ňUÙ-$°Â¶„„ÁÿH‰^yE3´„BP˜?ˆÍÛ«fñÕü&ÛIPS*rp©³7†Ös'® +ÿ²×Ȇn#à%¯ëMø/ndñ'ù¿J-ï‚Q͉ªãMË-½Z1*Šö|F:åµY¡´+çë‡ØLÂuhÂǖΨ°|Á¼Y—áûÝ÷é2HMšVîž:a§5qh~C{wW7x"”`›dþcF‰Øï ’£žV %v7”Mùv:MÄG=â@­ +ëQþkö隦ª%Α%Ö‹<«Ký‘ë˜q•&/ò—dÄÔ‘;òª…௽³Œ5kŽÅ¯‘m¾ÄÉS‰EmÏ€lÍ©m­'”´Š%ºÝ4q9ÞúгÉzJ™m¿A±!»±W‚KYf·¹ZÄK©BÝÛ +RËÙÍÂm*š¦­UÊÎÑxQ:ž7ëk5°2¥¿œ‘Ð6Ï8¢Mzê‡áñZ[Ålõô&éz#aE¿cB›Ê$=­95,ß?i2iCø‰ìy¢$ÿft0õwÓ" â¿,”¤š¾‹hCi‹@éÄ8q¹) @ç{Ý(µÍG}K¨U$¯ïÞ$ý””×0íÒWîc=^V_è0g¨‚’?Û]U +oSÔnp°#qþ·p®ÒßÐö Ó3˜6‹ÏÔ{·üÉ„ Ï``У6Õ–øA Ø榮ùå{ÀM°cþWHÄ.õvM Ÿ¨@ `4¦òÒdmY¯·i ×[¢ø¤co š‘ûàs™ÛÈ&ë2:Xx èÕÚös‘5Žd’’Ògû#tX…nnÿÓËçÿáU)ñ‰áG\ÁIìrš{òžÓc/\£]A„Ú•ÑcÐu0lª`¨ùUÇË©—¡Å—·dB“Ä€¾}aÆìawqòËq—¿ÈC…6¢"d›XÆÅ› ×bó]Ôì÷ðì««4ŪÁ͇ù.÷)~”ÑuÍÖïOÀ§íˆxË1$jœo &i•Ÿú I"aÐy\…Üv’¸*[Ñ5`Þmôzhê1íúíˆç…(lª -yµ‚ô£œþ[ gïI𬥦Påº,¾EHšJ¾z̘Z®Äoìõ¦k¹ûO3ƒè½ D&ò'à5÷îcÕCW¶…Å¡OKf^ÎTÕ/ñlíJ§ö±A­|6¬ þÿĬ`YüS@QÈ¿á†dEHºðÚ`ŒÙLä$Ý-bH¥3Ô•®þºSüMH7Iàb=Äae}ÆL*"Vô:­«ðÐá-õÂ<²þŸ7?†+›¸‡g„mJÛ +‚ „6Ùœ[°‚õœAñ#=š˜MdP'¬òV\'ÈÙC E4à« ©9\d{­ñ$eMqvƒ“¹¹bN6Õ«p–•E°È˜Œœ§$3c–ʨÇpRÆ]Z£<¥Ðt€ú*!'Ä›…À–4ÈÑÈa{K ¾£?J¾eRÓûraÀÎ&>6.å“ɯÜ*]Ì#ßO0¼ãË^ž»ÏN+k]üž¹¹1<«øÃÅ®ƒ*g×5]_$9Ï^6oMd§ÈGØð—âŸóèjô endstream endobj -123 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 539 0 R -/FirstChar 11 -/LastChar 127 -/Widths 540 0 R -/BaseFont /ARBLRW+CMR10 -/FontDescriptor 121 0 R ->> endobj -121 0 obj << -/Ascent 694 +518 0 obj << +/Type /FontDescriptor +/FontName /WYYAGH+CMSY10 +/Flags 4 +/FontBBox [-29 -960 1116 775] +/Ascent 750 /CapHeight 683 /Descent -194 -/FontName /ARBLRW+CMR10 -/ItalicAngle 0 -/StemV 69 +/ItalicAngle -14 +/StemV 85 /XHeight 431 -/FontBBox [-251 -250 1009 969] -/Flags 4 -/CharSet (/ff/fi/fl/ffi/caron/exclam/quotedblright/quoteright/parenleft/parenright/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/equal/question/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/X/Y/bracketleft/quotedblleft/bracketright/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/tilde/dieresis) -/FontFile 122 0 R +/CharSet (/Rfractur/backslash/bar/braceleft/braceright/bullet/element/greaterequal/minus/negationslash/propersubset/propersuperset/union) +/FontFile 517 0 R >> endobj -540 0 obj -[583 556 556 833 0 0 0 0 0 500 0 0 0 0 0 0 0 0 0 0 0 0 278 500 0 0 0 0 278 389 389 0 778 278 333 278 500 500 500 500 500 500 500 500 500 500 500 278 278 0 778 0 472 0 750 708 722 764 681 653 785 750 361 514 778 625 917 750 778 681 0 736 556 722 750 750 1028 750 750 0 278 500 278 0 0 278 500 556 444 556 444 306 500 556 278 306 528 278 833 556 500 556 528 392 394 389 556 528 722 528 528 444 500 1000 0 500 500 ] +519 0 obj << +/Length1 745 +/Length2 581 +/Length3 0 +/Length 1326 +>> +stream +%!PS-AdobeFont-1.1: CMSY7 1.0 +%%CreationDate: 1991 Aug 15 07:21:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /PXBGHL+CMSY7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +readonly def +/FontBBox{-15 -951 1252 782}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª/ ùÈ­éÙÀX¸~›id}S5žQ!gt¤ê¡âµŽÃkÑJc;•r´NŒ^ô¢¬µŠ ¦X€5¿.ØSyƒŠ– þ+'êIÃqV˜œ…â:¿r㚉#,Ùô#È ždèBZ£¾÷ÞÖ *R’*"7Ù¨ÝyÝçÒQI¿e©ŒŸâ±ÏrZp(IJÿæ8»¦±#†Çó+£PÖ.¢Õ²NæÂÂCÍ;ý ð+[i-{'¾Ç)ïÜù/•ÝëPphÞ Qãì¸äCæ¾ +A¡øÈœ;Ák5,4C«of^¬^ Ä"ìüXáWeBL‘œ'>¢@¾{.•·‰Ñ'b[¼·>PPë.±Èåó­D§W­,Å=‘{ý #VX†î6ÐÃÝnz¢ïœÄÇñTž`šqÃÂæN&=`¥~Ÿ+GãH —Š¯c†Šê%Ú=TF{vÒð/€—Ò„ÚfwsjÏì «ñj›-$ô{f¶wˆkªxzØeµ÷Žä4ªG·°ñ$JB%ÜÆpý©"&âÆgÂ4B˜ÐW[ßx-–ƒnÊâ)Ç¡~(÷›'?òCE-¨…Š‹ËQeSO9–ËØÙsÛY=`lzü%ži$/neu¶…*­TVyæõBÜ¡ m¢MÉ/¿|ä‹8ySx{+Ë„s®Òߨ39ÓžôÝ:QXE'¬:“c *àÈœ?/úvwC±'káæHÕñ¨ +endstream endobj -539 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 11/ff/fi/fl/ffi 15/.notdef 20/caron 21/.notdef 33/exclam/quotedblright 35/.notdef 39/quoteright/parenleft/parenright 42/.notdef 43/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon 60/.notdef 61/equal 62/.notdef 63/question 64/.notdef 65/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P 81/.notdef 82/R/S/T/U/V/W/X/Y 90/.notdef 91/bracketleft/quotedblleft/bracketright 94/.notdef 96/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash 125/.notdef 126/tilde/dieresis 128/.notdef] +520 0 obj << +/Type /FontDescriptor +/FontName /PXBGHL+CMSY7 +/Flags 4 +/FontBBox [-15 -951 1252 782] +/Ascent 750 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 93 +/XHeight 431 +/CharSet (/minus) +/FontFile 519 0 R >> endobj -110 0 obj << -/Length1 1336 -/Length2 6946 -/Length3 532 -/Length 8814 +521 0 obj << +/Length1 765 +/Length2 745 +/Length3 0 +/Length 1510 >> stream -%!PS-AdobeFont-1.1: CMR12 1.0 -%%CreationDate: 1991 Aug 20 16:38:05 +%!PS-AdobeFont-1.1: CMSY8 1.0 +%%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMR12) readonly def +/FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle 0 def +/ItalicAngle -14.035 def /isFixedPitch false def end readonly def -/FontName /UBIZKK+CMR12 def +/FontName /VOEFGO+CMSY8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 2 /multiply put +readonly def +/FontBBox{-30 -955 1185 779}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª/ ùÈ­éÙÀX¸~›id}S5žQ!gt¤ê¡âµŽÃkÑJc;•r´NŒ^ô¢¬µŠ ¦X€5¿.ØSyƒŠ– þ+'êIÃqV˜œ…â:¿r㚉#,Ùô#È ždèBZ£¾÷ÞÖ *R’*"7Ù¨ÝyÝçÕü! ƒž[Rß»*|]Ž~Š [êCÖ¨ía¯[#Ô™ Ø÷«jY!4ØJÀ‡¦Í€õÝÙÒ"¬±Â3&§ejc\J$Í2Ëýø62¸ª6áwõIaàUÇI¯òränÌFB/€Ð“(Hp%#ûÚÌO.,ÊÕñsü¾nݸt­%\ÕåÀøb9?Ë_\ œ<+µˆn6ü<Ì!H<:Á“HZFéÒ+× ”äÔZÝ›ñÌ\ö¥ VT¬ àÚ=µc±8@º0÷.Qã¼€cˆºø<}93’¼¼"wqÍË—n“0%0ú?Kï4—Ô0*H8JÎÿÁU”bê_`Ü$^„™Øæ—²À”ÎíònáZƒr ìæOïA«èݧ¾5ñNºÔ ï¿ÃÎ{IÖþu-œñcNhÜĨ)ËCnm ’ƒK@øÜŠ‚-Bͱ{R{›9éɖη I_õ€¢Ó&þ8Í"–Ýù´Ç9 ÞCsû Hë¤'³o ý)©ìGÕm ‹`ŠOÆ/=õ™‹=~?0å´ÑΕ,Õ~\Tö%ëÌqK)èor89îrø±Ù¥ŽõBÈPüYÜÔ¥‚ T¿lÕpë4űêãI=+r¼p%«Æ ˜À!í»<¸Ê'y1# – ¶Šõ0æwªy»rÈ(X¸|ãX> endobj +523 0 obj << +/Length1 1693 +/Length2 13827 +/Length3 0 +/Length 15520 +>> +stream +%!PS-AdobeFont-1.1: CMTI10 1.00B +%%CreationDate: 1992 Feb 19 19:56:16 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /NYFVHV+CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 34 /quotedblright put -dup 44 /comma put -dup 45 /hyphen put -dup 46 /period put -dup 48 /zero put -dup 49 /one put -dup 50 /two put -dup 56 /eight put -dup 58 /colon put dup 65 /A put +dup 66 /B put dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put dup 73 /I put -dup 74 /J put -dup 78 /N put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 79 /O put +dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put -dup 92 /quotedblleft put +dup 87 /W put dup 97 /a put +dup 98 /b put dup 99 /c put +dup 58 /colon put +dup 44 /comma put dup 100 /d put dup 101 /e put +dup 56 /eight put dup 102 /f put +dup 11 /ff put +dup 12 /fi put +dup 53 /five put +dup 52 /four put dup 103 /g put +dup 104 /h put +dup 45 /hyphen put dup 105 /i put +dup 106 /j put +dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put +dup 57 /nine put dup 111 /o put +dup 49 /one put dup 112 /p put +dup 40 /parenleft put +dup 41 /parenright put +dup 46 /period put +dup 113 /q put +dup 39 /quoteright put dup 114 /r put dup 115 /s put dup 116 /t put +dup 51 /three put +dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put +dup 120 /x put dup 121 /y put +dup 122 /z put readonly def -/FontBBox{-34 -251 988 750}readonly def +/FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ\ôéÒ@[œÕ6]nÎÕ×hÖmlha‹ŒH+4Œ£Ž›¹ºüú­œ/?Ð3¶&˜nÔ=œ“a6E¸#’ÕÊá|´~.‚ÜÔ…Ë Lw2.²æ§sÜNYÁ ¢Ú»›÷.,òVÝnµNìºX«Ù3µ|裠Ñk(Q×IOs mõ;Üf»ø–µ‡ß–C1}_a Ù˜Io#Ýà0÷²wÝ™\‹œ®œ™ŠÄáPÍü,fí’ë´Ì *ªŒábG¡3ZÓ2Ú©PÒ•§8L3ÿrê£[‰vnc_EÄÀh­~èg9°|¹M)ÿ }Yÿ™aÑ•©HãØ|1‚’•¥m!‡[A˜z¡XpPÃÇNCU»7òUÖ²7ΖòTg÷¡ž…x_ôh”œÌyòø®WÕ÷›¹ÅÏ^í]˜W¹–}›–ÍÏsÕÖ_÷Zú»fs@ºâdYr ÈŸÑsy&vJ“Ðx´ë)Œ‡Öî¢Ý±®ˆÅ~ÏïKqä -4•Ü5h¨LÉ#q§‰:4pPý¦ì÷?gÒ |GJS†nœˆæ^i2º‡§6†ê°“‰øM˜ Ęz0í”.²° ¿õ¼Ç ôâvÃ3›1¶ê»°xCj »7}0a¢ ¹‡–¸`~ì¼i”Eê¨fÃŽí}O>ÛÊ&*ö¤g¯Ï¿60ÉCúL͘Šsc÷·^¯X0°IF +3yˆñP¹.˜žwPŨ=óv…H?†Ñôtxˆ??jKv¥ª‰èñcšÝJ’ ÞŠO(WfÀn¨Yc›’ÌÍÊõ›+¸ÕˆÊuMW¿÷kS˜Mô“p“ªïy2¢šLûa }gH,H×ùèA ­ngV¶U4çŸÑNòN6ð9î<¯Šo±\îV·¡‹\;ùÊ­àÀåT!6é¨oÜïd"‰œ±Ç.JCȦŽ<^"ɶ2±¤î§4¿8ÓÏ[;OªÔD$Ã×ÐŒµÑ§¢o/0ìÀ¹OýxõPÉ®^[­ÌVZÍ)£8¡I:¹±u{Ñ÷$¬ÛxRlþ4sñÈ''ö DñœaqÑûpBÏÅFW|>í_ÜtaLúBûß&ÍÅŠPp®9ÒLŽŠù–\Ó‡ÔÞ_FÁ£X¦…nY`2–œ²n6C5A„Bk@r©uŸW¥Px -…ÕŠš=ŽY4\æ‰'Ë7BÐÀÀÉÓÒ'ÁL`ûÒÔ²k¿ Ú‹X݇ΡdøÜ;’³ÑÏêu›Îõ+µ7  Ò¯SJ´k¦! ú•¶ÈË+ ¡úNò±ª÷ë0ó‚ÈÚ"FQê–¨Ö†‹Â©T»ìqÙ\Ü?¿ø2î˜4ÆA(ПSKߎèüŸÂæf‹’Ì-æp–E®MnÏá¤Ø™zÀHc"¢Ë€êtn@Üîyq+^Œà¹Ò÷>[JóýgX6W'×8épä­El/¯7d9Ûz…/šü1ã•3«×ÁÛcÕ¥ôgœ×Rt³šŽ>Ð"RóU΂@œ÷Gå&Œ}kÊqû9eô×#r%oª§ -äyÑ -Ú -iÚj‰$y™E¿oè‰â¥û6uH1ž’W/܆y©¬7s¾u,/R>^Yâ3›¦H¶·èù=çæ“jß=Jî'@Rf„Cþ‘>Ì®rÐÂX'Ñ´_Yb‡w@ÿׇ1ûY‹ÑíÊ žEe{¦I‹|"/në,rÅ#§µl%‚eŠ½“Udþ¦Ÿ$·qQíúóÞC×ýÃ]Ä¿™®d‚äaÛksëÄ’>>ñŒ²è -goê¢]ž¹ ;u¡]z¹þ_(óÚëüýÍ8Ñ‘lŒ\Ìu 6 I‘ª Ï ¥¸­p§>5?øfш+Ëê“2•0H/^s°’Ëá“oÐÖ^AïÊLÐ ±KëØ…ïmÈ6lR»|ÒU_ÊWÝF¥0š¥*hXq„×ë pi~ÑôöRðXå2oW;7“ÊâÛžGɨ" ÇÿmïCf®p Á _o6¢æçÊÞ¹lvfªÏ9êèj®à=^¯÷gÿLVû›²D¼3Up¥¥AÈžº¶?>†n\Ê%ºgFa46U9G>NÑþF0«iÒùqÁ£Ž£±îŒ,ìÔ½Ú”i¥a·çù¡°Óº/&ËÑÚÆÂ÷Éà3~§è×|"W§Šßýhm†O°€´%#aôûðR­Å}üUƒ•Ú=[¯u[»1úBºf/¢ÛÑÀ9Á^}bM ¤]¨Ð׈³Ç&%ù¬Þz5q·÷½@¿Bó¢*éÒêüLJwƒ ˜¶±ýÀqG†àŠð vœo{[†Ë¦›£wäöÞ6©Ýb蜔êBêîÝ~Yh€ˆÑýwG‡û¢É%×HËùúqMÙ¶i'ÈÂr6ïü A©Gä™ôp‘s_Ŷ“¯ŠZH¯¤’—(pÄiBÐÙSÑ|ä×pÐq›ñÀÈQ¾dìUl«Â!«öØ:-4À—Ë«Ïp”r&ìüæz•ª¼âê±ðGx Çšñ]˜¢2™ ¤~DÝ>¸ÚïuÏ·´¬kÏɵÇdþëj/ZžX%K”ûÍO7£Ì¾ˆ›—Ç%[OMɹûñÌ£jÄÀš“V´3Œ;œQéÍæxÄI]|UÑ×h¯;=ZzÝÀFÚ ödû+t.E¡–…ì®{/ÊíØUhìyœZQ½E–˜ÆÖù»g©-è’\Ùš’àW=¦lƒÈQü±—´0!xÞFqÞ#¡"‘5\ucS0G•‰ðÐè_˜„t_²;5'ñrð“XW„Ìp[÷:m'ÖûYÎá/ GKFf§Y8pÈ›ÔÃ;0W)u'eI­.síió0:¿šE†Qšº‘Åa€amŒÖg#Ú~\8¦rmµàV…%‘«ƒ"R@î*ÕúòZ »‡“°ˆ·àʯDah+EbG°›ÝWPœ.E›ãNÌüz·tX¡©O_änuÕk†Uø ¨ZiÆH(Ÿa¶\-c¯w8<›ý ‹ìçcÎlW(üÎ¥^óR! ÂQÌî|ø¦†p/]5rÆU8ôýeÄ|qW«Öñ17 X/?á;“Oüÿ2U5Šµ'°¶’OŽP¤Šj·ùªìd[8|ès¯õµÒ¡ü+0G}9‡ZôzÉG¼3"¾Ö½Sß7¢3òõyGÉnk¹œn0ktcf4–~ŒvU †417rnØá"V·}Fª™ZÎ+Ñ[vn˜îBÒŒâ3Õ¿l*Q×$ 1̯JA¿”¦¤úfæÿãUœI]ó -P\é7p“=Ráñ´Ñ´Ûòß[GìTyÛÒº´@ìà6¸2 aZCÉ‚C›…¥üLâJëð×}gîZõîì»ÎËÆbä‹Bz‡î=òó.méQŠs°;­WahËpÞ -[”XR -™Ý -Ò~g:I‚ðdtŸc_ocïÉ»€ÁACz*Ž…÷7ü>‡ ÑFiÔ¨ÂMH·ƒ8> -Gb«ò@Z(I‡²†=èbã@I^š€Ê5¬Òì˜q:âGQ(^•GÛ´ûhG•ò‚gÌJzä*¾Çk-úŠ@p°ûUc „ØФù`JK‡àdÁà¼K;'Žiìà‡çf€Y1«óø++Ne Cg¾f–«dãP«Œ-„©ˆ[-é¯CÚ›0ÛøC$·xŠŸ¸ê‹á¼'Þ5zõh°wn —XI#Mw)}þ1 -n² _c+WqIZ7 aY´È²/ã°Ë—Bõp^ ­b*å€Óù—ŒÂ«<(ÅPýÒ`Þ´DÞYÕ'âtcß5 ø›CœNKO½+”nãWð™ ýqàin´$CúÕù·íÒÒèáNÆS Óf<; qçTb’Ç…¯Ž@­ âtèMÄ\nê°˜7œ&%j‡àZé¶@µaiÕsØãH@TBÜM#ëQ벓=‡*ΆŽdõ …ëþû.=Ó8ŒxGM—àÓá(ag›Eë«d »Î}[¦wýƒµX䃯OšÚ— Ö’ìÙÂ`ŒÊ¼¾Šzj.üüøwÚRèÀtì“ɇ²<0Låá_ºeIx`Î|ÇD\¹ôÍnÅ9w&sayÎt˜LÏš\›Vêìzš¥Hw*ª£Ó¿éTnÆ$ÒÄf&D9 ´£d‘ÐQ{‡8;ÃÉ ¢À^7‚KðŽìú‰ú¤à=r=óEI†)6š"ÙèòœE>êpäF$ᆵÍö±ÀÄ4âÙ ò¸±&hŸSªÇ|þ)39n¨¤ùí9¡pxÌC-—…É+“Èr—×·%·]j©ÇiÈ;]ô.„¯:«’¦ÝêŬºW)²«N ¾¡ »t¾;OöŽ5ú¯¼lápÜWô‰W´ÈìvQc¯Èwlw6‹!b5>ÒS¡uÚÚ@|öbóf’C— N9Š‘7QÆ‹økeòºiáHœì ®.ãp¬rL«ûMc jtb`W -•¨Y -1ömW£Ïí¨ÖÂôÄ€²×€ÝçzÙV܉Š¬ áKƒÍBë]åX‡È6ifþ»Êµmó‘@,yv‹× ü¡Ø¥ œèEõU¯ÒåÊ"¹Ê/¹oªmŸ¬Ðs Û„äÝíxë¿)Þ´„ ž¶­¦¿ò—OsIñÙÙ@ºVXvùÝÙ¶ð;UjÀéY-q–²7›} ->Šo-BÑ©aüØ¥`ýuB¢¬Ï£ÓºÅH -í§c íÖ² ²ýÐÁf~î©âyF;Ý“^ì>Jqª#ĪÙ฾”Llš†_0ö|ÈPÊ*FcÍÖÖ>žrÀ†Ü¿]ô ä@KŸ¦çhõs|ß”q‡©‰„Ï·»Ã]óŽ8LyÀ6To¤•r±,d¹KÇ@::G|3Ȇ™b}¿2^ÖÎ`Á9Á ÂF·Y@&êóO°^™Qú<;XÔðûNƒ ¸ò€ƒ—iLoÄ×[®såãŽÊö!ä;¤-d©ƒýòp¸\¹ûÑàuœ]±Ö_­‘PeÆÎ}ƒË¯R0“#ôÊúcøÛZSûK¾ ªdOeZWˆáJ·ýÊ"3÷|=ì3“à  -&Ä1ÉG°y_“ƒ/Ç•,b¾á'‡†ÈËböŸÎ蜖¯‡¢æœædç|³%yG3ÏB5*)…]°’Ö¦¿dò[) L{¹lµƒÑ FRÖç·táu¤§Jiß2¿›¶YvtÌúÕNœ$,·fÒïó×ÏÁ6v·ß‘TyCqý/±‹ž™.öúÑ„‘–¿„û…¹‡z:•$EYŽÈŸÆœ.Ý1¯#£ÀÖàe5W÷öÂõ0ÖVw?EX^Èž -Ö?íu3ƒL„ 8ºà"‚+0æPÍ÷ðÊÙ&P¤w\¼ÜV xr=« o–>5¢X¿Ÿ"JÑkF^Ö£k}õ]Û–&-[$íâÒößûž =õXØÌÀÒ*L9¢Íá'¶wÿ0³í= ¿N«¼ÚûߦÒñò;;˜JÞ"h¬ÄÀÈ:fPCb G7]|ð/‡kwûÙ›îÅeó³æº²uˆ¦Êâv¼GÏy®Ï?„@ñ¥Û¨![h\üPds2ººÃBÊÏ®ŒB g¹gæ;ìVá­:…a -žQ¬3¶d¬¦M+Ó §ƒ;yÊ1‚ƒu–öþœª¿è0c-†¼êB¤èÜŠ¯<ü9,ÓDÂwö\°øî'æ<\®”ô>ÏÆδ¸ 6yªb;-÷<.òØ.áÖ‡-œòÖ ÿ±J˜Š6„r³4S{¾ätƒH7· -V,_Ê[4ΑnnÄV¨€|ÉBy#ÉßÅ" btw•(º?FJW„ƒg ’+!§/ïzÛäW„ÍÄB< S d"õ4 -¥“ŸO@²Ž¥„ÚööçXºÖ z´ › Ò·ëv5V-éò’$¼Åå¶ -z"‰þ"c±‘°ÿ«Hòrƒ˜·÷µ]A­Ï`Á,.¬mô• -† È2í`¢*I£V[’õÌ·]:zóêÅÝ–+‡çƒ¹öP^ß"ÁCô¬:>›.¶ŠÄ7ˆÂ¤Z€ îÖß–À;Zø­FŒÈMŽÓ;àa–p$66á(Ïù› -|44=6ñ¿½¤Ù*Ñx ¯RòJjÀim¢OŽ´ß Ë™¹ô -Àl~{f© {áƒ=«Æ$;òŸŸ«v˜k6Ä.»¤œ÷lUÜù…KsJûY‡0ŒDƒrCÚ¸„+¼g׬Z{ü2Í9Æmim«€>ùÏÏa°õ'9nlÛ½Ú)E -Ñ[•®“Ô¢¾>Æýž—¿µ,MÈÇ\ŒËè‚~`­Ù’®WÔœm½Lúµ— -Ž?-,1ª‘Ëïrr×Ü$½xsÅï^±ÜóSÀŸÖ©8'É¿Ï{-ŸV -ºÈĹÅôžj’ahc0½e)?s1ÌÕE`G¡ÖÑ«HXêÛ0¼õÉaÊ~ .wQjµK¤üÉ›²¿öÔK<%–ìæzœ2&«§-Þ ÿ+Í`†R… 2¥§CG|?«ûË¥Š‚ÚC>#¯ÝI¯ÊúSE¶rÒ,UÛóŠæ‡MüNisQQ€~þ|¬—e]Ý$uÝǀƒ@4ª{MkßÏ(]ð>wˆ˜c¡^5@¿Ò_¹¨¹aˆÔ`Y³ŠÿYÈÃþ„S01nÚ£AÆhÆo‹9JÔŠÏÚÁ*#4ÖÏ0XÁVõsö 7ðQø=`”æTŒ£gE*ð/¤Q¢\µJ߶9K_է܊ˉÔÒÿO¾µµõ:Ø¡úÐKœâu‹¡ -ÜOÍG]˜(iñ_ŠóÇÙ¥šAm!C’³³¨ƒðm5ôV¾YíÁ„ŽOùiÃWïÆQ ð/ÄV€T@_cä ëÖˆYAÌå¾a[JÑ®ðËFnª6­ ͈ 'óú ÍcÂë`O“îóñU³¡¿'4£Ï(Q.&±{:-ÁüHaw°÷—c›1mÊUë$0Ï1ô*ö·àÌÏÎãÞŸã;¼¾±Uõ[wq¡o¬u NsõùçekzY2”´ÆŸ+Á·xÞ¬ †•¼@æü¯î èLøD ¸c /+ÈǨbíLÓ!â$Ôzƒ;’V[@±%½ÂTµ2×½£rXƒüNÀ…²Ð *¯?/‚̬ur 쬄–ß­ˆié4¦íßþpžÒ§M ÁÿËóPS‡=fèúó3ôj(läÛ\nåÉ:ÊÔ9WÍ}Z4|éFÓÊú³<8A¹ý—]€÷ cXÊ6#k·¤ò÷¦^¤vo¼Yø^kÌç(Û,Ué]gÙ|më½â¥"ËtBó?xÙ¦Ž-ãõ*„]¶¡Ž°Œïr,Ýmÿj_$Ã÷!4@Ñ}X®+Œ|÷žÌAJáAFw(Û¢FaÊÅû -çmYìAyµ­ô"Öfp‹»eŸö‹r–Êdå T㈮ G¬Ðï°ÚÍæ„ø³¢Ëó=ÞÕ.&ƒ­ƒTK7AˆütMPšÚ¿[z{ŸPâ‚4˜°r¯Ûªh<Ê|ÙÌa ÝŒ’4Õ1ßò­;Õ0„©)!U{–¥ìߤF¥á»"«SQŽP–:­ÊI›Kƒ‡‡0Ú—–$¨—…Âvǵ"µ/b¿° }/\®­+tFFÙö”±ÛËþ_n{OpÊ‚7”IÙa‹:1/µè9DäýZdË~ -èî$׫óbõr§XVir(阾Ӟ·êJm< -ˆþ‡¢™41Æ´Û_ßp†àµJ  -SØgpAò¬µ‹‰4°TÇçÖ˜¸ü=q Øèþ&œ³AE¼*™±™~J‚-„€'ºîšh#Ro‚k :ô¢\G³)€ÃzØ–e ¸vTYù/·L¯Rrw—D)è_{±äæ yô‘Êåø^ #Ô@Nee#a¨;Ðà7ä¾{¬¬@E\ËÔ¸ ìò\¼Ô߇6°¨²Ü£ûGIÀ:e£ w^ºÊo1¼¡-Z °lHÄ3• £|ûlîµÞMªi.TE¹î-ÑÛ§[ljfðÏäc¿³èA”KèdÒUÙãÁæ‚df `Ž•Šq…®Ì¸ùLŸÊôøp`¹h‚ôÝCÉoæ0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– +]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÕ™=ü 0)xfáÍ +1›kÙXž9Hÿ°´ç!.ÉvÖP™ØN 7§§qÃjÒj7!ì6CžìàÉ«T´w.]Ê‚ÐÔ¬Çô/´“ª£¿JÖìá†1]¾œýËèÓè0'Í:ú Ôf¨èÊqdÏU³2úÔ4‚tÔ¡Ë?@Ë^g+‚ Øþ0ùð[ðõµÌ +K–îT•B/ºU¾é¿ÙFM˜zÄÒ7Âú† .UÎ{7‚£KÂ.=ãUÙ¯ñžI ŽC¸^ì訹…ƒ$ÒO7Ûù—-tæìG„rzÀ œJ:ÓÚ"½ia~ +ÚõT"ò*Ê^MÍMùüч¥f·ûf0EM ÖÆÅ +z8uÆËøìwió*?ÁÀrºÞÉw”Ôé5(*5nZœÙ«Ø +Ä4*RƒäX§&’RôT»dR³žÕM3m ’ŽœÑ«&­ƒë ž.ÇP¢d8;]»F |H!µòÉ%Té ã[-¿Í˜€šŽÉü‘Þž †E|p¬°Vëù$MÀ¥»ÔUá]n1€1RÏP°¿} +dó¡‚ +í¼.{®µIþQŒ7™Æà‰µÕÖ^N-+C ßú#̲]•\MØ…1 +pk2 +²\t,o)•2TúTÚ®æÔw‡}¼ÒŽšµv°êqý `×;líSãgs3c-ðh®ðþ}ûW9;Ú¤9¦¤Ã–ø`2©€ êá${}è;;ämò‰…˜ÿ^l¦•1'C*–~OÔÝ`ÖäšXúUnó0‘xµ|§cÏɾì'iD½ê%W‰ïNÍáêCîÛ•Uô.ÝÏ9®R*ÂÜR?nìLÊâW’·ˆs/[µÌç趡¡Û†±ê8ˆ>Hêµ@#íÙ»”çx î¥w­ªžf«}†´ ažyòBÏRæ¬ ®C1|P|Û'êŠrÔèÙæ,˜ß°IÇŠÑU`ÎD£•½kUQe ]A©ÕmÃ\‚"Gm¸‰F”O½ƒ À)2rIuW‚\ñSøâWäš,'Ëv¾ÙÏdy]eqXH0#~èZ²9À…±|pÅžäPæO£HŠ¯au`öÎþ©C—Ñï©àbÇ鬅<Êç=ï?t8é!½Ô-~œC0¯VŸØY-™¤ð…¢aht×`õrxK[3ÍÏ,Øðf @Ñ=Ê]ëw˜G2C#ÜŽŒ»þƒd#QZ÷´^ÿ €â>~k†¤Ô!³ –î]lI½ô1”ÛöÄ“±h»ó÷K”*éQ9Aó–Lr íµÆ¢L¬X/’¾Ò‡'“Фô9׫Þô»á÷Þªáþ– <ü5ƒL +ؚ؞²EN_4, À5—éoÒ„v½%¸§ Êkj2àóÖ®àsÁ»&gëÂrÕ…ßdám|ƒWEOÈéÆšJ©ä!áAz¸â 5Q²{CA<¼°É>¹ÚŸrµƒ¶(.DÇ}ÿ`¢erÛÑ8ÞS!hÝ.íú=0 +XÄi“}w–B.ýúÓŒTI߸=fä~ŒÊ(Y&)ðGLig†»¥ú,`/^æ9¬ºæõ ™6¸…T +S1¿ŠÕ^WÖ6Oc—îú×ã _‘`6lÑ«K8\C/5ì¾–¶­_]P¸Ž®BÑîè¦2+µ¾#(¢, ’{j4 6â­ ¢>ßiØ'HâŽß¿{#Kºâ¸GÛs†%T{Åë;ÿƒ.™Hûž¡£!7H‚mÓ)€ª4*@r ¤ˆØŒ9¬`®ÃzpÔÜÓ™~´þ·(k²E{ %¡¤dKä^÷ 7)-ª må¸×twZऽ™«b²ëßOÓŽÑç29lP‹(¸LÉ5ÕóLÔæ1‹D´0ØgXðhGÏ€-ŠÃ*;c-4æ‰PÛÑF-í¬ËÖÕæ‘';äuÿ² àxã3 %Hâ#e#ñï¶ÙíÇö:¬ó·‰+]2»¨hÊÝ”“\0í”ÚyTˆ7?‰tömÆ 5”‰øXõ7 +qœ|HaXY‹'0d Œ‹ìJXø°†­H–'ñéMÁl‰A[l(,ºP9]âE,ÇÈ€vÑ?›)‹qs$åDkôª°=k·¼†Óþùà7r.®-ÔY)×):ƒd +Ó>µ2àÌqX˜fóô0|Bå•%êNß$ ãÅúÆ—§°mq¨2俳²qJyr2ø’ì¸ñ˜„Š‡´¥7\{|;±q’«4bUŸØ»Í?k¬’ï$¯có×\õUØ„©rx˜yOfÀˆ/ø,ÓQįå¯1ÂÚ:÷ÞOCµlòѲ’"õÇz”8sÑÿ€4ûl”£Q¡TÉS¶@ˆ0C„|®µU¶iøüz9,,„(ÿ¡î€×C`£4Ÿ$Iº±›þ5Ü4úS©°~ÇŠ½® ô„KßDªSÀ–l3Né¶Xàê dĨ5¼nEåI1ùÿÄJÍЛc(#3³õ„!Ï:Ú$Iàcxæ –4q‘4úÔ€¦íxŒÚæaCÿˆûqîC°okO`ï"OÇèy×åâŸ{AðêÊÓÖOƒh‰ixš¿¡Ráçš|N>ښͽ$zô5ncÿ6y¢ÃO㣜Q-Õ½ÚlÃ|Û/‡8q·¤£Ê›¹e™Õ•‡bÌ¿`€ËôVJ¿V[踒”g0qëºGÿ¹N€t!ü³&ý…¾›‡ˆ²®¶ÄyZÝ~öXëó•!#qV!ÿ!…ÙÅ@ÇÂTkê#ì´ê”7ÈÊl£î¯¿æ·ÌÙ¯®» ,“Éı¤·oV÷½\v\€˜§sc¯¦ªR ÌØÏ”œG’ÐôÑÿ–CÑkÄ^~¾øMÔ'U@µÝx˜2ŒËZ–/æ?bue–æÌ1°cõãAÒ¹Ø b^ô?Jé‘eÃ,%³ÂÉÕƆæÄ‘¶L}OÒ«Ž'ð– ÎB;¸úª?Þ²ƒ~ç€Øýuz%¾n$äÕò×ùäѯ¯°ƒ­&x\¯áÝ$~?PȦ©QG¬oOÁê…íÌM¬O)f+­ +þ®C‰3MÍ–y0ß~Ñ4Á.n—(j=oÑN¢…—2l¨)yìŽQg£Yðó×ûÂpOÕáñùÏð"£Æ¥®)%{èï„ÊK­XΖ] öÎÆ€bîò‘ßtÇ…äŠÂ‘óÈë’–iú –Z'Þ<8ü«-ÞÙý^¿™ŒG5ÃýÛJXtƒd…—Y•³È׿.qF75ÍWŸÐÚAË~†S†WÂ:Ë6ˆ%öPëÞ¤Îÿß>æªývüøÐ<}Êÿ>? d|…û€˜SÚ²ªØÕkªâHmƒâr˜¢´ÍAAq¯ƒpÀ3&êÚÊõ(¿kJf,ÈÿÌAj Îj䌯 dŠt‡ê6óeê`ŸÐ­ÞBûÊà¢r)s¸SžÏ™Ú»aŸd6µ° ­,QÓ ÕŽßwì€US“£UR8öÖþÚ?ˆÒvòp„:&X­¦×“9®¤zš$ +j#nzk3ùw…oaËñV Š}Z^4#¢4ëÐÛ*–w˜¨_Uh×oT:#8†`›~í¨ãÕÍä…qåB¯‡œ}êÒ9Ëò$ú&£3äE ‘–àPqãç×îJtL§gl­%„]Ð +Å\.éӞܨà÷Y:>ñâb¾×Ñ£Ꜩ–0ß¹´Âff«hÓßÊŠeÔ™žúîYPlÁïókÇ©F³¥°|Eˆ®8Ô–ÂûlkìG¢¯n•@kÀãdžĜ…$$eAð6OÙ>Èó&ôûÚØ=$8½džôÁ$°?û¼µDÒe7ßÒݦŸeâ´è9“.D3Tã ÏC#‰œc³å+Sã²e`—«H×Øï™4GjÊYüà”xqØ^8Ð$5z3”!K‚1Þ±iò¨k¾19n¸âƒÜ¿×˜¯–€Ý›eð)¡¨Þç`ÕÐRÞfæa½f¥º”~ÊÈýNýE·ºJ_Ši­ä6)æýÔ Î/ýØe®[¥V,fð,„/°3Y‚n„õ37€Eq ¨ï_žÏj·éž |š"„mÙŒ‹oIJÙ +îêfg!E}$3õ2Þ­¨ws8ºý€r¥¨a¥”ÖÿOç{ãµ.—IWM#(´ïÿPÇæý¹Ð¥½ÜÍ""™ÿÎ3bD>ÈÔ•¹ut±Z©ÇyI!?Ö|6áÇ KËå$èÐtÒmî†ÙLí:šŒÃÍiÊš„lÂåQ”¯ÖlZî*kYÏK3MÀfTˆ‘ÀùéSC^ÚJ?KµM”ÂlF´b'‡s +§ùpðJÔtVÃÝöOH´_ßÍŸ)þGy lŠNJß1¾¤DDÕú·§¯X@ß“`‹×†ýYV}Žuƒ¶®½ÓkY‹–ô£þŸb¶]3ƒ‡ÔpFE{~uÿh›vàvJu5àtýÿ?òó r:::cL…ËCW9•ezH.=gÕµSãšÊÒ(Á$Ìç¾oP‡ 7ÖÅ”¥Ï:íúÕ\™ì†ˆQ•»:&«2èçË£GaªfB 2¦ñ>kè +QºÃ ^Z‡òñ´â$Ž?üžá1Éz¢ëe‰lÈ0 àÚ|Ú‰>]µ~¯ce­}ûø"ò¾Yõôõ±IOVèƒpQ‹­¬Ýþ8È0G¡j&õÝqîÐ;k·rÛ?aLÿ 2w`'žÚEÂJ1†ïh îq +Ž±ÕPªô'5áÇ °Úшøº·}8äÔñtÒíŠ7ìã¤y}Ì´‡Mˆ»Kw™KÓÀ•ÏÛ^ÒR3—Mú(kŸv}8„®—oÏŠ¸Fªƒ?œ“‡g´i“t±¤JìÉØH¸ü:W˜¯ô +%b<1ã½è•Oz^D!{L%vÜv¢ OaÜ ÃP‰©d±ý‘¦¤V¯ ¾ ³è +dÔ|9 ,ô bfý>Ìe ŽŽB3»«‡4ê¸ ¢»5ÉŒi»E‚˜ð+mêŸÝÈ41iiÄ©ña~mŒÚíƒyŒ"ñœòÕ€1dv„E¿?ŒÉ†]DŸº‚~8ÕDÑjv3=T—1xìÎ8ùèÖ> +þo‰Éà¦[5qøx¿‘áI{ÞÌqî0¢\Ô“q~qI*žh|E~Ïw^UÏÒ:\#å4°±V”6æ# +;¡ä†‘¶`âáé‹*þË!²Ô¶ß+rg-ŒÓïH—% ÿu¯F-¹ñ›Õ$êO¸aW*.»=ǘ_Ñ|ÌŽm[BïK„ÉýC `?·u›@ßá•´n6jj!\”‘«™:-U2m›•(+b|Ÿ­ÏåJœÿ×o®‘Õ ?‚«e$5A#¯ÀˆÎ±©Ú-8'–ã@»'^àæŸxöý:ß(xj¾K­ Ù²)È8cà#eF)øDÑ[›× p>šñ<í4OýT¸‰}uuñr¯U»®¾šµ­>'Z;VÑP¢Ÿ‘'û—;ë4Η}ÿ?šM\#×BÀ¬âQLIudOÔ¢“ý#7—‚È4itó8H$—GÓðª¶ÇåËXÂ[°è6Bã ýÙ7v3f7ͨñ&|jjx§z«ÆýªAÆ,š(7^lþà»)S .ÉB®¥„*i!æÏ +ß B–ŽnØç1 ç½á¬kŸe;Ú$hÚÞî_¬µÚWý<Œß.—ã$úÿ€>ìª÷ˆfòÕØ!Äìòäv8¹Yh~Bg®Íà4ʺÜù$9ÆZyö:K;ùdý|ÉÀÓïD“HÜ¢Õ³Jì%L{YY¶Ä¥R“Ë'p·é§¸ŽJšPÕ€£@Ü®ÌfÅ*픸›R’"89¼Ô/¯Šó…ê‰å÷##o˜ÖŸZ}¦íT¢YUM¯vÃÒ–ŠôÀ¤í.§(Z®Ô›Lʔƽ¤4£ß ¡Ì“‡Q:MtÌëwÝsþIT1NP½¢š™o_°ÌþS©[/™íZT)þO‚¢ è'ðôï½Üoñ&ÎpŽsDC°+óÎÂüÿŠÜ4±n ÜóÙJÃjkéwáÁŒ‹V%û¼FfRBjCâ öS0ïàä¬pybYý¿=°!›•‰ö*£` éöOãuÖ¶éÓÎ’‚’-ã(ÆáBÄ ›ÈvwÈÌI`ùÿì¼â£:Ë×cîÎ>ئ>nòF]_·1O¯’¸Uå¸=={šAõÕô%Ó†f§wø®V6t…H0`³ÖÎH45• ¢ŠÒƒ]Ä +¶^%ŠO&·uç‹Ãl'žœ+@=M-{¶§’R.œº×Ëð!ž¥cµ|ÜIðqփ̓:4ÆÑMqªíÎôÕ¦7“…‚”î”.¡ãyª*±nwà˜^°>•' +Ô^Õ}JGâzÌë%«¹ ™)67ÿ€ÄgŠ÷¿†Aê`nÄ‘=-ÃäÍCÁÜÑûþØ”]Ú¾4ʸ`T€³3/0ˆSV¥¤¹¿-ñqÞ;‚¡†ks03‚㧯Z±ADéÖd-ìýÿwÚåÙuTUnÖ‚æ•bµ$Nš=ˆ›àüèK!2ÈÓÃe•›º¤è žÁ×ð\¬SfšdÎ6ò˜Aòæ+ן °¡)2wUgm'è?‡Ž§ÇUW¼:ü"¦,àÿÎI3ÕÂi®É#a`ð®ºÑ¯TE %½p<Ÿâj½…Nb‰FÈ1õEø^k¸.þ`¹•¥#–};A¥ºP©æº°É„âïË°ÿ‰J'ˆi â7?27Ôt}í¶.zˆâ³ÜÑëÙ~ÿ/‡åVÁ@‹%yɘAnÝ!àû9Šø~̨†½½£´jæ[ñçeUœ@]á}Õj¯ÉÌÖ?ØqÍÏIÂä=ˆ@B +=k7ÖÁ”5Bûñ\¾µA^‡uñzÚÿ¬È2ª•Su,iÞýÃèI× +?«Ã"ë4Rb]OPtÿÐ7™eÈN=£}Ê‘a7—#à {HXð>wBè}PŽ¼ fZ™6_A&ÈÐè3$Ü€QÎÿ'„ÔÀ Ö.á"+ŽyÝwƒÁÛ pĤ¥ÝwT!¹½PÇTVEXj ûp´õ¼2ña @Ù€IÐF’ÕJ滚ÅJáX>™l¯æ×t6›>4X¯ /Noç{龟â1B2Ôê‰LÓcø¾>1cÔ‡ÖÓ”çÜÄËÁPË0X3M€×O)¼M]ú€sÅ0ب«…êÆrŒ¸~ž‘Cj™ ÂØžídt€ušÏþq¸Gûƒvqâ›Læù€0Ú%„-;š•HUt[)RÄC"R]·ÊÛ®‘×!÷3°æ:ÕqÛ]­ŠLF$ x+‚MCÙì %×AŸÚa¾Òm>óCY˜ +6£D®ÀœÇ 5ˆ!#x­pyý: T¨¶¿N«ì6äaEf®¶0ÈÉ&Œj“D´&GœÔLyMèÞP +§ù~‹*0ªTèKÚVF‚µyÙbÑo"‰ÈÇÀŽ;µ.¥w)€ä‰¸pK”m¼\_F«òÁ¼©JDXŒ.[Üš["`lØ­Ž>þ@òHö7xzk*®]ãÈ{w;i3>Ž S´x^= Ø,õ^LÒê p…`r$XùWÝ{&¤Ó‹9½Õâ5Ì2¤twR!åž•tÐåú׺ïôXð™ÝFsî"„ÅB™{;)¦¿B ÇÒ£çtixæÚ˜˜ŸN­*™C³™5Ìù¨m Ó%¼ùÁga¥íéú¬ý¨!ßýl¶i —¥£{¥déyšÏ(i(jõ)­¢)-¸µ÷ÎÔý–y ÀÃ[« +‹ŽbúcÞTá}m£*0äò¬"!*ôRåÛ7‘,>´Ft-/&“¸ÿéÅôãe/Š]¹ÂGAà•m +~F”šø7Žâ&ÌÆÅ+sýÿrõÁÔPêVZœÆ 6Á['FK +·Ü˜šÃ‰®S#)½úSdßõHÖ»÷ 'cøešC=nÀá$jO¶€_e4WÂw˜ÓãHÑŠ'zð CH :œÅ›øT*Ð@–hA½g™¸ÚJ¤-ñ s×jc#OÈCk%H\Sê¿7f}Ž…n"0Ô…¨×%ÐtÊ(0áñY\Òk—Ь Yµ|eßGÍhR$ï„+A|ƒÜÌøÞ”BîO”Zm;Eo@B\ÞŠ +-à8¹²äq x]§ÃHÀá´ù£KÀ&{¶®ú•¦M]_ë"ºÈ¡Œ9Ê!.˜;-À—ƒâJq°kú»¿^;‡qUÕØ 2ß㹿¨¤è‡WŒâ¨šuñ•Æþ¯øôlì-?Ôd®¥lOƒÚ›ºÍ꧛ڪÈ)SîƆM²X.1l]¥_öçˆÔ茥²ªKºüúd“Ó§òΖO®06¼jþHÏ-¢EîO/Â)Û)o? /þ$°r}Ä’Î×u€âd”Sz2:@“t@_¨0'þÞ÷D[ôÙ<³‡"a$?õŸžÉYÆÞ§í$ßO*•ûÞçNI7»J×ToŒu:Ùæ‘MØC +i¦ôJ¸Ö³ð;“ÕµFÍázÙ7wäùìÇ>>>ö³ø' ¸«U•­.RLÿâ2ÓGr7ã8¡ú"hâ?9ôo]Y·ÕÎ4ž¤¦Ü£¥ËsÌ’«-SÞÓÑãã°­q¦:®öÞYÄÍG| F*ø\þ4þHâ’ ùE(ñ‹Ñ*ЪžÐ°Êa";™+Ú“ŠâXX}çr“ù•ŠÝ,}·£ ;4½ÎÜ5Cš£Ñ»úLRs¬™_vˆ ÏöeN¦JyÖ2çÅ­Fb.Ìd©Õ~À£‡­Åë iWoX,Ͷ.¯”aNÔ ˆ×êvÌ{¢¾ó;;ãvi^^Dôì•[ˆä ;Ä ³]Vˆ.&[Ôÿ6Iùu£.Y&ËÔšj]ÈÜÇ ãEKãD·†ÄÏÖÞvÚs°P‡\e‘hp¼ûù÷·Kâwró–;ž•HÆÐr§"OÜ€(X_ƒsºC<]×Mþ7ó¤n³@ + +‚ 4ñw£›c¥‰`mØ9»¯BÂäñD UÃS[iV=!²ÙÙ ž„¿‘1j§SZMÛ?ˆ¬×åÉ?‹ðLÒé…²‡àçFÝâ´w¦)r$PTÆF`&ÿ¥%PDÿ“âÿ,VI5Áì嵨b”“¿ú"—>hA÷eÇ%ï; ,åfl`Ê6‹ãú:@ìQ2ë†.(="r 5ÛRy0Aô 5P`äÅŽ"h©9D%#"ΣžqøØ÷Øk]›14\Š×d>è~¼#O>›"µÛfõYhG<^¸¨wgôÚ–%w‰2ïäÒ"ÿæP:Mâ.ÞëB­\ÖÀ¤T•ë•ˆ€Ë"mVë¼ÈÓÕHF½4/‚G9ÒÆ[§ôÚk©šèf„¼rÓ5VÕ¶eZõp#=†YqÍÚÊ 'ühq(Dç:"ªmIÅÌn-²k«}2»½¤€Z‰ÎWèˆN¢jkõ«,¨Yi'á9×îpÝtuc¤[΄¬6¾¿ï‡HõPôA˜”ä:j1•6h|LL¢lé'/Å´‹îojÁ¡´±Œ ÑXû€HÓpu ²ÊäÑ8¦U6¥Š1küêЭ‡\¶&›x\|­}b enÿ´Ù§~f'ø0/¾ÉÅüÜb ~Ù©Ô¾uZõz—v'õ^—ZO±ö‡¶á­7 w)hŠs1‹§Àû½°7ñˆÈ—^zð£7ïwY†/šSÅE&µ‚¤ÒùwkNÖ†+_ÚÙ¿Vê‘×m['ÔæнK*®LÒyà……CÃ?-Ún¬€Ô©¿rŽCÌ@5›æ’YbéJ‹o{ÖÖÀ*eJ>ü£Þ³3N¼“žùÅ°ž«\ÅþámV²Æ«ÂKwuƒcyבI$înß–2¨°)NË?ÓI­½„””iª$vãKŽu³ßµ1á,ëLe½9¦6]=Iâ}ÓEªÕ  ½pûÚÈ×Ú<¢}$Ë_š1rl|™ CÛ^B¶Ét÷ÐqóY‹r¶CAV«è5Ú+0]Òhì¦á]’е¨s|;—)¤«;Ñ=y'q;oÛóQgÝb"UJ¤Ì ѾxJ¥§š‹¬’T<µ)ÜÕÄaûšh ²Æ®ÛÉ)²ß{´90,þ¦<윣C¢Ãļ>ÿÏÖ²¸¢GÛϯøá7Z¦HéÆ¿æG(f!˜8‡âåÎÔ€$6f<øžC!/ñÀ?¬îX5“°Oóæ¾)IÆ~´|¿¤aêÅße§QkžM23J¥ +·`ȃ&<2˜AL0Œ uîêÙª÷\†aÄËIÛ|àD%î@L{ÔTÊo›do\pͯÈõ…qÊ1hÛ v¨ô¾læDEa0Ì•àT¡HᎠ+ùÏhÒRb_~m¶Øá¿<+±äñ¹Ÿ4ØÜD(ùP÷ò§d$B•:rðèc0‡WMA('=%‘ÖFô·;í–b+¦â±ñ5ÁNY&ï%b…+VæP”»Ý´ãåöžË v8rÕ¦ÝûÝf…“•'@9x„…*¸l4¤ÿ‹ Z0”°ycî§Ñ ®ß +~çF¤uoòÖz&|Eä¸>!ó™ï؈Dty±F¬ÓçCìdß:r»È˼CÊ‚vz   ×DGÇ1΀ o—ë9€ž¼ï@i€w9*ší6zgç À…>²šiài-ZøİЄhß¼E-@] €{ãøºŠÒŠ™É›Ow …¿„€—,úŒfýmVÕ›éAûS·?ÓϧÚ;¾HíX¦¹>’¸Ôn9‡‘3‰̎蹄uÉ™$¼l(¨´ ¥@‹˜ÍÂ1¯©”dóàÁË!^ôºUZ³è¸ñÐ4½Šo¾6êÊîÚpì÷K]êÀj Ñ)_¢ÑZ6Ç-g&³w¢é5·°ú¬ ,OäÔÒ#÷Á šÉµ£•ÈŸþßwŒGêcÊ6’™2tÚÛÖNŸ>!,ü…«ãò™œzÍUMÇ"´—tfdÁ´q-ˆÖ̳©:²¸©@ýoªž@ å.äâO:^¼Žº)-JMEˆ¤Aé76°R~=áÖÇ+±¢gKýy¯L¼ð¦om‹²š³¨r`í +w=å¢äÿÛ1–¥é§¡ÒÂ΢G5úø7<·³ÒpÇó»« “F±ÊêyÐܸa@f¤Ø,éMqÂRÉuI ŽýDÌ%S˜SUá¢F¶Diö•Vñe—à…kYÌî&  ð%³x͈‰)¯ÍU RnFäG”M@¢ºÒ‘qPr1­% ÆœlQ@À¦ò´>—íË¡Mƒ nçd¾0 ®pÂj|ãüuP7pÔ,Qy(‘Añç y›øy=ÄÒ° '3|ß—b}¾L׺¬¤–®í‹È|д.¶uDRjs$óC¸ùR´©ÁÇ\ÓvHj5RDùÌ1²ÖÁÔ… ŸD`ËY”1Ì=¥þ°µa@†?N¾ÞküsÚð Xy–Š¶·)aû¯÷+‰OŒwð³#æi¼¥7W‰|³hqNT;¯|ÂR†ü:¶çÈ“v”†mæ¤'ãM–"Î%Ñav`\ ÏH–užì¤î¿w$Ú—íSI&¸?xÙ¦»oÍÆ£‘í*HË#O!‰ü3Ý´{«'R”n𬴘 7såîbÂÈ—ÉLkôžºU7_+ŶüD‚x}B¯œYÁÙ:Ækëý-)T FgÖ4Ä'¼‚¥ %”¢8aSÛÊÕk6BÃ#À¬ˆön;ÃŒÈV`"ÄC©+Ù ±øø+:ºlܺ„ £ájƒ~Û_2X©9‰qö6$³ê6ŽÐrzn5a½¡WÁbHvn>ÆPä1‘ï3†‚æjzpl8ÿÿwêó 3M!t2؃yÕ+"D;™b0ÅåQ½^LÉCZaïm¯vwL¯cX_ZX÷RÙÈ;xÆýøðþBvaÇêÃ0ïÆd‰mÚ‰ €™%˜Ùå@y™JTáÆ›—uþCò,Ýö•uvƒƒ˜¡Îf!ž>5ŲŸÛñ1MaùÞƒFÒzÍçu÷UÖÛO½uüñ? ¬ó’¡¥”‚>[œoP¿×GܦçñRyTÏÆ™q£K÷).(¸„”CÃ)±'÷÷ÿ%+׬i¶³‹ƒZ+EGÈ„ÏÎýNdÞõÌuë ׄž¢å”¥ÇFÒžg/‚´.Ûÿlg/øï*²xƒ§^Åžûœhö‡.s\Fì°{FøO£:!U³Á„V3óüjCé¬Y{0PGô.¥ßòE™™øEíÕE' ’9P¼ªÍ•²v (êÉïÆ6b8&÷«Î Ôåã.e\Ïô<ÃeþE¼µN'¡KZ?Æ#ª{›¥'ÄáÐU0Ç>aþs'.ËkòURrËs»cÿÉÖu>%U†ºˆa#§¨<¦xjª%Ç3>¾äͼC[1»öL ׈Fª3?ØPá³õ96üÎ? 0õñ748í¹mî!‡kd[k®Ü­ÕUi#¿G•"óñÎ8aR§ûÄûÓÚÖºÞ„Xg…äZÞ>õ«>\fÎXÜNΑĒð’´A Í ÊuI¼™€ÝÙN>e›9ÆŸ…è+¥ÏîÈ[èPî[M´!—õüBÝ)B! án9Ëpó›[ç®×¡"óA×¼ZïkØ’û²z$¢Q«vª0’ý-ƇÁ¥ ·Iú÷¬Ò ^å*c¿ëÜ/)!omÇ<Ó-il9â$Ÿ&È9Û’Aä ©à&…=…¸´äCçØ‹Vˆ\c»f‡‚ë‰Wù8PwG…… +{ÃN ªö‚$# ýVcU° @£­â,æ¼KµN¢æÄEÿžO€¶Žòçã/ÈëîFî¼UNwŒÿ}fò¶WÌšÜ9Jš—Ê£·~èfΦ|~QéÌŽGä}0‹«Gô:3î:¦W?<æÀdù0§``ê¿·€¿Çt§?s"¨ê mQ’™ùà*Y…´®#àâ#®¶"œÐ(Çpÿ¾7›)Xzyˆ‚õ`j*ÔRŽõé&×úÄ*³LÝ °:í²Ú=_A·n\0ª¤x-vÔbozÜ? v²*+ÞèûXbb×·O4¼)÷‹/Ï>ªôâUŸŽß¢t:ÒÙîOÓèæ:R8Úé x³Íô°.ß»dŠï7N[ÈÄŒ3V)¯uÜ©‡ úiÈ7;Q˜ÖÕž-„pú瀗å×H– +ƒìEè¯Ì¥±WRÑ'XxÄ-Š{ …iÅdF¦)ßô¾<ÂN3bÉßÓA:Mû+DF²tÈg8•óª2¦—¡ñ±;e Æ¢ÊèÀJ‡ÉõQ+—ÈtCüøéÉ÷îwY¨ ŒðRN˜üÄã^mâB²îJGÉÍà€³Ž£þ]%&níèY/×òø¯—Œä†…,Ù +“D7½ +7ƒoi‰Ì`Nžäõ zÌÀˆôF’LÜ^s\"Ù&”zNw:ïÝáAWù Àu~Ó;òW— Kj.NÏ#XlÍ¢, qrâп߶´rKáŒtnõŠ-g¯»RŒË†`iK{wÃú*U ýúà&×ùŠzRÍ‹ó³H\†ª¶ñÔ|Á]†Êkô¾½ ΠÝht‰äa©ÖXZ8°S.GJÁˆô»»Žâˆ`:¨‡tð)}N‚Á’)fÈÕú-?’†´i¦„UÖï&X¸Ÿ³¿÷w9ÃokÂ]ú±»Ô•g3ù{ÔÅ(ϳ‰ÆM3( Lî%#‡?4‘›\.£Æ{H ;?þx>é$ò`óðù(­EX\w­X<™æ%ÞZS¡WÈI[2òïý—:»$ï)´/Iï¨æ¥¤ài ’ +Ï-#ëpQÄ ÜÓ€YbNM•w¹G§ )ŸdËZ¸(Ã9$†eÜdŠó¼q ÌàŒcþÐÌ•‘Ѽ‹óÈ/î2ÿõÝdÍ…Û>ŽÓÀ ¶=õ¡bõ™£¥Êë•´DedÇ(=?B¹ßŒžúP «fŸ‰p«zÕ‰ÛÖêÒOöÎn­ Yí¥ÌŸï ´µ¹ÆƒøX/°ò½@v\•«qµ%š²oFÝçËÏ«õöµè 8ê"3øÞ=†žÞÁ›TLÑ¢5º ¢Â…Ä=™ÎÕ€|.áÅÿ¶¼•â>蜫"0K ]V>?ÉùDO Ç£zZ‹Cß6l«EypÅßfq¡Y¤zƒ÷÷™R8£á•àbn®QÜ¿þ.Vx1:#ë®0f?ç'$A‚…¸è¯'ÁÞro½©óôK*‚ØŸÁyM'óêe–6„®yG™LÂëi©ó#»î„5WÍòÅû¥ß3¯DkžuÝë¯N¥BÂ0’§¶KV¢Ø²®¸`¦ê.7;õæ½ +œ«“Ì"’R² pH1P.¸±úkm‡¥þ±Vš„çy´VÔÛ†{` „‰yV±V6žß_¦Ð¾£—ã5C£Ô*}Md`M“Ëi½Hºž…ˆ! :.›sbBø:½Vs$Š¬‹*Ê54Aÿ7ú–σë†.OmQØ«üñüj/fB–"Ñ; rreO}ê. 2rÍRá¯ëR± )îí(ïùú+ìÏ"¡[Úh-¨.ʤñzÞÒ=¥›hmÆøåBî€fKÕ(@D º€é ¦ oçÐlÔ:ôˆ~Ë%ãû£íëÁÜâAÔÊ7Rð€vTðòLç_qN§$ˆ0r3©PJh^è·gj¶Ê!™Î=ÓíÁ¬ßÑ­ ³Áktfä%nãÍÕ´ÑÁÀíØwxØü5ënÞ¨ÊCF›Æºú€‡tÅ領͌j ý­á#­ë‚†«wrÃ;é°±ŸÅ<ĸÅwµS›lÞïŸù¢­Ÿ¿ßãvD5Y!Y>pë~½a[rÒÝçã³äAXþ¶/Ý)G§÷qä x_G£¤ADÁxƒ]Ó߸tŒÝ.–ðÐÎ%Ë=g»ôãfL#uF©ÀÿOz†´O)SŒéÏq¸¤lŠ´ f§ZL©i‰ì¶ §²)jÒ(g£¹ÛÙ..¤gÈK$ž)ˆxW*¤äŽxµÊtá¡ãc÷àľ¬-×ñ·–æöÄ©ê²÷ç“Ï`,§ùL±/å^§1üvKw·öy¥iöˆ6[‡{{F²BH€ŽŠš¨/–Kö`bõ.Wj„NÛ‰Ÿ}ÙÒÀÌ´J•–ó:ØßvSïÌÆrí€d Ó‘W>¹ZÕ‰?ÛÌ»w¯­ÍkŸ9=ÙêØ„Êç¦ã¹ˆ”eb›({úD;Á3´¹/ıɓ+SCŸ²ìÛ)!˜½™ø£ËNg·qôõÞ%©ïÁ;óþªIÛzÕ­ÛŒÆl8fõ®ÑfaëŽ$P$u2j}QO&‹ílj‘|$G>Y:,l³êáÒ…B´T{”S™-@¶.L‡€E@ùZܶ¥p}\5fô/€…z†žvxa„­cx.e-.ŸJY¶tNj™Oê—MI +Yüg½4Ø#ÜR–8¼aÔ°ž¾:<•þÏËå´£‡f™I™Ê\9õ’¡¢ý 6¸1;^_ÚQìé^̵­júŽéF±zÛ_)qT\ˆìòT9ÆÁgåBWAÖ}|[`[&wÚÙ”ºZCœ¿Aí,÷“38§HiL0%ñwñ£…)ŸUm½¶âëôy¥X Ë‚9J€Í½dšJuŒKÄ×Aão eéϳò%[é³;„T›aÅHq +09È‚Ò"»-šIT*lªß¢N]pyó܇;7i½`󄚆RÁn˜¨Û@d»3à¶Á endstream endobj -111 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 541 0 R -/FirstChar 34 -/LastChar 121 -/Widths 542 0 R -/BaseFont /UBIZKK+CMR12 -/FontDescriptor 109 0 R ->> endobj -109 0 obj << +524 0 obj << +/Type /FontDescriptor +/FontName /NYFVHV+CMTI10 +/Flags 4 +/FontBBox [-163 -250 1146 969] /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /UBIZKK+CMR12 -/ItalicAngle 0 -/StemV 65 +/ItalicAngle -14 +/StemV 68 /XHeight 431 -/FontBBox [-34 -251 988 750] -/Flags 4 -/CharSet (/quotedblright/comma/hyphen/period/zero/one/two/eight/colon/A/C/I/J/N/R/S/T/U/V/quotedblleft/a/c/d/e/f/g/i/l/m/n/o/p/r/s/t/u/v/w/y) -/FontFile 110 0 R +/CharSet (/A/B/C/D/E/F/G/H/I/K/L/M/O/P/R/S/T/U/V/W/a/b/c/colon/comma/d/e/eight/f/ff/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/q/quoteright/r/s/t/three/two/u/v/w/x/y/z) +/FontFile 523 0 R >> endobj -542 0 obj -[490 0 0 0 0 0 0 0 0 0 272 326 272 0 490 490 490 0 0 0 0 0 490 0 272 0 0 0 0 0 0 734 0 707 0 0 0 0 0 353 503 0 0 0 734 0 0 0 721 544 707 734 734 0 0 0 0 0 490 0 0 0 0 490 0 435 544 435 299 490 0 272 0 0 272 816 544 490 544 0 381 386 381 544 517 707 0 517 ] -endobj -541 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 34/quotedblright 35/.notdef 44/comma/hyphen/period 47/.notdef 48/zero/one/two 51/.notdef 56/eight 57/.notdef 58/colon 59/.notdef 65/A 66/.notdef 67/C 68/.notdef 73/I/J 75/.notdef 78/N 79/.notdef 82/R/S/T/U/V 87/.notdef 92/quotedblleft 93/.notdef 97/a 98/.notdef 99/c/d/e/f/g 104/.notdef 105/i 106/.notdef 108/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef 121/y 122/.notdef] ->> endobj -107 0 obj << +525 0 obj << /Length1 1144 /Length2 6097 -/Length3 532 -/Length 7773 +/Length3 0 +/Length 7241 >> stream %!PS-AdobeFont-1.1: CMTI12 1.0 @@ -10221,13 +6532,12 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /JOXOAI+CMTI12 def +/FontName /BABWJL+CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 45 /hyphen put dup 65 /A put dup 66 /B put dup 68 /D put @@ -10243,6 +6553,7 @@ dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put +dup 45 /hyphen put dup 105 /i put dup 107 /k put dup 108 /l put @@ -10281,266 +6592,420 @@ XÓ· ±œ5Æí[å%€¨atÁ¸’¥æý…Lo*-g£ehAZéÔ€ÜåN~:öhÇ–Rã{>*_³Û›ñ®]Äewã³Â-£›#¼'úåU™N€Èvk›Û9%*\¶] ‹ÎÀ'ÕˆGÝ™±[*`Ð8HB".åÆJ·¦=uÓ&LöŽö{ªœxm‡Äd[­„1§˜°Üy h}ýÛâ’™—clœáÓ xî³P”7…%‚•„‹Óç<4éÏâÝ«žP䬪F…ÍAj™3È"¶™ Øm×8ZÚ}!ê•z÷(°ÅM ézµðCùìè°]½üka,¦îÿ¿«ã“[&*+¬ûS˜~Í9$@ÖJ.±9ð,!uàúÓ›^N‰ÍuOÇtl±¦fú%2u~#”²ÉÒš“?ã=ó¤¹*áâ½3{ÆÙhÕgyp‘#MRã ,ºÉÚ¿›Ãƒã[‹¼yz]žšSša½ã"ðàÄÌ1uÚÂêóýf©Þ^±Ç»Àäcš_¿Q$„GWèUI3¤†X}¯B×ÁùF1ÌÇáö³¼áO˜ ÈÁÜ„h¡»mò÷ܵ6ä ïa’U¨Êbfýï>]kÀ™=«ÿóO`L§ÍtR¶õÿdN>~évœ-Êw½C':‰x¦úd 6Â^j˜º¬s ¹u:(A–8vQTõ¶0ÐA¶„š‰’€fß(FNC»@jò”U’1™Å¾Ñò›P":µZCÊdÛÞ¸£mº¸$W¿çWØËÞ¶7—îÈ+X_÷K …yK5£R^ýÃX$‹œ1ÿV#ˆÒO2ÂÝ>™*絶Óêÿßph!Ýù‡¦{W.g~ƒØBX0tö"Ü!›»ÜŒIŽhªFŠäKpÙ0­ÆÒ\«¡i綀ú«^Uý¾&o¦¦e„G Y|úa‰žfe‘F*¤ð}±Ã^ -˜GDðïÛ+„âY‡ž|jÅX…GíÛf- Z™ƒSRs Å« qñvî’[bõ=í¤áoˆ‘µrnúù´µüîËÓèãL€•RÛ¦DÆ7oìà0n*X<»ërS™¾â ^'×N‹”`8i›ÀÚ$)o/ŽŠ["8³4²Y®aØcßèqn T€¥2ç>³NÔ©åÜ9È Ȩ×ÀÛ•×ÆDsÒc¦žñµð0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +˜GDðïÛ+„âY‡ž|jÅX…GíÛf- Z™ƒSRs Å« qñvî’[bõ=í¤áoˆ‘µrnúù´µüîËÓèãL€•RÛ¦DÆ7oìà0n*X<»ërS™¾â ^'×N‹”`8i›ÀÚ$)o/ŽŠ["8³4²Y®aØcßèqn T€¥2ç>³NÔ©åÜ9È Ȩ×ÀÛ•×ÆDsÒc¦žñµð endstream endobj -108 0 obj << +526 0 obj << +/Type /FontDescriptor +/FontName /BABWJL+CMTI12 +/Flags 4 +/FontBBox [-36 -251 1103 750] +/Ascent 694 +/CapHeight 683 +/Descent -194 +/ItalicAngle -14 +/StemV 63 +/XHeight 431 +/CharSet (/A/B/D/L/M/P/S/a/b/c/d/e/f/g/h/hyphen/i/k/l/m/n/o/p/r/s/t/u/v) +/FontFile 525 0 R +>> endobj +527 0 obj << +/Length1 2088 +/Length2 13404 +/Length3 0 +/Length 15492 +>> +stream +%!PS-AdobeFont-1.1: CMTT10 1.00B +%%CreationDate: 1992 Apr 26 10:42:42 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /FRDBIF+CMTT10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 97 /a put +dup 126 /asciitilde put +dup 42 /asterisk put +dup 64 /at put +dup 98 /b put +dup 92 /backslash put +dup 91 /bracketleft put +dup 93 /bracketright put +dup 99 /c put +dup 58 /colon put +dup 44 /comma put +dup 100 /d put +dup 36 /dollar put +dup 101 /e put +dup 56 /eight put +dup 61 /equal put +dup 33 /exclam put +dup 102 /f put +dup 53 /five put +dup 52 /four put +dup 103 /g put +dup 62 /greater put +dup 104 /h put +dup 45 /hyphen put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 60 /less put +dup 109 /m put +dup 110 /n put +dup 57 /nine put +dup 111 /o put +dup 49 /one put +dup 112 /p put +dup 40 /parenleft put +dup 41 /parenright put +dup 46 /period put +dup 43 /plus put +dup 113 /q put +dup 34 /quotedbl put +dup 96 /quoteleft put +dup 39 /quoteright put +dup 114 /r put +dup 115 /s put +dup 59 /semicolon put +dup 47 /slash put +dup 116 /t put +dup 51 /three put +dup 50 /two put +dup 117 /u put +dup 95 /underscore put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +dup 48 /zero put +readonly def +/FontBBox{-4 -235 731 800}readonly def +currentdict end +currentfile eexec +ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ_ùc‹‚2BžØ·Ïj=‡š-8Ý\DgùÝŒ] ³¦¿/%b›®Á™®‹ÔºnÙ»÷Ú¿ÐáSº±ÁyÔüâ b*ÍçÇL(Ð9sWí«F Rë:E·¬Mks­ƒH…02§Eô”?›Oíe+ƒZ¤—'¨´zÿK΃µ¶…–оi‚·f Ë<àÂ,¬ÝE“òDÁNìZ|JÄ#’ø¼BWþ¯3ô¿ê‘ÿÏ—MÖìp¢ÄÁäó(¡ë%ä5%ûÀ~(Ì5öBk}Aêj „Ýc'S•¥ªéáÈ-8ŸÑ*!èi™yž$©”G.¡®w g ¾ ªÒJ0Ùn¥r +û;Òà¬Á¡ Kèr^×ã©o™x¼7p4Ù= C‘åyÃOùü#yËŸ[¾©â4éê¨9'nÀÙ*¹xÁxÛ/J}û¥oÖ¯†pë6OÞÊû¯e}hà1‘W6Ϋª‹¥À¬%(ƒi]I½‰«ïèiš +ãí…´ŠË""žb3™É=çÙ5sJÚÚzbÁÔJÕ>£[Wåеü H ä2"ÛŽüÕÓùº0O¨y9.à¼Àá¦t³¡ü:=×$E€Çª Æ]t¥þoŒ¿`% +Ì'EK¿—ÊKœƒ¥fr•‡RíK^yá†`vO^†ðžúŸv…òõ~ÈZwR‡³ iÞNMWçÐ3HS¢p+§T,q!s0Ï(عÆ;U–©´+3çÙ"”J8q3ƒÓdŠJñ`£°Èó7›¤7+âçêIªºu®îÅÝáØ¿hH<=!'€«¹TÌ–€2.«rá% +v ÈÚrdïä c[[ Hu,>’½àdÄ*,RŒŠ`8'ξðÉD À4ÚÙÁŸ²}³™½®â SYe8X|vŒ{ }"--Šó¦G<ÄÀÖÃàÛIŒëŒ›ÑÅÍHjPÚ¡ Ç}b†#UãòÒTâ|ÄBrŠ ®ÉÓñzéÎ2 1z,æ¶.R/½ó÷Ñ ‡…Nk³ß}~i‹±|Äk>dvIš—ª¼‡mD‰‰R•M&·ñ†OTÏ`Ü¡M”ßæõ aæXc¶:rNê…S؆–á'GSkˆ,¢åÛ Ä>a càÖµpeW¸1“J¾m=Ì6·dgae­Ÿ·R#¦¸l¶/`˜Nj5NENªžÄ~QJ—ÊÇSYm#ØÁM$Ú÷ã¨ÿéË_#ê8ˆÙ˜žw¶É 8H¿Èž2€'{’Gº× [þa%ºQ†E%1µº”l$ûks@+Ê¢·@óU³4ëx ®R3óO×ïè¿šš¦#0G ªL + G(‰‚»Å•!8BÂcÈÔzœí^‚¡í<õgC]µIœÑ’Œ$v´½Ô>4«8…ÇG‡`xÑ°N–¸çEò@ÌûPC@€aø9gà­.7ÒQ‡úŠÆ$à»hWøû¤J\àÚUÐ`Óz„¦§åõ›¿ ‰< )ÜÉQÅKÌtïX’cs[§)&:SÂ[Þ¬¢]+39n¨\q•¬¼“ñ¦xÖÒ†µ 3–Jœyó>Dg"^ݘ³X4dò{ åúãÓh‹s¿KA_”éË&ÁF05nÈ—=È:#Îãê7GÛ…Júp\ãSž=j¡é48Ä¿ìIÜgi'9óÓ)2+$„Þ¥ÃüÙ\±†Äš»Ò®'çÎÈ°;Ó cE§¿¾³ÜzŸMþhi®å#1“P]+îä>áûN\Úr®®€&fÁÄB¯ób­f›³šI) h[&€²]­Ú/òŠ4ù­¨Z¼¶îµãƒùYÐk0°&Àgv£r¶ï&×Ýtÿ¸AØgDÑ=Q:ÙÂt`{0ø¡Àa¬ª]ÇU$©qpÌH«ìs¢S@%%üÂ+tv ¶ñ Eÿu ð$ïåÇà`”óÐi ÷3SμƒúºíÃVÜï,Vw-a?vgª»)ô÷K}ko†üz|¯n«B 7mÆi”k 8Ø[ ô¡yôa ­·©6o!:zÙ~­üù4…]:1!jíôl0ËRlæ*aÓAƒÎ-d—~Ô‡ %Ë~ôØn†ó:†™ ‰•ÛqK‡V“Äs=ýÞ-0üчg#}œ$;ÿAKðhjP½ª#Ué^¡ÝŠí8¤u«¨fiåÒžæÄ6=]êŒL|ï¸\' Õ‹ŸOΓY©WîÛ}@<´~­c3zÃEc·!ï±ïN‘¥jÛHßÀÅß Ê7ägjð~Õ…Nø}Á¢8Áü`Lå–4_R±ã©ƒ`pJø[ +¦6>ùbE½©@¦ÝGG(è ›&¼â6GqL\#Ç¿{Ê'2¨:´ ›Ë¦•5§)!#øW:tÄ)à÷ï1¯%à“@¹gŽovØiåŸWv0Bƒ%‰±ºŽÀî¡ÁÁÕf©m§šLgìP$”Ô¾TGèhþÞ +†•þšwú|=ÏŠʼúh`@eã•’ýDË–­aûr&­|£[J ߀”ýæ ÷ìïO j®'þFÈÓÚ™3æu°ƒ¢Ð§¾¤;ôëÿLÆ/ËÛ7)]Ÿú4·ýAb r´3‰,Ì–‚ÒI’M’¥”¶.I‚v6Ãy,m²zɱ ~èúËŽþ»€MìT1ÈŒò©f…øÅ‹ƒŸªúèÏÍa¶ì€Ìíö:Šô¼/̼Ö±‘Èœ¨ 'sòÃ. +)G X’ÉÜJ»ñµÃytC÷KØ]˜n TM—ew©±–‡Ì%ša{zs:o óú;L“@ªð<¿tæ–"ÊC#6‘ÕñÒ– Vh8'yòo¶,c ‘/}bhM<Ë©ƒõ›K7_ˆœ2×9MX#›Ì†˜vXŽmíᘥsÉ|PÝ1ÂôŽð¬œÙæ£ibÅwKÔ‹¹ÙXŸÆ¤;^UCOqårò¬6ÂÈF3Ý>’u˜¡ÃýM‡0—§&á:óJ¦#n•ú©5„ºÑ‘çŽ}¸&»z÷]ö‚PÊ¡¯ð5#c¥°©Ü­´MØâ«ÍE³ôVIÃÅÊÄÚ„dè$”Šöt¯–ÆÇRIØQtñ,šž¿§½D%žö<³:´|–¬ÊÖîà(%IT 7ý©ñú1 ÅJLg3êþÝiˆnÔåîÂF&‚[Qáî^—rV_ŽWv4T=„°² †Æ°x\³é°@RªU©¢u'*äšþR¹.4¶€p˜»'‰·8G{ˆ)ů²ºùâÿ )¿µ“ þ/„¤On.¥ÃÑyQ+9i`ç¾·9£øܤ*ÛÝ–vWÈ¥ßÒ"ÞæÕ´–‘‰;Q$Ú¥óºWm˜‡Â2¶¶$o¶_YyÓ\Ø Ï;›S34zÍ2=õºQK+GOYéÂB©”µÒ¢ ó_qX¤û¬|’ïµù±½×.p|¼JôjšmÈÒ„ü´¤É¥¹ù î‘ÑèÊ´’õ.£7w«!J4°a]ùÖö¡¶o +BQ2^m¬ü†*(ïpð'™¥P3Zé8¾‡º«S¾cðJ*Tô§2d±P£”¾¢d µö…è5‡lÃúa*/òº Sßïõ:¹ÕS¯àíؾça¡| ÑÜìÝËÍ6ùÊ_ßf,üÈ—zÊ%Î3| Uù £zVÖ5áœð¤ªÓQ jq2# ®ÑT£_x$¤â¸[ii Šå4ªŒj¢£J>¥åËÇcÖ•:«"?uí[yŸÊF)Í•c²Oï;uQäë;·{ƒÅ£´Ëürú(­å¥½m„v/cøFxsíëGDXˆìmøß~ã¢ØÔ¶9,U‹nŒñÄ®CÝ’ùf™î>="#ŒˆøBÑÓ‰‘2%d¼h¶ ÿ—ÞºÒVH-„Q)?Š•<ÈÉ¿Þj®ýç‘æ°ŠñÌí03þ",éâƒ'?×æEœmôÇwß1ÜuHµ‡tu}|Õì–QBòWdàQf,á[Æ°¡š#dÃâ|°muVc è +‚™F%«ë†x‹íKØÆ•:8|s,È&D¹ŽQe;?ƒÝÖɯ` Þá^€÷é (4¶m/ ¾?p€µq6ûöváÛ£±èÔ}…¤®%=iLì÷[]ÓJ/2v×J8FÁËï¹ÇBá'ño®Û\÷ÓQJ”©jºÝïÿ.lGò×òt$À¤›*iT2´©ànÍ$ÇÌè]™KtËñîr‘ŽX¹Û!¨V}Âriçéܺ¸5D;sº_û>N¸òb8€ž¼ÄY¦opUN‘Uõ' >VàT ‚ùq˜ÁÝB1»g¯¼¤„oq»üùþé—uõhë¬~ö3tO3—÷iŽ4=«BÆ×ö]®Æ÷gì8D6ÿêæÔë©L|W~ÉK?LÔ\™ÞFç?iæ<;ŠJSýLS;.ax—ñ +-ë¹eÀS±lSV"57Q§:•]-¥ÁÞIÄo-pÁÌUWøÑb;âùÖv—$]ÓFBØ3Óó°ƒ!~ƒÅäªâäGS )+C£¥P&œDqÁ݇ËÏÜýÎrƒEUž9¾¬?£ºký•ÕÊÝÑr$F+Ö)¦ßU)ÙŽ{x…gc'¿*5Å‹õ>èäv‚•c6¶õÿÐÏl%d‚ê=³ÎÆÏáN(2ÂåçGz0ÃGcÏ÷€ÎÂ>cX±”Á—GRßî„*/̸Nkë @á›ãÑókv”md¾Ðdz¾žýj£ù¤ÍÂ.é Á˜;+ÚÎ×K³¼3íð§3öþ'ìI15˜DŠ÷ª%øh›èw"RŒ§Ø'Ü¿ÿ{y2uÿÁwtÒþ¸uÌØÎî‹æs[M͵ó3Eœ:!Þ±ªw­¹'ëG #{•ú¼-{¸\‹qróäQQî7i¶ŽýÙ¼yµ¢g‚e÷rt“Šéß@ß +Ã?⿪òÈù‹™_ÿa‰z®†Åàˆ-L7„G×BÞÄDRlµ¡AîxCO0bz¥ Õ ¼AQ·ìY6>×Q¤RhCVâ$ÈÐʽòú»ðO#U[§ÕüÌ!â*°Rá_³ÿj­ow“YW«¤½dvÇÕªžÉ;:ãönæL…Í4ˆç–Bòl©¸‘ää3¿MìjçóSCüL+úa¤Û²Âéä±à©ôÊbu,Ú]ôÅ cp²©ÌT§É‰‚!Äõÿ𛃌'₲"Ú)ú{³ÆËOK'yz0'Ôo|.®X0Íq ãΑæë’™b jB±/h‚3B”à9tŽCùåO©Ý`É¥Mi“Tè€Áhýboæ›R¾sŤ +q;–TÁøôxOÓÁ¨ÙÒƲµêXCpƒ:€¥$ ÏÑBnÒ +m¡”´¿Ñ#·+V+J>ìÂ7kس[¶¾ÑóýQ_’cÒgŒÄ.ó’N#µ“'õüì Hò¥¿±Ö]K8?>b¼Õ`‹¬¦[zªŽþæ/ç3 䮀o£'¹*›I¤ œ,Æ€hì8Z¨ä¹ñúnË.c¢·¹²Ìį׺ª®×™#l·K½²˜÷¬g. +Œ4ã#d Kñ€X–ê+jν Fû¶­ßO鉎•çä¶Vmß››x„ÕSìõÉžW¡TÆœéý5Š–âå6wÁÊ®‘aztA¯”Ü‘;}?+.¶ú¯ÞûöÙ\¿ù䃻c-³JuG0xHÙ½9MªG"¬?’M‹í‚ Å| ®‚5h󀺽*ˆ™{Àso‘q÷•’Û[=ËûÕŠF{Wñ ¢„ ¡j%¦Ïòf_i »fùÿUÞ„¨sœùcp¡©¡<Ö¥TTX +‘«jNõ8h¿–ac]næßÕ}O}ndO÷ +±ŸÅÉùËîºÿô5Õn±O^µñíxQÓêTwÇŒÛÄÙË/twæ°ÔLÕöÔQÍ_ñÍra¸#¿9…¯5¥˜¬÷TÜÚøµÓ}Ð g7qtˆØ¡\ˆÙy}O|D•ðŸdˆpcç\AÚÐÛod#”2è§~¾³dÆ" ¯yÉ’Ee¾œ\“êBînq×ïçZ0JT[àÐÂ=Cž­ÛTò§¦ö³Õ/K +Wš0¡G¤­ Ï„G¸eјÒJ¤ôðÿWYÇK\¹›»„WB*j³Æž†$XBk‹z8'V«Qn`e¼“Æùó8‡’O ÞK?•…n'ðÁûz\M|¥CžK ÊâþnI ‘æ‚.2Ï&õr©:oã0%h^’Tÿ=™F583|H1ÃðJuR˜©8cÉë' õòœÿC]Ç$WH»Çħq-#ŒçT…;¿´l%{df‚¯jÔLÏiÙ›o7å/ ¸z)™Ý Páä…ÅôƒÒÚßF=W•(øÂÛõ@-Û +_zŽ7Q‹4Ü€EÕ׋Œ”Ò:hHèµY@5HSðŠx„’dò0—…c"ÇÚƒÝûóãž¿ý¾~ê}€/¶¨ÄN(¡R’{©ä¿Âµ¥ÆDHIöÆ"^>º•49éúNýþØWÙõ®£6‚>€PRËùáÅîåïtÃG ¸ˆÚ!GCÍÈnI£#E!‹?Ò FŒ5acÅÔåù,†E‚)Á~Ž};Ÿî‘ÇŒ Š<®HO’:±…/Ȇîø=[Á­Ñˆ‚«3·(Ъˋ§ËåãjÊ ³t[™ 9ÚOë†4ËÆõP˜=«þ1?«?“χRÆvz‹6  Θmq•â?döÎ{Ï‘X*û†HðìÖ€ì U¹ºwöÈÖc{‘E}+ø™ÚfäÕÏ’3ï¼ömcŠbC]ÉþSô™3ˆ á´-ôOÎDÄKŠÍŒ]T&HR7²2s: ÁB‡ÞÚ»`„î, +!³røáM\m#hÕÔ%/…]LÊ©Àx§” x`Hù9_*ÿî~WKôêJÜ;g-áEƒâ1[2¤²‚Õ+lвÇÃ'r±vŠ2/’mâIRøا0;Oï0«|èû¥Ú½ð'-hMqœ!ÏV1q†?þd˜—`7yÜ3rk‹\%f ’Œ&¸˜k¤„ìrè€Kòóf"ä,g *{µ÷›ú¼¸U6 paQsCÏ—ü}“ÎŒ™gÕn»&”ð1‹ƒ?êh¿Z˜ÇpKmâÇåètÁ_r'Ó§Ú ò­Â‹šKÒ) ÉM«ô[1„‚á°‚xèáwI’96KTì±H;.JJÒ ç–äãa¾0xà|«‹ò“Ö¡B!,\ÎÉÚ)w­ ðT%¨K#Dé§t°ø“YçAÙú=<,| +鎩+÷WœQE=ºì&àÿÉÕm‚ßõU#„üŽO¬‘,¿w‘ôŸóÔ+„Cƒš«C)]Âqî[øúù&§6„¶½SÛ A…L;µ ˜]Ù™éS½‰è Ä%8æHMz•ð—.?ë{ÅA\ÏÛýr(ÀââcNˆnÑåDhµÃ‘æ•äd +!'Š+Â)y5Èûb÷¥²HªâÌëQ:¯Sî•]º¿ê@Ë™ÇÐt”x B@TƒÇ+K _Om‘ã¯ÂõkP]û·D°‘ÁlÇñ)°C˜aÛ_îe©ñ .“QªcK]U ®ždõQ¢øvm¸yܵ¯òŸ? x_Uì„’™Ûüái™GÐŽ9(G‡NeðäŠÐ=½“Q5ƒéðj®’éÞ”£wA p6À®×K_¯{h2jeæ¾£ž| f­°‡ãm3:³ïÞŠ¨v"rŒäL-ãùiDG_à&´ö0ÑÜ„”f¡ÒŒŸ¿IŽ¢‹Ú=ñl­"á£s‰*s,µ72,àWQòýœ¢Å +±š+MÇÄM¸4t²“ͲDê"È:Ѹ/ᙀÉj¿vœ±La»Pì<ê5žLˆ-ÝŠñEWsl›êüm®&VåcŒÌ†àÔ2-f‘=›tŽÅùÙ0ûõʵ1½ðH*ÀÞ²¾VžÂ沨ÌHlWåHaª§ïǤº{v§1¼QVžvýŒ=ÀäKø« ­JÈšq/i&çì_—æb/ ‰ä»ˆJö¯ýÍMPšçg÷‰BÙÝþ ¾Œl 8”xÛØ¡¶/HaF­f3Z6΄ÎYÅgÿfÖö®hr€V@wjàËòžž¹^›2 áÚaÏ6Å•bpÔh“ÿ°ËÒ›%nuWçB.M6pÿ 2bª°Yoz׋.ai)‡lÕÌXu„qƒL6ïb%;34jDd±¹FG¶KÊšœ§%)‚³‹’·VÐqÌŒ¢cù°¿Ì&Áïö:ŒDuÝ9BšïgAñÉȳ½ƒi†&ݾk£1uQBs•(} Øžý½ÝHþ%X“¡ ÃqñB»Êh>¢]3ð#šGCeŸt• ±Ðˆ×ÅÁ…äWo¯P7L²°Æ0Ó¦k½E8¾o /2ö}‰6••rž•¬²ÁJŸ;£+ÎÓúðX1ݾ7šÈäsE +?|û4&$,دÒôP wtb×CëöMj—ôï6'€î¥ã)5p$AH‘ŸàQLÿAù_þÊ¥B3ÌFÎ9"l»¦:H”qøTuçãf5æ^1…í¯«£©µvÄ’Z\)Ã?aýâŽeáÕ#œB\›Oç”øðùöÀëA[äÿd£÷¹áë} Jc(²€“„ã‰øçr˜„R[Ø8¦›†cé|Ö¨²×óÅìÇ>0U¬)´ÉÔ—ë=Ç\ŽòÈì ŸŠþ9ÒüÖ»÷Vht Ú‚ÙŽ“!zêñÇÊ U¤÷Hª,¶Œ#"¬›ö‹®C£S +àËfûaC;}æd-KŽ¡ÂQ)9ÅOÑT³rpÑô40ã‘ÕW`ö"´B› àÖšãƒÅ°O 0íßµÅ0 ÿ?%˜\ šh‰.؇‚ÈìÿÄ°qŠ°Äž¾)Ï +6¤‡ ìÃy˜º–EŠÏ¦ÌUPDP:VVZÜÌ’<"5h²ÞÇ‘õ[Œœn¢?ÛtÈ5ƪ‰Ÿåþ@mÒl›p¹ЖA!’›XÙP;:ŤŽÂŽ´×áE‘p`p¯šùóÿ`Z³c<—ÂÞ õU!ýÒ¥ˆ ¾'ó(‘êͳ±ýœ»=ˆñ¨×—¥>³Ÿ8Ò¢Dïš¿?'ã½`lȱÖq%íî…åßíq·‹7PìlhuÝeöð™ Ó…ß# Ÿ¿Oiß+·j1¹«ø°ä¦šä;;l‘0ER|hòßa‹gó@g®=ìþ㟠;çäÏd“‹mà+)ê:òhí(t¬fc„¯qœ÷lÌ{}–çç7§§BTÞ¤¼¾­ÑKi7Ît{‡Dî2a;7Æ'èæý÷ Üö`ƒ Nj`ÇOV$F£xþTí.ôb¢pC…æÕ‡7gmœÚ\zb¨3ix<Ù¯ÁÚG»fB3ŽÇ(øûGçäy£2!b„ÛʬDس£ìüÖPI?Þa±¦È*B˜ÝYslºi^uˆ©MP A×çwjë/iwh‡-α‚°PÈ3Ù(yÐW>…7{äò’:¯ŒR¦«ï­…‰[S«Yj!ÎÀ¦ÔÌzf¨Á‡‡ `¬2,$&‡Dyç£7‘m¡^I©` t¨ö‚Ýé›ÝzŠÑÌ×!qKÃÇù`ÅT¬–·M±™É­¤7€>xäú¢Ñ­tð(™¨‚\ï}qpµ%^ [*ó½cöEt`뀾9K‡M–S(’^/,(Hz» µ$KÞr pyä»Ð3ìÁ¤¦|ÿ!D]ùÜô·@Té¸< +#ÁTn†pm¡ŒÏL%2þš*_‚dy…פ¼2 »ÿdvå²ìŠ²Ï-Z¯|—›Þ&ö‰ rðÒÃu¾†\î1fç¥ãÏØVò-dÙA{¼Nó0ŠÞ¡ÞþøÏÁ&YŸÓê}yÀaðsôð¼ÿñ™›=ÿ`³tÈ¡ÿa\Ê>flhΈó¦Ý,²Â‹Y4^ê‰*ÎôX}Î9׆׈ò‹&ÃÊq]Ê‘ÎþôŸàèÞôÞìŠ#鮥ijïç7=&t“Çf5/ÛfÐz:ÃU´Ù É[ä¬í¡m>ž°A-¼ÆT +õdÁÝÿv﯎®x—î«SÌî  S«æ^ÄÖgg\i è +‰³ãøB'¨º–8v’JðÈ "îÿS¼Ûžœu¹NÀ£t’D ²ŒÞ—Æi±¬jBókt¿~ÝÆ_(9ÃÎb`ƒbß?µ#mVß\æÒ”eЙÏèGj½Å¯©nwa|Oîøl·~z(• –7uZw“‰ñK¤%VsvO÷aåX7:­k%¡}GF^C±Ê0×σÁ~ Ó’×AuÞs‰YÅoIO`)¹Uøœƒ´‡!'í&‹ÈÒ7eIÑ¿¨ÇNçöF¥†C¸¶K4»’#_Vê)«•Ú›Gá”dǪðÕOR‹¯ûÃ¥ª~í +IÆóŠßTtòE½MÃX¯¹â h#8[Ȩ~ÒÈn$Ÿåƒ³o»úc>­h6;N‰ †f»±é<„ÇváT9 3S'QéL£ÙèÚZØ}Ì8zÙ_9Ï*<ÄWÇí&³.ùtÿì ‰ç±Ëc/òBŠµh gí £xèöÁ·MÉ?™Œ‰9g»ú1º*³ C½·Í|T‡~²wWg^½[?†M¸ÅŒæËÀ¯ƒ=º¬ýŠ.ù•ÅìÞp¯ÀZ¿Ñœ_ǦݴÀ/˜ûdm'ÿ;Ñéâq³îÉ‘'lMx!ÒîÚ²s,Ð £é>OBÑ+ò0u­«¤8/¸fÇ âR±\¶”L¥’ÙVG +åUÈHMÛ/Òï6ˆÚ¯f½§|œP(ùD™™íº ZGžÐìŠt;+UçCÌ#7 ? ˆ0¢º™é¤¥Ôd¬—¼±&—^lms +2†â³1Æ Ú‹'P5jhs$ò\ ¡ìÀlÏ _yâ¬bT‘®„l'kœ) _ ê…3M€Qk ÉQ&tzïÊÚcA_‘ÎΊ¹^šMb}®°gßM<íLš£EÄBwøýÔ:¶nqS7¯K ’‘ ^ü³„2ܦçßüFd.jR£%¾ÁèÛX­Ì/®Owº/_ ÷i!#s[ìôYÒ‡Mê³ûé Ôè¨ïL¡¨Ž8飳”ÁÕÈk½Q åÌæC¿Ö™Å\øëS¬iâ<*MÎûi6Èt2]ƊІ_ÁS‡û@@h&q$4zÿ«.þTÒãþ4s¹ÅrŠå¤6ø)„¢Ì÷_i8FÚAš ‚3 ÉS€%ô©àˆyw¨k~ëñÇn¼¸Ä5àŒ|—Y÷—Õøk™ÉefË¥•#¾šC_ºz …Q%Š“xÑÈ{éΊå­U®´Ño‚¯2BQwÌßúΠó†Ña]ºÇºã0 &%b*`ä<„™$Íæ´í€óg¡)_¿ZÇèPâ¶õ¡°*(P³D€™ÂŠŸ¦î†ª·ì†F㔢ŒzgX oÛÂñ2+®hÈ™›iÌ+’AHApDç]¡bÚ\öÊ=®ÓhO ÃÁȲâZ ¿9²Ô¼î5 >+óFø9†yÎì.ò>Ÿ¬uèë`]ÕºŽ?àT9ÿc¼‚ùÔ¾­±ÛòX UæW_ö +2ÞÿòmÀ,³;“(}#uß.ýZfüå9¼ñ‘Ì%E¦ßzà® û4ŽÛÕÅe$@BŠ(©ÇþøAb³¼¾þÃ5-o"²ÕÓWx‹ü3qÈìH¶›²> w+­p¨B<êÃÃË—¦×¸nFN´Oþ +"—}£®FÕìvc +™¢/W÷ÔóàY®Ûaû¿þ"^[Ë[´´¥†æ¤&O9y\¨"\¨ÒRÇï9òo­lújöFð­OåQÙžåò“úO{9Ô ‡~CÅ‹U4oK¨´_¤ ÙB…Á/"®ÕdÌ★#5<÷qÞÖQfÿ[/u2²9¯™=ãòìûF…Û,ŸJŒp5¢ {sG2wñB#@š­ÀXYq0;<í(¸}:屣̻Ž +R+ò\¯h±S2xæOPÇ‘‡ë;OLV©¤r`Èâ ù`0|²M$™¸Â +E/ÌîvðÓ{D,Yâ+#œЬܑ®iÙß:µìœñW=L\ç^¶ÐQ½†X%y¢œ¯4R§ëH«u⣄<ÇÖ' ö‚¹Ë«tC—.˜yšzuøÑŽ÷¢‹SP‚_ä€çy•‹(äÜ,­‚àDæXåÁko>Õ¼¨[:[7WžÑo×`8¦äinNÝt}®4ï2œ’¬ÊYr3šæ½ê .ÏI»¯kþaÏÕÐî:R141omLRodñè ÂV)–ˆfÊ!Þ‚¬PõBU-@*¹?á›ÿzcƒ[•ë÷€TÄÍAÜþ-­“Ïúx—âÖQç÷gP©IÿK}γ?È™ÎBóvv‹NUâ¸91‰6ôM™D>ªå‹pEMøæ¨?"¤š1Zj焸DN°÷ÝôÈS¥7VbÇRVñÒû‰³YÚ=Y2Ò2¯*(x‘š@)›”ÑÍá_í1Bebv[ºV~ï®æqÌÖB¥?„·%µKGU_¨7N2ïÉÚŸ×b…=‘åü†­}JˆˆÃ«¨¦¸»¹8É»ÅçºLç·"4}'Í¡¨Û‡ý¾E(§aJpö¹X5ÑQ¡øŽZÓTÂNë¿$‘‹dµûŒïW}¢I‹>„`œñhÌÜ+Ö×ù²ÉLÝZm]ÿI‚A­4Ä)«‘Ét"˜ü‰fÉ9väD­Wª4VRW|Á½ÀÜ,<Ⱥ%ò‹·PÚK(‘^?cZ\So>šÓÿT©E€†JÁ{éÏ[¹å‹÷ˆ*Kuö7Î÷{ hÂÌJQ…4Só3«5ÆÜÞ™3+V ß[2•'žñ<Œy•ÛI›j¥í«¹Ù[ 8ü ó±ò9IIì,`ôeTt¢“Ï.LçÎ$ȪwíS@†ßÿüÞÃÃÙœ$JèC (÷ÎÏQè þE;8Àî ElÄT ¿lB²”é(½€!`ó'IÇ”¿n— #I!þªÜÛ=´5žªÿê?SW_Ç%Ò^“Â"STD¡ÄºQwÞP‰ƒ7a_ ±ÊÅ!¥?ÀýRPa1è‹ëÌ•[Za_m˜õ’tànoöu^s%—Ùe­zFﯕ¹en¤D;BÚ·ö`6öwýŸRê—ž5{hh×3–á~G„t•ŒDq寃Äà›h!ÜÑÔRQ0²bOþã †§Ó™5jE‚C ]]X»›ƒZÁ2Xu¿u1’núáöé ÂVáÁ#ÌÝ决‹q2Fr…åºÅüê³±¼w¨íC©¿uôó$g3§,†æ̪¾2œÊE¢cüÁ(^]ÛsM{à…¨›G´Ô­XÀa¤aÒ¿“Ès¹+¾ipk^dÆ™”€ÖÈCu~·lñw\Ú$Ž`^øUé]$õXNp„ú,n¹q6æQØ•Ê*’LY{;Ìvú»>\RÌ…yemÅ’Š+“Í»ïN½*{êÞ®ÒËA ¤ªU–*­ +Øò$K[î!Ù.ÉݦØ~é!LnÈ$æÞ“ã;w¸[y¾º@H„X&Ëg«Ý"dút†¦ûÒo¸—G.I´Ë~§5®éó^=•²Üé‹ñax}¡ùfPìOå* ç¥ 6Zfíxwtxœ¸§)ü|o†Ošø®x…]´Ô~¼J»PtÝjɬ€£x0€\à4xC냫! +‘ô—‹s*ë½ „gÑR(÷=Ö“ ÕAÄáÍm mðu±ŠÔÝEÂ6V}þ.£òàáŒ×ɼÌä*Ce¢šY•N +Þ‚»Ó÷ÛÜïsÆ‹]Ô<5&uwét—½.¤ÓW ˆ°JíÓÁ +endstream +endobj +528 0 obj << +/Type /FontDescriptor +/FontName /FRDBIF+CMTT10 +/Flags 4 +/FontBBox [-4 -235 731 800] +/Ascent 611 +/CapHeight 611 +/Descent -222 +/ItalicAngle 0 +/StemV 69 +/XHeight 431 +/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/a/asciitilde/asterisk/at/b/backslash/bracketleft/bracketright/c/colon/comma/d/dollar/e/eight/equal/exclam/f/five/four/g/greater/h/hyphen/i/j/k/l/less/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/quotedbl/quoteleft/quoteright/r/s/semicolon/slash/t/three/two/u/underscore/v/w/x/y/z/zero) +/FontFile 527 0 R +>> endobj +116 0 obj << /Type /Font /Subtype /Type1 -/Encoding 543 0 R -/FirstChar 45 +/BaseFont /IZMJER+CMBX10 +/FontDescriptor 494 0 R +/FirstChar 12 +/LastChar 119 +/Widths 488 0 R +>> endobj +103 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /OBIUXM+CMBX12 +/FontDescriptor 496 0 R +/FirstChar 12 +/LastChar 122 +/Widths 492 0 R +>> endobj +117 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /ZTPMDH+CMCSC10 +/FontDescriptor 498 0 R +/FirstChar 39 +/LastChar 121 +/Widths 487 0 R +>> endobj +252 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /QZSJAN+CMEX10 +/FontDescriptor 500 0 R +/FirstChar 0 +/LastChar 112 +/Widths 478 0 R +>> endobj +165 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /QSIFYW+CMMI10 +/FontDescriptor 502 0 R +/FirstChar 14 +/LastChar 122 +/Widths 485 0 R +>> endobj +251 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /OFGSEC+CMMI6 +/FontDescriptor 504 0 R +/FirstChar 14 +/LastChar 105 +/Widths 479 0 R +>> endobj +293 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /CFAIUE+CMMI7 +/FontDescriptor 506 0 R +/FirstChar 84 /LastChar 118 -/Widths 544 0 R -/BaseFont /JOXOAI+CMTI12 -/FontDescriptor 106 0 R +/Widths 476 0 R >> endobj -106 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /JOXOAI+CMTI12 -/ItalicAngle -14.04 -/StemV 63 -/XHeight 431 -/FontBBox [-36 -251 1103 750] -/Flags 4 -/CharSet (/hyphen/A/B/D/L/M/P/S/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/r/s/t/u/v) -/FontFile 107 0 R +248 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /VCFHMD+CMMI8 +/FontDescriptor 508 0 R +/FirstChar 14 +/LastChar 115 +/Widths 482 0 R >> endobj -544 0 obj -[350 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 727 688 0 738 0 0 0 0 0 0 0 613 877 0 0 663 0 0 550 0 0 0 0 0 0 0 0 0 0 0 0 0 500 450 450 500 450 300 450 500 300 0 450 250 800 550 500 500 0 413 400 325 525 450 ] -endobj -543 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 45/hyphen 46/.notdef 65/A/B 67/.notdef 68/D 69/.notdef 76/L/M 78/.notdef 80/P 81/.notdef 83/S 84/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v 119/.notdef] +115 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /WOSUPX+CMR10 +/FontDescriptor 510 0 R +/FirstChar 11 +/LastChar 127 +/Widths 489 0 R >> endobj -104 0 obj << -/Length1 1545 -/Length2 9023 -/Length3 532 -/Length 11100 ->> -stream -%!PS-AdobeFont-1.1: CMBX12 1.0 -%%CreationDate: 1991 Aug 20 16:34:54 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMBX12) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -end readonly def -/FontName /BCRBPZ+CMBX12 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 12 /fi put -dup 39 /quoteright put -dup 45 /hyphen put -dup 46 /period put -dup 49 /one put -dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 54 /six put -dup 55 /seven put -dup 56 /eight put -dup 65 /A put -dup 66 /B put -dup 67 /C put -dup 68 /D put -dup 69 /E put -dup 70 /F put -dup 71 /G put -dup 72 /H put -dup 73 /I put -dup 76 /L put -dup 77 /M put -dup 78 /N put -dup 79 /O put -dup 80 /P put -dup 82 /R put -dup 83 /S put -dup 85 /U put -dup 97 /a put -dup 98 /b put -dup 99 /c put -dup 100 /d put -dup 101 /e put -dup 102 /f put -dup 103 /g put -dup 104 /h put -dup 105 /i put -dup 107 /k put -dup 108 /l put -dup 109 /m put -dup 110 /n put -dup 111 /o put -dup 112 /p put -dup 113 /q put -dup 114 /r put -dup 115 /s put -dup 116 /t put -dup 117 /u put -dup 118 /v put -dup 119 /w put -dup 120 /x put -dup 121 /y put -dup 122 /z put -readonly def -/FontBBox{-53 -251 1139 750}readonly def -currentdict end -currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª*Bg·N³ÀÓ½ ƒØ‘l¦ÊKq*Þ²Xú«šææwüsŠ¼|QÍFïq˜Õþæv`æšz¹XòšMyåp"÷ƒë»¶Ôôì5OÒÞË©”Y¤ÅðÆë¡P(DTçÜ!Á[v´Á›„67XFšlU‡…²&3!R˜q©ˆ4‡Ýw”’Ýσ~j‡¸+Ûño¼uú£ “þ_dÍV`÷Kî–y ãZúÌ÷±€]¨Šãu M™YŽ­üb[Üœ1[lòŒ›Ô'ó,t\™®¾pÚ®Ôž¤ZùO4ªG‰J7 iŠº½¤!U±¯&Ï·Ý¢¼h`ZNöÌ£ÖhKGÿµˆz;íà´ÓŽº¿ ˜ #1&ë¯(›)$ÿJ3K…ÙÖ…Eý­´™s±èjF¥¯ˆfÀ"P$Õå†-IÞµØìË•ÙBƒÅ -6=h¤qDVð<ã` EŠkÀ³ªE“NrraÆŒJGø ×~Lò{6ö¶ó¬IŽE6ùà¯U'õãÌy 0„gK>&)o>2\U]$XWŠ‰ç-1f£Å×@³«±'ÏB 1mùW‡= LðÛ%§5t¤Þ.O-]NŽ CTÏ4Û>&wÁ”vN­XÅ…ôžñCþŸßÙf å ›×¢¨r™¼1žf×¹VãC¡›“È–~äqŸ0 þXfðÖÚ^Å^$Ó·ï£%ÔG7dé›È±\ò¬­úlFcè0…]g<銷_‚Ÿ¢&«Wð{>}N|ãÓ·ë 05ŨÙú4H4ý¨ãÜžlGž>îš TÉ_¤cÑœé6àYŽ1— §»nUÏÕïr®Á-š–u$zq1k.â¡s+6'ž¤FË2»âç‚Íð‰.r¶q5…#3|uç)p“Õ¾Àc ÜN•r3ì ùåÊp<~“„˜s„?ÆaàÈG:m+å-뢅¹¡Ì^dÒ­¹æG)q„„Q¢EÝöª;‚%鬎F0°ÿ2Öyì'¬­…Æ9N¦÷#¶`îˆ=‹gh7éë¤ä+¨óeC:éðèŠ&3BÚ­øœ^y¹ia4eM‚ÁÛweî~ú+Àáݯ`Úûæé0—€¢µï>Ÿ¥&½GŽ%FJÆAÐý‘{-‰Ý„Ý`ÛÞ;êÑ‹«ø‚äáCy,.äÑ=¥ƒrSøW{gØ¢ð“aR«Uî @l™²y\[ 9Nöx”nÉ«ÆAÃû ‹ÖÄ­+Ãç!V­ô9îr‘Ä`$³dÐŽukÂi,#r—G§¥Žzk ð GMõ0]xjýKEužù÷Ž¤iI¾»7xÍG æñ­ ~xKÈBiŸêz‚Ð3ØÄiRXÈöx=¡°¿YCªF_‡£>—´w}­×)\N…¤k’p–êÞÅWÍ/TˆØ*ÈÕ ©epøóžp˜ èÈ2æ'èùû2° órdwC¥lyЃœ}¨}ììP‰qe³5%Sý´mªñ´‰„²âÕå8D²ÇÖÜz{*®UÅU{dàªíœêþ¯éº½,^ä·HÅ¿»n_N|2ú²òGÔ"þi'œ„…'äú»Ñ‹ö3Öd|”_ôܺÀ³œwrêÛç°êöyÎ…¿j„§¬·Àˈ…Ôa!gŒ0Ð?lE`I¤Íï¥*±!J­ŠöÞá‹ó3¶ÿMóµ[(˜N«Hõ×­ÝÇUh4×|†ì·ä[ç-*²_÷Ö2˜±cúÌN×#òâDL–D=»úEÊã?%ƒn9z”KtVޱђ¤Â,®_ç@¿í°Ô”9_±(0ZD…vß‚7²=¦¹KÉœQþÛã5€sˆ‚Q& 2ù+lŽFÞ~?Í“šˆ.÷ù5ÌPDГ½Wt¹%45+ÑO¾S¼ù ÚßõÙbefâR†Ö}1 šÃ-öš˦ß óF0;l²µÝ~3êuhÝåAÿuÛ.üÈ–ÄÕEû NÀ‚£üZÞQÚÈÀ5¯Ëùh™&*„]^òþïð“añ‡VÚ¹ŸfRÛÍB…=Ý ÞèÖŒ¤W£J¤>´9¸4=îô®†.£ôáh q`yYÀ~\P¬Ï *—ž=D®”³Òkr?\À29Qò› -IeæZ欈¼AzZÃŽ!6‡¢Ý9Nd…u$QÌ$Þ¡¡Âã »ùØÙ;Õ”|¶y«6³îõƒ³±ùÖR°Tbbw0<°6YØÎn/x¹’ûYÅã,Âr–é>;)lè©û3‰õÊ®I_r]!o}¿® œHº¿YŠ(³kHUÚ»6ÀM+sÚê8ÁUÀ‰Î¢^Q·ïëDð×BXKArÔ;â Œðc™ˆµ©c6c~iïr—uÆøg•:Ut°²Ä®æ|5þÆÕ=ölG›T5e q/}C’ËzJƒ3·³²FG´‡’|`´ø+ŧ$wîôƒÿ:6À œÿdÐá µqü|±Ãøm°ˆüYƒoå¤Dã#Òw|ê–jó”ª7mU©ÿEDš4 ‰Þ¼³ ÞÂÃejB vòâ< YB’oRBby49{¤ 6Ñ/¢•I]9G“Ç¥ C«ÛOœœ*ú$²mp—X²6 Œe¥í”6|W["V“…?6沩ßrEk#Â|o·ÞÎd"/jhÿüSQ誈Íé™ÅâÄ{D¿xäg,°U¡…š$)`«6Þ£#ÉÒñBw^º:¤*HŒfe*Ïkýâ‚g—C¿‚1žï%Ø Ìl²ëhêQ‹9°Si¸ 7„5»aZs…ð‡kÃÎÑÎ,»6üô°ò^÷ý ÙŸ’¸cÐmv@ n‡4dY+×õ¹hkŽJMaóîEé°ÄNeC+ömOHœ´¶ã~úãèiàbówÆ\¤6-Æ7×ï<ÀÕqêËÖ­öø˨{ž¬âÃ!‘¯ëTÏuV'¹^,ñ©~ìºBå@Úr¾gVr¼¨ì4wà(‰5ë ‡E²ˆ9dK~ˆZ,f´B ë:Ët!´ßÓf.JbißîvãLVünÈÇl %ýH eO¤‹¼xeK¡|÷DƒA{œâj¿Î~ž$'uè?ÎR€@„«`ûo–mUKtO%DF£`V¯eE›.0ß½#צ¼×-nw ñg½}‘\'·yüÆí½¨Çv†áð|›Ô‹¼1êKu€\ß'6ò½#Ì$³NO÷õ‚u¿ZÓœ¹w\w·Ã¢¾(µAïzò…;vB¼Ã×—I²†»GQ ¸Š ¡ã8Ź†ôKžD©„RfÄ~8£n&0 ç7û$¼4׎-šù1Òâ²WË È,,dêñWrJßS¾>º£Ÿ€è±ÁkÐoiÏDE–éÃ9Ñ‚« kTMÁd—?\À2›‡Ñ(bû¶ /ö› - aÔeqÁAÌ=7/‚¥ö‘Íï3z£+Añ:¤GâþטöE¬é‰9¿ ³Øãè+΀¾eËÖ5^N̘"ÝÞ37ªÒ6J:², -ù,L­ºÿ?Ms¸¬?zZÞnävºVÕU V6=×p£nÊYÒaÓǾž Ëy8öÆdQ±-a% Ìb.™'9¹»ÿþÿ‰]Ñâ4iŽ‹Ä„ºþ^¹Â}Š}4RoÕî»uKʇϚђÚ8ƒ4ÕÄ -ºœÙ½îE;)e”„,5ÕØŽ;4ü V‘Y?S99ølÚ¶e^ Îð^*³¯‰Ëƒæµ‹È$¹¡yý“ç)òuÄ)b ±_å›1Ñy&Œ‘ÝÙQ \p')—³—¸ý‚‰qC Ùæq…]u^Vµ— -ÊÈ餙‰Ü \NùæŽcÉ %ì§øñÜÏ7îº ßÒuà úºxÀÉ£É5(^÷ÓNG… |[ƒIWÈlê+í¦ûRá,£úL½ª8jLm’ |»éL°Í:ùˆA×å™\O<U!³me¿ïF%W>ñN=2À$n_} -‘q›Æ=¢ûLóÄ/N—Ûþùâ,šÌ¤uDÀGr½†ùl -|OÈ.‚úMzÜ;*FËþÔ%JŽM£›.á^Ñx§·[æŨøKñ"`hT}Q]ö’¯Â+(‘CvÍé!kN±Q³—i§ß„+c–Y¡|¯Užî=UQÝ™ ".@óV2C®Ë&µÖÁŸåãeq£R :%.õyùοkWôÚÌ_û~*Ü|íJÊcv‹‡õÇõ¹Â ËS>å/ŠKÕEÿH€µÆŸmêOÙd§, ˆÈ‘q¦Ìv ÜO¸Ì×ﮟå©[5¼§þágÑþPÆ%sƒ´£åj"dþÛÕRX{—ù³¡^ðhÑ”Ýt¦…ü/Õ2}ùePbï!bŠýÅ ÜÚüˆy¤ -ïû`ïè\1&’äü+Î^$Q ÄQ#ëðãÁ¶“ëÚL3ÓuÙêh)š1ÏF63ûþÆO=ÏÄO–ÏZ_Ó …`Ûéà€ªŒ1>Fd¢1búë¼ °q·‚cÎt~ž›e슩Û§òÁ·ÜÈJhBŸ&h›œô§Àt² ðCY”àe,HÆÙ‰›x4k’©EŠ8XØRÛmUc¥ÊMû%“ði>TXc€_°•ÌDJÞêœÆ1šæL¯wgUµ>¸Ö#²¡:÷ Ê3k‘èÝ6H%±\bÑ«‚!Þý9Î"?!ë¸sY£ë¡ë1œš.&„,Á%^ÀustpÔyÈòal€ÐÃFAýN‚¹M¦Vž¾h€SXæþú³VÂÏ…¬<, -'¦M«±™° QÅÁX³Ñ»ÇðRà…lHùdÉGVŒ¼E˜èÇs™ÙþYÖ¦µ%OE†ÌfÄÖÏÅ"¢õ=ã"o*3w)—Š«yuyé#P«áD‰V˜\_'wp4vwCºDÞòäÓq!‡9e´Ûÿ_9Ⱥµ^£ØQrÈžxÄlÌù±¾Žöþ -Ïp12Š¨Dsö„Èž–j§Ø”_!ÜX›Bsåd•=3ë'\3Ý>õŤ -VÁ§ðä×Ý#«OÝ04$t: }ü¶TsÔúÆ\{‘»ìTìQ§ÓeÁc$ {Ö9T”Ï÷±p+Õ˜^,¸ç¢`@º&ÖHíôqdñïû¡Ø» *·ÐÏdµ+ãHì{aÚ»28OçJ=TJŒöë[ -Kž:M°´xkNLoê‚žIxÆ‘JªX9\l!ávåöûfd=x¤®Ü·=øï¥ljw %î$¸Ñåµp¼¿HCmänXþ|]6”ù€CAÕî ñæºÖßÒíGü¨œ sD’|ŒÛÒs~ÃvmRNy·ž¼xbÒ ËôaÍrd];ôœ Žu8Àq`—"î‚ëʾüDää5ô´¾ªNݬF¥òèDs+à`ªêo³î.¸/žýϯm ]$—àdÔø6_%ûÁ^%jtsëC¼Ÿ‹~c–Ðüxizs;8 ¦H”û­¹;æñø=…)ogºñ“ÂÈà9¨^°>Ï@ó‹ƒÞz¢áQŸƒ{w5çî8Ü7í:©Eö—ö–>×5sï»û(‘‘ìÁ¢zÅ'\ò˜ý¤öUBut®và7ˆH,ÕÑmpBÅæ´±n8R#Ûiž[b¬?c àããÓëWqæ^ÏÀUA¢yãææZ³+ÛÖ (0ì[Ì™f—“pÖÈø䎜åsŸ/·šÖ™>Ñß3T@iðu+½@bæ¸$ÍÅííþõÇ{¦Ü+®‘äS"ë#û‚P&܈5i;îˆD'k „üš¤JŸ;m%_t=èc!:·ä¤éw@#û½›P`þÃÑÃz4Lf\|nD9’ôßb>aïk] -¾±9½ˆ“ˆHâ.Ÿž0°”°“õK¨¶™nÆ{·ŒÓBOUJÈ"íœ'ø”^þáÐ ) ¾}‡œZ¤SÝ|ûþ—µŒ [·è0“ç ±'?|Xú}Œ¶óÑ€àX! A濃FT ÜuqÕ©AÏ<ð­ÿsÜÓ–ÐÚœ'n/y`¾ѸT¤1Â…c1@ 1wé¦Ô_­Ðž=¦áŠÀÓ=BßßH~Û^¼Y«fa9Ãw^“º%ÿÓáâ -¼ÉÌ -Èñ6ïUkM¨Ó‘ -óþoqÂBæóE8’÷þ_Ò€äNê<(ø…Ï] -¤Áñ]2[_õ,kq_\‰ßÉ£*´â‚È º¯ÁöÄZ…?C ~âYâñOgyßbHýKÊpBøw‡¥ºóñ&¹1}]P×£\ë\@\‘.ñš/¨úse¸¦Jõÿ£åœ1üùÕR¤=³æô6 œ'ËH;d)âs‚öòƼD„¡\«êPÉÅÓnÆàSP w`~]²E w"“žŸ¡'SVá(]nnbMP1í@Xæ\$kAÚ{­°ã›aÇ~”‹yûGSí’š»Ï9 ˜Mó¼½?uX§Ú6ÊÖÛÞG%Z±&#h=q‡vw¹™ ÒÍnú››EŽëØB¬;…hñÌðû‰ë½cdF4éfÜñ;#o‹2ä sÈN|Ô5nr!h.íróÞ1RžÝM -¦O 7û¢ù6¿r‹c7­³×U„Õä@‹ä -ZúE¼]\ÏgiàiõiýWšp{UkH…!=ïQw".ÓdϤq½"˜&üÁÊû1a*¯…ó -ï3£ý2²ËÚ¦<ÍÏ|ëO æ]th5ì;ຫ÷³]á*©¸ãðwþÙaf®Ç¨ä -–3XÊ/nÀ§£¡°Áu˜bø¦p—žº;¤ëêj€9æL”9¢–òór”Ü¢|Jô×Æ®CmÕÙkí¨bœ«T˜VAÝ ©ñy<Ÿcæµn—>óÚ~so¹Ÿ’¦m=‘ T­ÑÁ4`L±³ æ‚)çýd¤#ÀÔ1áí ˤ¶~©vRÇí&Ž µ¥!•¬mõzã²ýÈçŸFún¿*3]ŸF5B]ǧq9[+˜[ž­ï–^m¤ˆN ™»Œ#e7eW!æ ¤¦)H¹Ñbû·ùóO÷ëÊÜT–˜¿‘ãqTîp›Ó@À|IŸÒ ]ܸÙì[Њ%|¾ ª€ŽFY)ïGØÔéŸqÆD&©¿ìú+^é÷Óáƒcwv¶J*ŽÙ’yÇ"x‡L{¢O›ŒØÆw$Ñïc.zyfÕfê‡×j¢:„G®;3îç×–œCað³ŸãhÛ$å2tQ+`wñ6¹ýÍT±¾5ÃÑóÔÝ«YÁ~$\¨öæùg‘0C¤ÛªT4zÅ;2Õ½î~§ãäÍ´ ;p36Mø¥Šä­¹Ìçx•J[ŠÖÓ'§'±›ýÇ’}µÔé+߇ÍÊ”Ê+ðÿ¯OÕÙ ¯GY)z ÛjƒüåEû%&ìï¸àbÒm<^s>cl43÷e.ÍoŒ„ Q%Ð8ý‘«¨ -UW…BßA[<Ã@X°ƒ~ÉRÔ„)oÿH^V¤á0¿®in-Gí.ì:¦¬a¸’¹ÌÇ¿nÞ¾kT’ »Ia_œ£fb€"¾J:8½}ÇAµ¥-…Í}„ON»m¾ØkË­WþÍœ?ÖJůÜU@„>wÝF#Ï(¼‘3gaÂ6Í÷šLŒ•þkk »9¹S²»-‰·’[Šø/s'¤•T¾Ï¨Cý«cÑ[¤Â3Ž µ÷\І=Ŧ¸QÄw—`%¦¢ë”Æ¿Ãû±HwÇt·«<éq°Y¥ã]&NBV±SËÌa¤ÇRcEÛˆþ&öw~‡â½$Ǥ„Ü o!¬ôÀW ÿüIeqày -Û)„SJÈ$Jœ–)˜Ð¸‰xÌëáLrˆ‡¿ôÞU°uŒ®$ -ä·òEyD½µ`DÕYÒÅe«A*toì1¹§‡[”ï^ŠÑžù‰†ÿÍ{¹‚Ö‰‹ð«ùâSûgDó} -‡ý=‚XQ–½£nðC÷€Ÿà_¶’C*;vþ¢SŒÐ­Òl¸guŽQÍrü-š!ÆZÝ-Z:±¦;]hâé÷1ùñzØGBHäuáѬ]ÇBHXe‡öý¯`mbÀw+e„`d’¶È ò®Ž Ì6©f1šwéÛoóä´¸ز&à«„c„‘;9,T9ÝÃÕ!¤þ¨zÌŠ'0ôëB†ç]HHÜÎ=…¶Eѽ¶kŠ–R\ªEuœ-ÌIók‡`ýeÔV!§L ƒ´w`yxÍvl:¿·yþâ%¡eH/x<\œR–hu¶ çÿXze?Þô¢cÆŠeñõ:úšGXâBKbF$|•uµžÍæq5~?J™y¿NŒ’KÝ»NŽùžP€`rçH½]êŽ÷T;„|4Ã0È âjÚPî¤yÕÖ…_z8ÆÀ= -«¶ÖUù,Üì²ë<›ÒïT vÚ9”ÿ…~W¸Â!5LwlÜþ ’Ñ4ËÓ–IÀš×3:W‰ÜŸ©?dš·eKV”N£ÈHtZmÉÐUDv1ˆæ1¢ž±_˜Š™ˆae°§ú’¯ï±[7¸üËX"`9/¢Êè -dªiMǾïú]™T,ì[Ь8vÆàáÏÍ…Ñc>FmBÁœñÒ¾ý"|Fy,8H†å„@À$xl¸ñ—_„ž>ˆš;döP7«‹Éï9G{z°JÂ~šøq”‰WàHÕ™U趕÷nN#8¼HWè‘WÁ‚Øövv!Z×,ø¢%‹U…oÊÄÌ}žNf%…½*#},.åó$ÀÆ”2R'Þ¸~q=ÃÆ ”sZL‹`å#>Ãy‰ý]Ùü¨™8ˆylW®Uµ»êçödω1ŒiÑî±x6xGÍg ¥ÛSߟ—6@!dÙc› -‹ÌïuÕvùØ®ñ’Rç櫪‘ñK§¾M³f÷•× X&yªy§°a”ÃmÚ²—ׇ=Ì±á Ž]I‘¢²Ó’àËPÁ.?»×#ð¿Vî Öè@c—4¥vÆ°%‹Þ¶÷atH‘ô›.~E2EeÇe}E÷ŒÑ0ó÷ñââ:'JIä¤;t$±©ãú13—gHÛÁjžeµ9Vw?«·$ïËã3ÁN£ -ô|8…Êò©Íºõó<ðëÜ1L>e²Ôq®eZÔ†ŸiÁ§ fâ6µ¯›?ˆ¿:ÒmÕG‹W4 -ÑAþbŽþM;Í1&F²—´±GÔ¾î:{ -¬²Ñõ°M÷ëûâ2‡U¼°Ô!«ëwš²ï%T÷ã*MüÒÁöï×´Ü ˆp‡µÇòf뙲'xË¢o²@N#gV‡áœ Ô•å<^૽î¶}Œ÷ûÌ ?AÚr ΰZ´1Oýæmñ¹%zl5ýÄÙÌum^]œ›:#{àOãlˆ‚†´|‘ùüF$´z²}ù2”°0ä;Ã]JÁv<ÁÑû?Ü¥ŽmDrãˆLbÎôÄ¿™4f"}Ž‹˜ÆŸœã÷%ìó²i—¨z(àRë¹Uøüù‚õ©Ùq%Ê÷ì×¢EäP©Ö§º.©cXI JáN7·Ó_B¾t›…n¦·ìžxñ©Àðuã»›Ó«1I³±œ7CjxOÊ }´ ª.n…GQíó¥¢¾-¡Ü[ú·Ev™ÃLÑÖZ.µ¼( Û›×ŒC0|8ó¾ÂH¦ X¶ÍůLÜÑO²œð3De¼ú¯cÐݳÁ¡*kYeȾ¦ºR[dIY‰cüq˸Õ­ïóN£ò±þ}6z{Jbí²OX"YQg¦åi‡¢ªhÞt6;›.q»ÄGeûŒØzÑF+*/ôžü}ZKŠÅŸ×çXYóSSø0ÔÏoÏÑb"5÷y£É‚ÕhEqö”{Äk'Hú?–ë¦uÓô«³ã¯RÖÎUd˜O 0¾Ó;}%w¡þ´êP8·ŠI$oë/?U¾‚TJÊob¬ aáí¾8žú…Çã~< Ýý¼˜0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj 105 0 obj << /Type /Font /Subtype /Type1 -/Encoding 545 0 R -/FirstChar 12 +/BaseFont /KBJWDR+CMR12 +/FontDescriptor 512 0 R +/FirstChar 34 +/LastChar 121 +/Widths 490 0 R +>> endobj +292 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /TQVOAL+CMR7 +/FontDescriptor 514 0 R +/FirstChar 43 +/LastChar 49 +/Widths 477 0 R +>> endobj +250 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /CGCFOU+CMR8 +/FontDescriptor 516 0 R +/FirstChar 48 +/LastChar 61 +/Widths 480 0 R +>> endobj +166 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /WYYAGH+CMSY10 +/FontDescriptor 518 0 R +/FirstChar 0 +/LastChar 110 +/Widths 484 0 R +>> endobj +294 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /PXBGHL+CMSY7 +/FontDescriptor 520 0 R +/FirstChar 0 +/LastChar 0 +/Widths 475 0 R +>> endobj +249 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /VOEFGO+CMSY8 +/FontDescriptor 522 0 R +/FirstChar 0 +/LastChar 2 +/Widths 481 0 R +>> endobj +163 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /NYFVHV+CMTI10 +/FontDescriptor 524 0 R +/FirstChar 11 /LastChar 122 -/Widths 546 0 R -/BaseFont /BCRBPZ+CMBX12 -/FontDescriptor 103 0 R +/Widths 486 0 R >> endobj -103 0 obj << -/Ascent 694 -/CapHeight 686 -/Descent -194 -/FontName /BCRBPZ+CMBX12 -/ItalicAngle 0 -/StemV 109 -/XHeight 444 -/FontBBox [-53 -251 1139 750] -/Flags 4 -/CharSet (/fi/quoteright/hyphen/period/one/two/three/four/five/six/seven/eight/A/B/C/D/E/F/G/H/I/L/M/N/O/P/R/S/U/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z) -/FontFile 104 0 R +104 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /BABWJL+CMTI12 +/FontDescriptor 526 0 R +/FirstChar 45 +/LastChar 118 +/Widths 491 0 R >> endobj -546 0 obj -[625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 312 0 0 0 0 0 375 312 0 0 562 562 562 562 562 562 562 562 0 0 0 0 0 0 0 0 850 800 812 862 738 707 884 880 419 0 0 676 1067 880 845 769 0 839 625 0 865 0 0 0 0 0 0 0 0 0 0 0 547 625 500 625 513 344 562 625 312 0 594 312 937 625 562 625 594 459 444 437 625 594 812 594 594 500 ] -endobj -545 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 12/fi 13/.notdef 39/quoteright 40/.notdef 45/hyphen/period 47/.notdef 49/one/two/three/four/five/six/seven/eight 57/.notdef 65/A/B/C/D/E/F/G/H/I 74/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S 84/.notdef 85/U 86/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef] +195 0 obj << +/Type /Font +/Subtype /Type1 +/BaseFont /FRDBIF+CMTT10 +/FontDescriptor 528 0 R +/FirstChar 33 +/LastChar 126 +/Widths 483 0 R >> endobj -112 0 obj << +106 0 obj << /Type /Pages /Count 6 -/Parent 547 0 R -/Kids [98 0 R 114 0 R 118 0 R 131 0 R 135 0 R 162 0 R] +/Parent 529 0 R +/Kids [98 0 R 108 0 R 112 0 R 119 0 R 145 0 R 150 0 R] >> endobj -185 0 obj << +167 0 obj << /Type /Pages /Count 6 -/Parent 547 0 R -/Kids [166 0 R 193 0 R 204 0 R 209 0 R 217 0 R 222 0 R] +/Parent 529 0 R +/Kids [161 0 R 183 0 R 187 0 R 192 0 R 198 0 R 202 0 R] >> endobj -230 0 obj << +210 0 obj << /Type /Pages /Count 6 -/Parent 547 0 R -/Kids [226 0 R 232 0 R 236 0 R 241 0 R 252 0 R 291 0 R] +/Parent 529 0 R +/Kids [207 0 R 212 0 R 217 0 R 227 0 R 245 0 R 265 0 R] >> endobj -311 0 obj << +281 0 obj << /Type /Pages /Count 6 -/Parent 547 0 R -/Kids [301 0 R 314 0 R 334 0 R 345 0 R 367 0 R 375 0 R] +/Parent 529 0 R +/Kids [277 0 R 289 0 R 302 0 R 321 0 R 337 0 R 352 0 R] >> endobj -401 0 obj << +365 0 obj << /Type /Pages /Count 6 -/Parent 547 0 R -/Kids [397 0 R 403 0 R 407 0 R 413 0 R 427 0 R 438 0 R] +/Parent 529 0 R +/Kids [362 0 R 367 0 R 375 0 R 384 0 R 395 0 R 402 0 R] >> endobj -447 0 obj << +411 0 obj << /Type /Pages /Count 6 -/Parent 547 0 R -/Kids [442 0 R 449 0 R 454 0 R 459 0 R 467 0 R 474 0 R] +/Parent 529 0 R +/Kids [407 0 R 413 0 R 419 0 R 426 0 R 434 0 R 440 0 R] >> endobj -486 0 obj << +450 0 obj << /Type /Pages /Count 6 -/Parent 548 0 R -/Kids [482 0 R 488 0 R 492 0 R 497 0 R 501 0 R 507 0 R] +/Parent 530 0 R +/Kids [447 0 R 452 0 R 457 0 R 461 0 R 465 0 R 471 0 R] >> endobj -547 0 obj << +529 0 obj << /Type /Pages /Count 36 -/Parent 549 0 R -/Kids [112 0 R 185 0 R 230 0 R 311 0 R 401 0 R 447 0 R] +/Parent 531 0 R +/Kids [106 0 R 167 0 R 210 0 R 281 0 R 365 0 R 411 0 R] >> endobj -548 0 obj << +530 0 obj << /Type /Pages /Count 6 -/Parent 549 0 R -/Kids [486 0 R] +/Parent 531 0 R +/Kids [450 0 R] >> endobj -549 0 obj << +531 0 obj << /Type /Pages /Count 42 -/Kids [547 0 R 548 0 R] +/Kids [529 0 R 530 0 R] >> endobj -550 0 obj << +532 0 obj << /Type /Outlines /First 7 0 R /Last 7 0 R @@ -10705,599 +7170,702 @@ endobj 7 0 obj << /Title 8 0 R /A 5 0 R -/Parent 550 0 R +/Parent 532 0 R /First 11 0 R /Last 95 0 R /Count -9 >> endobj +533 0 obj << +/Names [(Doc-Start) 102 0 R (Item.1) 253 0 R (Item.10) 327 0 R (Item.11) 328 0 R (Item.12) 329 0 R (Item.13) 389 0 R] +/Limits [(Doc-Start) (Item.13)] +>> endobj +534 0 obj << +/Names [(Item.14) 398 0 R (Item.15) 399 0 R (Item.16) 400 0 R (Item.2) 254 0 R (Item.3) 255 0 R (Item.4) 280 0 R] +/Limits [(Item.14) (Item.4)] +>> endobj +535 0 obj << +/Names [(Item.5) 295 0 R (Item.6) 296 0 R (Item.7) 324 0 R (Item.8) 325 0 R (Item.9) 326 0 R (appendix.A) 94 0 R] +/Limits [(Item.5) (appendix.A)] +>> endobj +536 0 obj << +/Names [(cite.BREZINA_VANEK) 169 0 R (cite.CAI_SARKIS) 268 0 R (cite.Cai_Widlund_92) 230 0 R (cite.EFSTATHIOU) 269 0 R (cite.MPI1) 173 0 R (cite.PSBLASGUIDE) 172 0 R] +/Limits [(cite.BREZINA_VANEK) (cite.PSBLASGUIDE)] +>> endobj +537 0 obj << +/Names [(cite.SUPERLU) 469 0 R (cite.SUPERLUDIST) 474 0 R (cite.Saad_book) 261 0 R (cite.StubenGMD69_99) 256 0 R (cite.TUMINARO_TONG) 257 0 R (cite.UMFPACK) 357 0 R] +/Limits [(cite.SUPERLU) (cite.UMFPACK)] +>> endobj +538 0 obj << +/Names [(cite.VANEK_MANDEL_BREZINA) 170 0 R (cite.aaecc_07) 259 0 R (cite.apnum_07) 260 0 R (cite.dd1_94) 231 0 R (cite.dd2_96) 168 0 R (cite.para_04) 258 0 R] +/Limits [(cite.VANEK_MANDEL_BREZINA) (cite.para_04)] +>> endobj +539 0 obj << +/Names [(cite.psblas_00) 171 0 R (equation.1) 164 0 R (equation.2) 305 0 R (equation.3) 306 0 R (equation.4) 307 0 R (figure.1) 282 0 R] +/Limits [(cite.psblas_00) (figure.1)] +>> endobj +540 0 obj << +/Names [(figure.2) 355 0 R (figure.3) 356 0 R (figure.4) 358 0 R (figure.5) 359 0 R (page.1) 101 0 R (page.10) 229 0 R] +/Limits [(figure.2) (page.10)] +>> endobj +541 0 obj << +/Names [(page.11) 247 0 R (page.12) 267 0 R (page.13) 279 0 R (page.14) 291 0 R (page.15) 304 0 R (page.16) 323 0 R] +/Limits [(page.11) (page.16)] +>> endobj +542 0 obj << +/Names [(page.17) 339 0 R (page.18) 354 0 R (page.19) 364 0 R (page.2) 110 0 R (page.20) 369 0 R (page.21) 377 0 R] +/Limits [(page.17) (page.21)] +>> endobj +543 0 obj << +/Names [(page.22) 386 0 R (page.23) 397 0 R (page.24) 404 0 R (page.25) 409 0 R (page.26) 415 0 R (page.27) 421 0 R] +/Limits [(page.22) (page.27)] +>> endobj +544 0 obj << +/Names [(page.28) 428 0 R (page.29) 436 0 R (page.3) 189 0 R (page.30) 442 0 R (page.31) 449 0 R (page.32) 454 0 R] +/Limits [(page.28) (page.32)] +>> endobj +545 0 obj << +/Names [(page.33) 459 0 R (page.34) 463 0 R (page.35) 467 0 R (page.36) 473 0 R (page.4) 194 0 R (page.5) 200 0 R] +/Limits [(page.33) (page.5)] +>> endobj +546 0 obj << +/Names [(page.6) 204 0 R (page.7) 209 0 R (page.8) 214 0 R (page.9) 219 0 R (page.i) 114 0 R (page.ii) 121 0 R] +/Limits [(page.6) (page.ii)] +>> endobj +547 0 obj << +/Names [(page.iii) 147 0 R (page.iv) 152 0 R (section*.1) 148 0 R (section*.2) 387 0 R (section*.3) 388 0 R (section*.4) 429 0 R] +/Limits [(page.iii) (section*.4)] +>> endobj +548 0 obj << +/Names [(section*.5) 437 0 R (section*.6) 443 0 R (section*.7) 444 0 R (section*.8) 468 0 R (section.1) 10 0 R (section.2) 14 0 R] +/Limits [(section*.5) (section.2)] +>> endobj +549 0 obj << +/Names [(section.3) 18 0 R (section.4) 22 0 R (section.5) 42 0 R (section.6) 54 0 R (section.7) 62 0 R (section.8) 90 0 R] +/Limits [(section.3) (section.8)] +>> endobj +550 0 obj << +/Names [(subsection.4.1) 26 0 R (subsection.4.2) 30 0 R (subsection.4.3) 34 0 R (subsection.4.4) 38 0 R (subsection.5.1) 46 0 R (subsection.5.2) 50 0 R] +/Limits [(subsection.4.1) (subsection.5.2)] +>> endobj 551 0 obj << -/Names [(Doc-Start) 102 0 R (Item.1) 280 0 R (Item.10) 357 0 R (Item.11) 358 0 R (Item.12) 359 0 R (Item.13) 425 0 R (Item.14) 431 0 R (Item.15) 432 0 R (Item.16) 433 0 R (Item.2) 281 0 R (Item.3) 282 0 R (Item.4) 310 0 R (Item.5) 326 0 R (Item.6) 327 0 R (Item.7) 349 0 R (Item.8) 350 0 R (Item.9) 352 0 R (cite.BREZINA_VANEK) 187 0 R (cite.CAI_SARKIS) 298 0 R (cite.Cai_Widlund_92) 249 0 R (cite.EFSTATHIOU) 299 0 R (cite.MPI1) 191 0 R (cite.PSBLASGUIDE) 190 0 R (cite.SUPERLU) 505 0 R (cite.SUPERLUDIST) 510 0 R (cite.Saad_book) 289 0 R (cite.StubenGMD69_99) 284 0 R (cite.TUMINARO_TONG) 285 0 R (cite.UMFPACK) 393 0 R (cite.VANEK_MANDEL_BREZINA) 188 0 R (cite.aaecc_07) 287 0 R (cite.apnum_07) 288 0 R (cite.dd1_94) 250 0 R (cite.dd2_96) 186 0 R (cite.para_04) 286 0 R (cite.psblas_00) 189 0 R (equation.1) 173 0 R (equation.2) 338 0 R (equation.3) 339 0 R (equation.4) 342 0 R (figure.1) 312 0 R (figure.2) 391 0 R (figure.3) 392 0 R (figure.4) 394 0 R (figure.5) 395 0 R (page.1) 101 0 R (page.10) 243 0 R (page.11) 254 0 R (page.12) 293 0 R (page.13) 303 0 R (page.14) 316 0 R (page.15) 336 0 R (page.16) 347 0 R (page.17) 369 0 R (page.18) 377 0 R (page.19) 399 0 R (page.2) 116 0 R (page.20) 405 0 R (page.21) 409 0 R (page.22) 415 0 R (page.23) 429 0 R (page.24) 440 0 R (page.25) 444 0 R (page.26) 451 0 R (page.27) 456 0 R (page.28) 461 0 R (page.29) 469 0 R (page.3) 206 0 R (page.30) 476 0 R (page.31) 484 0 R (page.32) 490 0 R (page.33) 494 0 R (page.34) 499 0 R (page.35) 503 0 R (page.36) 509 0 R (page.4) 211 0 R (page.5) 219 0 R (page.6) 224 0 R (page.7) 228 0 R (page.8) 234 0 R (page.9) 238 0 R (page.i) 120 0 R (page.ii) 133 0 R (page.iii) 137 0 R (page.iv) 164 0 R (section*.1) 138 0 R (section*.2) 416 0 R (section*.3) 419 0 R (section*.4) 462 0 R (section*.5) 471 0 R (section*.6) 477 0 R (section*.7) 479 0 R (section*.8) 504 0 R (section.1) 10 0 R (section.2) 14 0 R (section.3) 18 0 R (section.4) 22 0 R (section.5) 42 0 R (section.6) 54 0 R (section.7) 62 0 R (section.8) 90 0 R (section.A) 94 0 R (subsection.4.1) 26 0 R (subsection.4.2) 30 0 R (subsection.4.3) 34 0 R (subsection.4.4) 38 0 R (subsection.5.1) 46 0 R (subsection.5.2) 50 0 R (subsection.6.1) 58 0 R (subsection.7.1) 66 0 R (subsection.7.2) 70 0 R (subsection.7.3) 74 0 R (subsection.7.4) 78 0 R (subsection.7.5) 82 0 R (subsection.7.6) 86 0 R (table.1) 363 0 R (table.2) 364 0 R (table.3) 446 0 R (table.4) 452 0 R (table.5) 365 0 R (title.0) 6 0 R] -/Limits [(Doc-Start) (title.0)] +/Names [(subsection.6.1) 58 0 R (subsection.7.1) 66 0 R (subsection.7.2) 70 0 R (subsection.7.3) 74 0 R (subsection.7.4) 78 0 R (subsection.7.5) 82 0 R] +/Limits [(subsection.6.1) (subsection.7.5)] >> endobj 552 0 obj << -/Kids [551 0 R] +/Names [(subsection.7.6) 86 0 R (table.1) 330 0 R (table.2) 331 0 R (table.3) 410 0 R (table.4) 416 0 R (table.5) 332 0 R] +/Limits [(subsection.7.6) (table.5)] >> endobj 553 0 obj << -/Dests 552 0 R +/Names [(title.0) 6 0 R] +/Limits [(title.0) (title.0)] >> endobj 554 0 obj << +/Kids [533 0 R 534 0 R 535 0 R 536 0 R 537 0 R 538 0 R] +/Limits [(Doc-Start) (cite.para_04)] +>> endobj +555 0 obj << +/Kids [539 0 R 540 0 R 541 0 R 542 0 R 543 0 R 544 0 R] +/Limits [(cite.psblas_00) (page.32)] +>> endobj +556 0 obj << +/Kids [545 0 R 546 0 R 547 0 R 548 0 R 549 0 R 550 0 R] +/Limits [(page.33) (subsection.5.2)] +>> endobj +557 0 obj << +/Kids [551 0 R 552 0 R 553 0 R] +/Limits [(subsection.6.1) (title.0)] +>> endobj +558 0 obj << +/Kids [554 0 R 555 0 R 556 0 R 557 0 R] +/Limits [(Doc-Start) (title.0)] +>> endobj +559 0 obj << +/Dests 558 0 R +>> endobj +560 0 obj << /Type /Catalog -/Pages 549 0 R -/Outlines 550 0 R -/Names 553 0 R - /PageMode /UseOutlines /PageLabels << /Nums [0 << /S /D >> 2 << /S /r >> 6 << /S /D >> ] >> +/Pages 531 0 R +/Outlines 532 0 R +/Names 559 0 R + /PageMode/UseOutlines/PageLabels << /Nums [0 << /S /D >> 2 << /S /r >> 6 << /S /D >> ] >> /OpenAction 97 0 R >> endobj -555 0 obj << - /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 1.0) /Subject (MultiLevel Domain Decomposition Parallel Preconditioners Package) /Keywords (Parallel Numerical Software, Algebraic Multilevel Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) /Creator (pdfLaTeX) /Producer ($Id: userguide.tex 2008-04-08 Pasqua D'Ambra, Daniela di Serafino, Salvatore Filippone$) /Author()/Title()/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfeTeX-1.21a)/Keywords() -/CreationDate (D:20080720121947+02'00') -/PTEX.Fullbanner (This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) kpathsea version 3.5.4) +561 0 obj << + /Title (MultiLevel Domain Decomposition Parallel Preconditioners Package based on PSBLAS, V. 1.0) /Subject (MultiLevel Domain Decomposition Parallel Preconditioners Package) /Keywords (Parallel Numerical Software, Algebraic Multilevel Preconditioners, Sparse Iterative Solvers, PSBLAS, MPI) /Creator (pdfLaTeX) /Producer ($Id: userguide.tex 2008-04-08 Pasqua D'Ambra, Daniela di Serafino, Salvatore Filippone$) /Author()/Title()/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfTeX-1.40.3)/Keywords() +/CreationDate (D:20080722181223+02'00') +/ModDate (D:20080722181223+02'00') +/Trapped /False +/PTEX.Fullbanner (This is pdfTeX using libpoppler, Version 3.141592-1.40.3-2.2 (Web2C 7.5.6) kpathsea version 3.5.6) >> endobj xref -0 556 +0 562 0000000001 65535 f 0000000002 00000 f 0000000003 00000 f 0000000004 00000 f 0000000000 00000 f -0000000009 00000 n -0000004337 00000 n -0000506382 00000 n -0000000052 00000 n -0000000103 00000 n -0000040592 00000 n -0000506310 00000 n -0000000148 00000 n -0000000185 00000 n -0000051114 00000 n -0000506224 00000 n -0000000231 00000 n -0000000274 00000 n -0000053817 00000 n -0000506138 00000 n -0000000320 00000 n -0000000358 00000 n -0000062961 00000 n -0000506015 00000 n -0000000404 00000 n -0000000456 00000 n -0000063023 00000 n -0000505941 00000 n -0000000507 00000 n -0000000543 00000 n -0000070221 00000 n -0000505854 00000 n -0000000594 00000 n -0000000647 00000 n -0000070284 00000 n -0000505767 00000 n -0000000698 00000 n -0000000742 00000 n -0000085519 00000 n -0000505693 00000 n -0000000793 00000 n -0000000841 00000 n -0000098268 00000 n -0000505570 00000 n -0000000887 00000 n -0000000951 00000 n -0000119436 00000 n -0000505496 00000 n -0000001002 00000 n -0000001060 00000 n -0000152785 00000 n -0000505422 00000 n -0000001111 00000 n -0000001154 00000 n -0000188971 00000 n -0000505299 00000 n -0000001200 00000 n -0000001236 00000 n -0000217354 00000 n -0000505238 00000 n -0000001287 00000 n -0000001318 00000 n -0000237571 00000 n -0000505115 00000 n -0000001364 00000 n -0000001399 00000 n -0000237633 00000 n -0000505041 00000 n -0000001450 00000 n -0000001499 00000 n -0000248468 00000 n -0000504954 00000 n -0000001550 00000 n -0000001598 00000 n -0000300248 00000 n -0000504867 00000 n -0000001649 00000 n -0000001697 00000 n -0000312376 00000 n -0000504780 00000 n -0000001748 00000 n -0000001797 00000 n -0000312501 00000 n -0000504693 00000 n -0000001848 00000 n -0000001897 00000 n -0000317558 00000 n -0000504619 00000 n -0000001948 00000 n -0000001998 00000 n -0000320617 00000 n -0000504533 00000 n -0000002044 00000 n -0000002079 00000 n -0000326288 00000 n -0000504460 00000 n -0000002125 00000 n -0000002153 00000 n -0000004093 00000 n -0000004397 00000 n -0000002203 00000 n -0000004213 00000 n -0000004275 00000 n -0000502243 00000 n -0000490881 00000 n -0000502081 00000 n -0000490137 00000 n -0000482102 00000 n -0000489975 00000 n -0000481061 00000 n -0000471986 00000 n -0000480900 00000 n -0000503304 00000 n -0000004875 00000 n -0000004689 00000 n -0000004494 00000 n -0000004811 00000 n -0000010165 00000 n -0000009980 00000 n -0000004916 00000 n -0000010102 00000 n -0000470401 00000 n -0000451977 00000 n -0000470240 00000 n -0000450939 00000 n -0000438747 00000 n -0000450777 00000 n -0000437733 00000 n -0000427172 00000 n -0000437570 00000 n -0000010733 00000 n -0000010547 00000 n -0000010263 00000 n -0000010669 00000 n -0000027004 00000 n -0000023088 00000 n -0000010805 00000 n -0000026878 00000 n -0000026941 00000 n -0000023398 00000 n -0000023551 00000 n -0000023706 00000 n -0000023861 00000 n -0000024016 00000 n -0000024177 00000 n -0000024338 00000 n -0000024498 00000 n -0000024659 00000 n -0000024812 00000 n -0000024972 00000 n -0000025133 00000 n -0000025288 00000 n -0000025449 00000 n -0000025604 00000 n -0000025765 00000 n -0000025926 00000 n -0000026087 00000 n -0000026247 00000 n -0000026408 00000 n -0000026569 00000 n -0000026724 00000 n -0000027572 00000 n -0000027386 00000 n -0000027102 00000 n -0000027508 00000 n -0000040718 00000 n -0000039276 00000 n -0000027644 00000 n -0000039466 00000 n -0000426013 00000 n -0000409698 00000 n -0000425851 00000 n -0000039621 00000 n -0000040654 00000 n -0000408647 00000 n -0000398464 00000 n -0000408485 00000 n -0000397530 00000 n -0000393366 00000 n -0000397369 00000 n -0000039779 00000 n -0000039944 00000 n -0000040116 00000 n -0000040275 00000 n -0000040436 00000 n -0000503420 00000 n -0000343871 00000 n -0000337144 00000 n -0000344127 00000 n -0000337836 00000 n -0000337773 00000 n -0000343935 00000 n -0000049164 00000 n -0000047720 00000 n -0000040855 00000 n -0000047918 00000 n -0000048074 00000 n -0000048230 00000 n -0000048386 00000 n -0000048541 00000 n -0000048697 00000 n -0000048853 00000 n -0000049008 00000 n -0000051176 00000 n -0000050754 00000 n -0000049249 00000 n -0000051051 00000 n -0000050896 00000 n -0000053880 00000 n -0000053455 00000 n -0000051274 00000 n -0000053753 00000 n -0000391933 00000 n -0000375646 00000 n -0000391771 00000 n -0000053597 00000 n -0000063085 00000 n -0000062601 00000 n -0000053991 00000 n -0000062898 00000 n -0000062743 00000 n -0000070347 00000 n -0000070035 00000 n -0000063209 00000 n -0000070157 00000 n -0000075038 00000 n -0000074678 00000 n -0000070484 00000 n -0000074975 00000 n -0000074820 00000 n -0000503537 00000 n -0000079451 00000 n -0000079265 00000 n -0000075136 00000 n -0000079387 00000 n -0000085581 00000 n -0000085159 00000 n -0000079549 00000 n -0000085456 00000 n -0000085301 00000 n -0000098331 00000 n -0000097235 00000 n -0000085692 00000 n -0000098204 00000 n -0000097409 00000 n -0000097575 00000 n -0000097732 00000 n -0000097890 00000 n -0000098048 00000 n -0000337458 00000 n -0000337521 00000 n -0000119687 00000 n -0000117374 00000 n -0000098442 00000 n -0000119373 00000 n -0000117596 00000 n -0000117751 00000 n -0000117917 00000 n -0000118082 00000 n -0000118253 00000 n +0000000015 00000 n +0000003678 00000 n +0000416229 00000 n +0000000058 00000 n +0000000109 00000 n +0000028463 00000 n +0000416157 00000 n +0000000154 00000 n +0000000191 00000 n +0000035802 00000 n +0000416071 00000 n +0000000237 00000 n +0000000280 00000 n +0000037776 00000 n +0000415985 00000 n +0000000326 00000 n +0000000364 00000 n +0000044873 00000 n +0000415862 00000 n +0000000410 00000 n +0000000462 00000 n +0000044933 00000 n +0000415788 00000 n +0000000513 00000 n +0000000549 00000 n +0000050610 00000 n +0000415701 00000 n +0000000600 00000 n +0000000653 00000 n +0000050671 00000 n +0000415614 00000 n +0000000704 00000 n +0000000748 00000 n +0000063961 00000 n +0000415540 00000 n +0000000799 00000 n +0000000847 00000 n +0000073318 00000 n +0000415417 00000 n +0000000893 00000 n +0000000957 00000 n +0000090366 00000 n +0000415343 00000 n +0000001008 00000 n +0000001066 00000 n 0000118418 00000 n -0000118577 00000 n -0000118737 00000 n -0000118897 00000 n -0000119055 00000 n -0000374880 00000 n -0000368203 00000 n -0000374719 00000 n -0000367862 00000 n -0000365564 00000 n -0000367704 00000 n -0000365182 00000 n -0000362127 00000 n -0000365023 00000 n -0000361588 00000 n -0000358546 00000 n -0000361427 00000 n -0000357741 00000 n -0000353675 00000 n -0000357580 00000 n -0000119498 00000 n -0000119561 00000 n -0000119624 00000 n -0000119212 00000 n -0000343999 00000 n -0000344063 00000 n -0000337207 00000 n -0000337270 00000 n -0000337333 00000 n -0000343807 00000 n -0000136875 00000 n -0000136005 00000 n -0000119889 00000 n -0000136811 00000 n -0000136171 00000 n -0000136333 00000 n -0000136495 00000 n -0000136653 00000 n -0000337396 00000 n -0000337710 00000 n -0000152910 00000 n -0000151578 00000 n -0000137064 00000 n -0000152722 00000 n -0000151760 00000 n -0000151915 00000 n -0000152072 00000 n -0000152230 00000 n -0000152385 00000 n -0000152550 00000 n -0000152847 00000 n -0000503654 00000 n -0000166935 00000 n -0000167126 00000 n -0000165883 00000 n -0000153099 00000 n -0000166871 00000 n -0000353331 00000 n -0000350622 00000 n -0000353172 00000 n -0000350160 00000 n -0000346708 00000 n -0000349999 00000 n -0000346403 00000 n -0000344289 00000 n -0000346245 00000 n -0000166998 00000 n -0000167062 00000 n -0000166057 00000 n -0000166217 00000 n -0000166389 00000 n -0000166548 00000 n -0000166708 00000 n -0000173954 00000 n -0000172884 00000 n -0000167340 00000 n -0000173700 00000 n -0000173050 00000 n -0000173763 00000 n -0000173827 00000 n -0000173205 00000 n -0000173370 00000 n -0000173891 00000 n -0000173536 00000 n -0000189418 00000 n -0000187284 00000 n -0000174143 00000 n -0000188907 00000 n -0000187490 00000 n -0000189034 00000 n -0000189098 00000 n -0000187653 00000 n -0000189162 00000 n -0000187807 00000 n -0000187967 00000 n -0000188123 00000 n -0000188277 00000 n -0000189226 00000 n -0000189290 00000 n -0000189354 00000 n -0000188430 00000 n -0000188586 00000 n -0000188747 00000 n -0000201468 00000 n -0000258803 00000 n -0000294810 00000 n -0000201532 00000 n -0000200609 00000 n -0000189542 00000 n -0000201405 00000 n -0000200775 00000 n -0000200930 00000 n -0000201090 00000 n -0000201249 00000 n -0000217417 00000 n -0000215031 00000 n -0000201656 00000 n -0000217290 00000 n -0000215269 00000 n -0000215423 00000 n -0000215576 00000 n -0000215732 00000 n -0000215894 00000 n -0000216049 00000 n -0000216204 00000 n -0000216362 00000 n -0000216517 00000 n -0000216671 00000 n -0000216825 00000 n -0000216980 00000 n -0000217135 00000 n -0000221940 00000 n -0000227091 00000 n -0000337584 00000 n -0000227155 00000 n -0000227219 00000 n -0000222004 00000 n -0000221580 00000 n -0000217541 00000 n -0000221877 00000 n -0000221722 00000 n -0000503771 00000 n -0000227283 00000 n -0000226905 00000 n -0000222102 00000 n -0000227027 00000 n -0000237694 00000 n -0000237042 00000 n -0000227381 00000 n -0000237508 00000 n -0000237192 00000 n -0000237347 00000 n -0000248658 00000 n -0000247069 00000 n -0000237870 00000 n -0000248340 00000 n -0000248404 00000 n -0000247259 00000 n -0000247412 00000 n -0000248531 00000 n -0000247568 00000 n -0000247722 00000 n -0000247876 00000 n -0000248030 00000 n -0000248184 00000 n -0000248595 00000 n -0000252547 00000 n -0000251512 00000 n -0000248795 00000 n -0000252295 00000 n -0000251678 00000 n -0000252358 00000 n -0000252421 00000 n -0000252484 00000 n -0000251833 00000 n -0000251987 00000 n -0000252141 00000 n -0000258867 00000 n -0000258617 00000 n -0000252632 00000 n -0000258739 00000 n -0000272238 00000 n -0000271814 00000 n -0000258965 00000 n -0000272111 00000 n -0000271956 00000 n -0000272174 00000 n -0000503888 00000 n -0000282383 00000 n -0000282133 00000 n -0000272375 00000 n -0000282255 00000 n -0000282319 00000 n -0000294873 00000 n -0000294450 00000 n -0000282546 00000 n -0000294747 00000 n -0000294592 00000 n -0000300375 00000 n -0000299545 00000 n -0000295010 00000 n -0000300184 00000 n -0000300311 00000 n -0000299703 00000 n -0000299866 00000 n -0000300028 00000 n -0000312563 00000 n -0000311852 00000 n -0000300512 00000 n -0000312313 00000 n -0000312002 00000 n -0000312438 00000 n -0000312157 00000 n -0000317685 00000 n -0000316969 00000 n -0000312752 00000 n -0000317430 00000 n -0000317494 00000 n -0000317119 00000 n -0000317621 00000 n -0000317274 00000 n -0000320679 00000 n -0000320257 00000 n -0000317822 00000 n -0000320554 00000 n -0000320399 00000 n -0000504005 00000 n -0000321382 00000 n -0000321196 00000 n -0000320790 00000 n -0000321318 00000 n -0000326350 00000 n -0000325928 00000 n -0000321467 00000 n -0000326225 00000 n -0000326070 00000 n -0000327053 00000 n -0000326867 00000 n -0000326461 00000 n -0000326989 00000 n -0000337899 00000 n -0000336896 00000 n -0000327138 00000 n -0000337018 00000 n -0000337081 00000 n -0000337647 00000 n -0000344191 00000 n -0000343557 00000 n -0000338023 00000 n -0000343679 00000 n -0000343743 00000 n -0000346634 00000 n -0000346610 00000 n -0000350468 00000 n -0000350368 00000 n -0000353572 00000 n -0000353534 00000 n -0000358310 00000 n -0000358045 00000 n -0000362007 00000 n -0000361797 00000 n -0000365451 00000 n -0000365395 00000 n -0000368108 00000 n -0000368078 00000 n -0000375380 00000 n -0000375120 00000 n -0000392843 00000 n -0000392469 00000 n -0000398124 00000 n -0000397858 00000 n -0000409257 00000 n -0000408947 00000 n -0000426774 00000 n -0000426406 00000 n -0000438342 00000 n -0000438062 00000 n -0000451612 00000 n -0000451275 00000 n -0000471388 00000 n -0000470958 00000 n -0000481659 00000 n -0000481385 00000 n -0000490623 00000 n -0000490399 00000 n -0000502943 00000 n -0000502592 00000 n -0000504122 00000 n -0000504240 00000 n -0000504317 00000 n -0000504387 00000 n -0000506478 00000 n -0000508979 00000 n -0000509018 00000 n -0000509056 00000 n -0000509254 00000 n +0000415269 00000 n +0000001117 00000 n +0000001160 00000 n +0000146016 00000 n +0000415146 00000 n +0000001206 00000 n +0000001242 00000 n +0000166896 00000 n +0000415085 00000 n +0000001293 00000 n +0000001324 00000 n +0000183270 00000 n +0000414962 00000 n +0000001370 00000 n +0000001405 00000 n +0000183330 00000 n +0000414888 00000 n +0000001456 00000 n +0000001505 00000 n +0000191489 00000 n +0000414801 00000 n +0000001556 00000 n +0000001604 00000 n +0000230755 00000 n +0000414714 00000 n +0000001655 00000 n +0000001703 00000 n +0000241021 00000 n +0000414627 00000 n +0000001754 00000 n +0000001803 00000 n +0000241142 00000 n +0000414540 00000 n +0000001854 00000 n +0000001903 00000 n +0000245056 00000 n +0000414466 00000 n +0000001954 00000 n +0000002004 00000 n +0000247494 00000 n +0000414380 00000 n +0000002050 00000 n +0000002085 00000 n +0000252560 00000 n +0000414307 00000 n +0000002132 00000 n +0000002160 00000 n +0000003441 00000 n +0000003736 00000 n +0000002210 00000 n +0000003558 00000 n +0000003618 00000 n +0000410723 00000 n +0000412863 00000 n +0000411871 00000 n +0000413151 00000 n +0000004105 00000 n +0000003924 00000 n +0000003833 00000 n +0000004043 00000 n +0000008185 00000 n +0000008005 00000 n +0000004146 00000 n +0000008124 00000 n +0000411728 00000 n +0000410579 00000 n +0000410867 00000 n +0000008605 00000 n +0000008424 00000 n +0000008283 00000 n +0000008543 00000 n +0000015076 00000 n +0000015226 00000 n +0000015377 00000 n +0000015528 00000 n +0000015679 00000 n +0000015836 00000 n +0000015993 00000 n +0000016150 00000 n +0000016306 00000 n +0000016456 00000 n +0000016613 00000 n +0000016769 00000 n +0000016919 00000 n +0000017076 00000 n +0000017227 00000 n +0000017383 00000 n +0000017539 00000 n +0000017696 00000 n +0000017852 00000 n +0000018007 00000 n +0000018164 00000 n +0000018315 00000 n +0000018589 00000 n +0000014769 00000 n +0000008677 00000 n +0000018467 00000 n +0000018528 00000 n +0000019009 00000 n +0000018828 00000 n +0000018687 00000 n +0000018947 00000 n +0000027515 00000 n +0000027669 00000 n +0000027830 00000 n +0000027998 00000 n +0000028154 00000 n +0000028311 00000 n +0000027364 00000 n +0000028585 00000 n +0000027177 00000 n +0000019081 00000 n +0000412719 00000 n +0000028523 00000 n +0000411155 00000 n +0000412296 00000 n +0000413267 00000 n +0000264850 00000 n +0000260052 00000 n +0000265098 00000 n +0000260723 00000 n +0000260662 00000 n +0000264912 00000 n +0000033135 00000 n +0000033287 00000 n +0000033439 00000 n +0000033590 00000 n +0000033742 00000 n +0000033892 00000 n +0000034044 00000 n +0000034196 00000 n +0000034349 00000 n +0000032940 00000 n +0000028722 00000 n +0000035590 00000 n +0000035862 00000 n +0000035451 00000 n +0000034434 00000 n +0000035741 00000 n +0000037561 00000 n +0000037837 00000 n +0000037422 00000 n +0000035960 00000 n +0000037714 00000 n +0000413007 00000 n +0000044661 00000 n +0000044993 00000 n +0000044522 00000 n +0000037948 00000 n +0000044812 00000 n +0000050732 00000 n +0000050429 00000 n +0000045117 00000 n +0000050548 00000 n +0000054903 00000 n +0000055115 00000 n +0000054764 00000 n +0000050869 00000 n +0000055054 00000 n +0000413384 00000 n +0000059279 00000 n +0000059098 00000 n +0000055213 00000 n +0000059217 00000 n +0000063749 00000 n +0000064021 00000 n +0000063610 00000 n +0000059377 00000 n +0000063900 00000 n +0000072481 00000 n +0000072643 00000 n +0000072797 00000 n +0000072949 00000 n +0000073102 00000 n +0000088728 00000 n +0000073379 00000 n +0000072310 00000 n +0000064132 00000 n +0000073256 00000 n +0000260357 00000 n +0000260418 00000 n +0000088890 00000 n +0000089049 00000 n +0000089216 00000 n +0000089375 00000 n +0000089530 00000 n +0000089686 00000 n +0000089842 00000 n +0000089996 00000 n +0000090148 00000 n +0000104845 00000 n +0000105003 00000 n +0000088577 00000 n +0000090609 00000 n +0000088358 00000 n +0000073490 00000 n +0000090305 00000 n +0000411585 00000 n +0000412579 00000 n +0000412155 00000 n +0000411299 00000 n +0000411012 00000 n +0000090426 00000 n +0000090487 00000 n +0000090548 00000 n +0000264974 00000 n +0000265036 00000 n +0000260113 00000 n +0000260174 00000 n +0000260235 00000 n +0000264788 00000 n +0000105161 00000 n +0000105314 00000 n +0000105530 00000 n +0000104682 00000 n +0000090811 00000 n +0000105468 00000 n +0000260296 00000 n +0000260601 00000 n +0000117573 00000 n +0000117726 00000 n +0000117879 00000 n +0000118028 00000 n +0000118189 00000 n +0000117422 00000 n +0000118539 00000 n +0000117243 00000 n +0000105719 00000 n +0000118357 00000 n +0000118478 00000 n +0000413501 00000 n +0000129902 00000 n +0000129045 00000 n +0000129201 00000 n +0000129368 00000 n +0000129524 00000 n +0000129680 00000 n +0000130087 00000 n +0000128874 00000 n +0000118728 00000 n +0000129840 00000 n +0000412014 00000 n +0000411442 00000 n +0000412439 00000 n +0000129963 00000 n +0000130025 00000 n +0000134594 00000 n +0000134755 00000 n +0000134917 00000 n +0000134443 00000 n +0000135324 00000 n +0000134280 00000 n +0000130301 00000 n +0000135077 00000 n +0000135138 00000 n +0000135200 00000 n +0000135262 00000 n +0000144573 00000 n +0000144732 00000 n +0000144880 00000 n +0000145036 00000 n +0000145188 00000 n +0000145338 00000 n +0000145488 00000 n +0000145640 00000 n +0000145797 00000 n +0000154917 00000 n +0000155073 00000 n +0000155228 00000 n +0000146449 00000 n +0000144370 00000 n +0000135513 00000 n +0000145954 00000 n +0000146077 00000 n +0000146139 00000 n +0000146201 00000 n +0000146263 00000 n +0000146325 00000 n +0000146387 00000 n +0000155441 00000 n +0000198688 00000 n +0000226633 00000 n +0000164861 00000 n +0000165012 00000 n +0000154766 00000 n +0000155503 00000 n +0000154603 00000 n +0000146573 00000 n +0000155380 00000 n +0000165161 00000 n +0000165313 00000 n +0000165472 00000 n +0000165624 00000 n +0000165775 00000 n +0000165930 00000 n +0000166081 00000 n +0000166231 00000 n +0000166381 00000 n +0000166532 00000 n +0000166683 00000 n +0000166957 00000 n +0000164626 00000 n +0000155627 00000 n +0000166834 00000 n +0000170887 00000 n +0000174842 00000 n +0000260479 00000 n +0000174902 00000 n +0000174963 00000 n +0000170675 00000 n +0000170948 00000 n +0000170536 00000 n +0000167081 00000 n +0000170826 00000 n +0000413618 00000 n +0000175025 00000 n +0000174661 00000 n +0000171046 00000 n +0000174780 00000 n +0000183053 00000 n +0000190315 00000 n +0000190465 00000 n +0000182902 00000 n +0000183390 00000 n +0000182755 00000 n +0000175123 00000 n +0000183209 00000 n +0000190617 00000 n +0000190765 00000 n +0000190915 00000 n +0000191065 00000 n +0000191214 00000 n +0000191674 00000 n +0000190128 00000 n +0000183566 00000 n +0000191366 00000 n +0000191428 00000 n +0000191550 00000 n +0000191612 00000 n +0000193317 00000 n +0000193467 00000 n +0000193617 00000 n +0000193166 00000 n +0000194013 00000 n +0000193003 00000 n +0000191811 00000 n +0000193769 00000 n +0000193830 00000 n +0000193891 00000 n +0000193952 00000 n +0000198752 00000 n +0000198507 00000 n +0000194098 00000 n +0000198626 00000 n +0000208820 00000 n +0000209095 00000 n +0000208681 00000 n +0000198850 00000 n +0000208971 00000 n +0000209032 00000 n +0000413735 00000 n +0000216955 00000 n +0000216710 00000 n +0000209232 00000 n +0000216829 00000 n +0000216891 00000 n +0000226421 00000 n +0000226696 00000 n +0000226282 00000 n +0000217118 00000 n +0000226572 00000 n +0000230225 00000 n +0000230384 00000 n +0000230542 00000 n +0000230878 00000 n +0000230070 00000 n +0000226833 00000 n +0000230693 00000 n +0000230816 00000 n +0000240809 00000 n +0000244629 00000 n +0000240658 00000 n +0000241202 00000 n +0000240511 00000 n +0000231015 00000 n +0000240960 00000 n +0000241081 00000 n +0000244781 00000 n +0000245179 00000 n +0000244482 00000 n +0000241391 00000 n +0000244933 00000 n +0000244995 00000 n +0000245117 00000 n +0000247282 00000 n +0000247554 00000 n +0000247143 00000 n +0000245316 00000 n +0000247433 00000 n +0000413852 00000 n +0000248079 00000 n +0000247898 00000 n +0000247665 00000 n +0000248017 00000 n +0000252347 00000 n +0000252620 00000 n +0000252208 00000 n +0000248164 00000 n +0000252499 00000 n +0000253145 00000 n +0000252964 00000 n +0000252731 00000 n +0000253083 00000 n +0000260783 00000 n +0000259811 00000 n +0000253230 00000 n +0000259930 00000 n +0000259991 00000 n +0000260540 00000 n +0000265160 00000 n +0000264545 00000 n +0000260907 00000 n +0000264664 00000 n +0000264726 00000 n +0000265258 00000 n +0000265283 00000 n +0000265514 00000 n +0000265573 00000 n +0000266269 00000 n +0000266833 00000 n +0000266936 00000 n +0000266973 00000 n +0000267602 00000 n +0000267997 00000 n +0000268633 00000 n +0000269254 00000 n +0000269923 00000 n +0000270437 00000 n +0000271052 00000 n +0000271696 00000 n +0000272180 00000 n +0000272537 00000 n +0000273178 00000 n +0000284675 00000 n +0000285033 00000 n +0000295700 00000 n +0000296071 00000 n +0000305936 00000 n +0000306287 00000 n +0000309659 00000 n +0000309985 00000 n +0000319473 00000 n +0000319792 00000 n +0000322140 00000 n +0000322368 00000 n +0000325126 00000 n +0000325353 00000 n +0000331336 00000 n +0000331595 00000 n +0000349325 00000 n +0000349904 00000 n +0000358285 00000 n +0000358631 00000 n +0000360648 00000 n +0000360873 00000 n +0000363236 00000 n +0000363471 00000 n +0000366941 00000 n +0000367287 00000 n +0000368710 00000 n +0000368935 00000 n +0000370542 00000 n +0000370776 00000 n +0000386396 00000 n +0000386808 00000 n +0000394148 00000 n +0000394429 00000 n +0000410021 00000 n +0000413969 00000 n +0000414087 00000 n +0000414164 00000 n +0000414234 00000 n +0000416325 00000 n +0000416498 00000 n +0000416664 00000 n +0000416833 00000 n +0000417073 00000 n +0000417302 00000 n +0000417538 00000 n +0000417736 00000 n +0000417910 00000 n +0000418080 00000 n +0000418249 00000 n +0000418419 00000 n +0000418588 00000 n +0000418755 00000 n +0000418919 00000 n +0000419106 00000 n +0000419295 00000 n +0000419475 00000 n +0000419695 00000 n +0000419915 00000 n +0000420098 00000 n +0000420176 00000 n +0000420292 00000 n +0000420408 00000 n +0000420524 00000 n +0000420616 00000 n +0000420711 00000 n +0000420749 00000 n +0000420945 00000 n trailer -<< -/Size 556 -/Root 554 0 R -/Info 555 0 R -/ID [ ] ->> +<< /Size 562 +/Root 560 0 R +/Info 561 0 R +/ID [ ] >> startxref -509929 +421688 %%EOF diff --git a/examples/fileread/mld_cexample_1lev.f90 b/examples/fileread/mld_cexample_1lev.f90 index 9939d779..171fd99d 100644 --- a/examples/fileread/mld_cexample_1lev.f90 +++ b/examples/fileread/mld_cexample_1lev.f90 @@ -56,6 +56,7 @@ program mld_cexample_ml ! input parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_cspmat_type) :: A, aux_A @@ -86,6 +87,7 @@ program mld_cexample_ml real(psb_dpk_) :: t1, t2, tprec real(psb_spk_) :: resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -105,7 +107,7 @@ program mld_cexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -114,16 +116,35 @@ program mld_cexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -281,14 +302,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,itmax,tol) use psb_base_mod implicit none integer :: ictxt, itmax real(psb_spk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -297,12 +318,14 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_cexample_ml.f90 b/examples/fileread/mld_cexample_ml.f90 index 9cae2bbc..2396058a 100644 --- a/examples/fileread/mld_cexample_ml.f90 +++ b/examples/fileread/mld_cexample_ml.f90 @@ -59,6 +59,7 @@ program mld_cexample_ml ! input file parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_cspmat_type) :: A, aux_A @@ -89,7 +90,8 @@ program mld_cexample_ml integer :: ierr, ircode real(psb_dpk_) :: t1, t2, tprec real(psb_spk_) :: resmx, resmxp - character(len=20) :: name + character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -109,7 +111,7 @@ program mld_cexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,choice,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,choice,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -118,16 +120,35 @@ program mld_cexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -318,14 +339,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,choice,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,choice,itmax,tol) use psb_base_mod implicit none integer :: ictxt, choice, itmax real(psb_spk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -334,6 +355,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(choice,5) call read_data(itmax,5) call read_data(tol,5) @@ -341,6 +363,7 @@ contains call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,choice) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_dexample_1lev.f90 b/examples/fileread/mld_dexample_1lev.f90 index a91d5444..73ecc9ac 100644 --- a/examples/fileread/mld_dexample_1lev.f90 +++ b/examples/fileread/mld_dexample_1lev.f90 @@ -56,6 +56,7 @@ program mld_dexample_ml ! input parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_dspmat_type) :: A, aux_A @@ -85,6 +86,7 @@ program mld_dexample_ml integer :: ierr, ircode real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -104,7 +106,7 @@ program mld_dexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -113,16 +115,35 @@ program mld_dexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -280,14 +301,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,itmax,tol) use psb_base_mod implicit none integer :: ictxt, itmax real(psb_dpk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -296,12 +317,14 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_dexample_ml.f90 b/examples/fileread/mld_dexample_ml.f90 index 2d7e6327..84b756db 100644 --- a/examples/fileread/mld_dexample_ml.f90 +++ b/examples/fileread/mld_dexample_ml.f90 @@ -59,6 +59,7 @@ program mld_dexample_ml ! input file parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_dspmat_type) :: A, aux_A @@ -89,6 +90,7 @@ program mld_dexample_ml integer :: ierr, ircode real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -108,7 +110,7 @@ program mld_dexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,choice,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,choice,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -117,16 +119,35 @@ program mld_dexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -317,14 +338,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,choice,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,choice,itmax,tol) use psb_base_mod implicit none integer :: ictxt, choice, itmax real(psb_dpk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -333,6 +354,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(choice,5) call read_data(itmax,5) call read_data(tol,5) @@ -340,6 +362,7 @@ contains call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,choice) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_sexample_1lev.f90 b/examples/fileread/mld_sexample_1lev.f90 index dbae52af..e3e916cf 100644 --- a/examples/fileread/mld_sexample_1lev.f90 +++ b/examples/fileread/mld_sexample_1lev.f90 @@ -56,6 +56,7 @@ program mld_sexample_ml ! input parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_sspmat_type) :: A, aux_A @@ -86,6 +87,7 @@ program mld_sexample_ml real(psb_dpk_) :: t1, t2, tprec real(psb_spk_) :: resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -105,7 +107,7 @@ program mld_sexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -114,16 +116,35 @@ program mld_sexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -281,14 +302,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,itmax,tol) use psb_base_mod implicit none integer :: ictxt, itmax real(psb_spk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -297,12 +318,14 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_sexample_ml.f90 b/examples/fileread/mld_sexample_ml.f90 index a7bf7545..01d90ad7 100644 --- a/examples/fileread/mld_sexample_ml.f90 +++ b/examples/fileread/mld_sexample_ml.f90 @@ -59,6 +59,7 @@ program mld_sexample_ml ! input file parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_sspmat_type) :: A, aux_A @@ -90,6 +91,7 @@ program mld_sexample_ml real(psb_dpk_) :: t1, t2, tprec real(psb_spk_) :: resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -109,7 +111,7 @@ program mld_sexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,choice,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,choice,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -118,16 +120,35 @@ program mld_sexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -318,14 +339,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,choice,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,choice,itmax,tol) use psb_base_mod implicit none integer :: ictxt, choice, itmax real(psb_spk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -334,6 +355,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(choice,5) call read_data(itmax,5) call read_data(tol,5) @@ -341,6 +363,7 @@ contains call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,choice) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_zexample_1lev.f90 b/examples/fileread/mld_zexample_1lev.f90 index f5d17d5a..e6b1c854 100644 --- a/examples/fileread/mld_zexample_1lev.f90 +++ b/examples/fileread/mld_zexample_1lev.f90 @@ -56,6 +56,7 @@ program mld_zexample_ml ! input parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_zspmat_type) :: A, aux_A @@ -85,6 +86,7 @@ program mld_zexample_ml integer :: ierr, ircode real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -104,7 +106,7 @@ program mld_zexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -113,16 +115,35 @@ program mld_zexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -280,14 +301,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,itmax,tol) use psb_base_mod implicit none integer :: ictxt, itmax real(psb_dpk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -296,12 +317,14 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(itmax,5) call read_data(tol,5) end if call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/examples/fileread/mld_zexample_ml.f90 b/examples/fileread/mld_zexample_ml.f90 index 959b9e1f..52f24bb6 100644 --- a/examples/fileread/mld_zexample_ml.f90 +++ b/examples/fileread/mld_zexample_ml.f90 @@ -59,6 +59,7 @@ program mld_zexample_ml ! input file parameters character(len=40) :: mtrx_file, rhs_file + character(len=2) :: filefmt ! sparse matrices type(psb_zspmat_type) :: A, aux_A @@ -89,6 +90,7 @@ program mld_zexample_ml integer :: ierr, ircode real(psb_dpk_) :: t1, t2, tprec, resmx, resmxp character(len=20) :: name + integer, parameter :: iunit=12 ! initialize the parallel environment @@ -108,7 +110,7 @@ program mld_zexample_ml ! get parameters - call get_parms(ictxt,mtrx_file,rhs_file,choice,itmax,tol) + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,choice,itmax,tol) call psb_barrier(ictxt) t1 = psb_wtime() @@ -117,16 +119,35 @@ program mld_zexample_ml ! using PSBLAS routines for sparse matrix / vector management if (iam==psb_root_) then - call read_mat(mtrx_file, aux_A, ictxt) - - m_problem = aux_A%m - call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) end if - + + m_problem = aux_a%m + call psb_bcast(ictxt,m_problem) + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -317,14 +338,14 @@ contains ! ! get parameters from standard input ! - subroutine get_parms(ictxt,mtrx,rhs,choice,itmax,tol) + subroutine get_parms(ictxt,mtrx,rhs,filefmt,choice,itmax,tol) use psb_base_mod implicit none integer :: ictxt, choice, itmax real(psb_dpk_) :: tol - character(len=*) :: mtrx, rhs + character(len=*) :: mtrx, rhs,filefmt integer :: iam, np call psb_info(ictxt,iam,np) @@ -333,6 +354,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(choice,5) call read_data(itmax,5) call read_data(tol,5) @@ -340,6 +362,7 @@ contains call psb_bcast(ictxt,mtrx) call psb_bcast(ictxt,rhs) + call psb_bcast(ictxt,filefmt) call psb_bcast(ictxt,choice) call psb_bcast(ictxt,itmax) call psb_bcast(ictxt,tol) diff --git a/mlprec/mld_cprecset.f90 b/mlprec/mld_cprecset.f90 index 11f0ea55..ee2739a7 100644 --- a/mlprec/mld_cprecset.f90 +++ b/mlprec/mld_cprecset.f90 @@ -168,7 +168,7 @@ subroutine mld_cprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif @@ -246,7 +246,7 @@ subroutine mld_cprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif diff --git a/mlprec/mld_dprecset.f90 b/mlprec/mld_dprecset.f90 index 5909ab01..abf7a7aa 100644 --- a/mlprec/mld_dprecset.f90 +++ b/mlprec/mld_dprecset.f90 @@ -168,7 +168,7 @@ subroutine mld_dprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif @@ -246,7 +246,7 @@ subroutine mld_dprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif diff --git a/mlprec/mld_sprecset.f90 b/mlprec/mld_sprecset.f90 index 28ddd81e..09b4c510 100644 --- a/mlprec/mld_sprecset.f90 +++ b/mlprec/mld_sprecset.f90 @@ -168,7 +168,7 @@ subroutine mld_sprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif @@ -246,7 +246,7 @@ subroutine mld_sprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif diff --git a/mlprec/mld_zprecset.f90 b/mlprec/mld_zprecset.f90 index 50c51ac4..73614bad 100644 --- a/mlprec/mld_zprecset.f90 +++ b/mlprec/mld_zprecset.f90 @@ -168,7 +168,7 @@ subroutine mld_zprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif @@ -246,7 +246,7 @@ subroutine mld_zprecseti(p,what,val,info,ilev) case(mld_umf_, mld_slu_) p%baseprecv(nlev_)%iprcparm(mld_coarse_mat_) = mld_repl_mat_ p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val - case(mld_slu_dist_) + case(mld_sludist_) p%baseprecv(nlev_)%iprcparm(mld_sub_solve_) = val end select endif diff --git a/test/fileread/cf_sample.f90 b/test/fileread/cf_sample.f90 index 3b47c681..96cf4ed1 100644 --- a/test/fileread/cf_sample.f90 +++ b/test/fileread/cf_sample.f90 @@ -47,6 +47,7 @@ program cf_sample ! input parameters character(len=40) :: kmethd, mtrx_file, rhs_file + character(len=2) :: filefmt type precdata character(len=20) :: descr ! verbose description of the prec character(len=10) :: prec ! overall prectype @@ -96,6 +97,7 @@ program cf_sample character(len=5) :: afmt character(len=20) :: name + integer, parameter :: iunit=12 integer :: iparm(20) ! other variables @@ -124,7 +126,7 @@ program cf_sample ! ! get parameters ! - call get_parms(ictxt,mtrx_file,rhs_file,kmethd,& + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,kmethd,& & prec_choice,ipart,afmt,istopc,itmax,itrace,irst,eps) call psb_barrier(ictxt) @@ -133,16 +135,35 @@ program cf_sample nrhs = 1 if (iam==psb_root_) then - call read_mat(mtrx_file, aux_a, ictxt) - + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) + end if + m_problem = aux_a%m call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) - end if - + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,dim=1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -347,14 +368,14 @@ contains ! ! get iteration parameters from standard input ! - subroutine get_parms(icontxt,mtrx,rhs,kmethd,& + subroutine get_parms(icontxt,mtrx,rhs,filefmt,kmethd,& & prec, ipart,afmt,istopc,itmax,itrace,irst,eps) use psb_base_mod implicit none integer :: icontxt - character(len=*) :: kmethd, mtrx, rhs, afmt + character(len=*) :: kmethd, mtrx, rhs, afmt,filefmt type(precdata) :: prec integer :: iret, istopc,itmax,itrace, ipart, irst real(psb_spk_) :: eps, omega,thr1,thr2 @@ -366,6 +387,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(kmethd,5) call read_data(afmt,5) call read_data(ipart,5) @@ -401,6 +423,7 @@ contains call psb_bcast(icontxt,mtrx) call psb_bcast(icontxt,rhs) + call psb_bcast(icontxt,filefmt) call psb_bcast(icontxt,kmethd) call psb_bcast(icontxt,afmt) call psb_bcast(icontxt,ipart) @@ -453,8 +476,3 @@ contains write(iout, *) ' 0: block partition ' end subroutine pr_usage end program cf_sample - - - - - diff --git a/test/fileread/df_sample.f90 b/test/fileread/df_sample.f90 index 3a34f80e..4f3e975b 100644 --- a/test/fileread/df_sample.f90 +++ b/test/fileread/df_sample.f90 @@ -47,6 +47,7 @@ program df_sample ! input parameters character(len=40) :: kmethd, mtrx_file, rhs_file + character(len=2) :: filefmt type precdata character(len=20) :: descr ! verbose description of the prec character(len=10) :: prec ! overall prectype @@ -96,6 +97,7 @@ program df_sample character(len=5) :: afmt character(len=20) :: name + integer, parameter :: iunit=12 integer :: iparm(20) ! other variables @@ -124,7 +126,7 @@ program df_sample ! ! get parameters ! - call get_parms(ictxt,mtrx_file,rhs_file,kmethd,& + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,kmethd,& & prec_choice,ipart,afmt,istopc,itmax,itrace,irst,eps) call psb_barrier(ictxt) @@ -133,16 +135,35 @@ program df_sample nrhs = 1 if (iam==psb_root_) then - call read_mat(mtrx_file, aux_a, ictxt) - + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) + end if + m_problem = aux_a%m call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) - end if - + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,dim=1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -347,14 +368,14 @@ contains ! ! get iteration parameters from standard input ! - subroutine get_parms(icontxt,mtrx,rhs,kmethd,& + subroutine get_parms(icontxt,mtrx,rhs,filefmt,kmethd,& & prec, ipart,afmt,istopc,itmax,itrace,irst,eps) use psb_base_mod implicit none integer :: icontxt - character(len=*) :: kmethd, mtrx, rhs, afmt + character(len=*) :: kmethd, mtrx, rhs, afmt,filefmt type(precdata) :: prec integer :: iret, istopc,itmax,itrace, ipart, irst real(psb_dpk_) :: eps, omega,thr1,thr2 @@ -366,6 +387,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(kmethd,5) call read_data(afmt,5) call read_data(ipart,5) @@ -401,6 +423,7 @@ contains call psb_bcast(icontxt,mtrx) call psb_bcast(icontxt,rhs) + call psb_bcast(icontxt,filefmt) call psb_bcast(icontxt,kmethd) call psb_bcast(icontxt,afmt) call psb_bcast(icontxt,ipart) diff --git a/test/fileread/runs/cfs.inp b/test/fileread/runs/cfs.inp index d34b949f..09bcc374 100644 --- a/test/fileread/runs/cfs.inp +++ b/test/fileread/runs/cfs.inp @@ -1,11 +1,12 @@ -qc2534.mtx !This (and others) from: http://math.nist.gov/MatrixMarket/ or -NONE !http://www.cise.ufl.edu/research/sparse/matrices/index.html +qc2534.mtx ! This (and others) from: http://math.nist.gov/MatrixMarket/ or +NONE ! http://www.cise.ufl.edu/research/sparse/matrices/index.html +MM ! File format: MM: Matrix Market HB: Harwell-Boeing. BICGSTAB ! Iterative method: BiCGSTAB BiCG CGS RGMRES BiCGSTABL CG CSR ! Storage format CSR COO JAD 0 ! IPART: Partition method 0: BLK 2: graph (with Metis) 2 ! ISTOPC 01000 ! ITMAX -01 ! ITRACE +-1 ! ITRACE 30 ! IRST (restart for RGMRES and BiCGSTABL) 1.d-5 ! EPS 3L-M-RAS-I-D4 ! Longer descriptive name for preconditioner (up to 20 chars) @@ -22,8 +23,8 @@ DEC ! Type of aggregation DEC SYMDEC GLB MULT ! Type of multilevel correction: ADD MULT POST ! Side of multiplicative correction PRE POST BOTH (ignored for ADD) DIST ! Coarse level: matrix distribution DIST REPL -BJAC ! Coarse level: solver BJAC SLU -ILU ! Coarse level: subsolver ILU SLU +BJAC ! Coarse level: solver BJAC UMF SLU SLUDIST +ILU ! Coarse level: subsolver ILU UMF SLU SLUDIST 0 ! Coarse level: Level-set N for ILU(N) 1.d-4 ! Coarse level: Threshold T for ILU(T,P) 4 ! Coarse level: Number of Jacobi sweeps diff --git a/test/fileread/runs/dfs.inp b/test/fileread/runs/dfs.inp index bec94877..347bdc6c 100644 --- a/test/fileread/runs/dfs.inp +++ b/test/fileread/runs/dfs.inp @@ -1,5 +1,6 @@ -thm1000x600.mtx !matphi_140x33x45.mtx !A_1M_gps.mtx !thm1000x600.mtx ! les_t4.mtx ! young1r.mtx This (and others) from: http://math.nist.gov/MatrixMarket/ or -NONE !tnoto_phi.mtx !NONE !les_t4.rhs ! rhs.mtx http://www.cise.ufl.edu/research/sparse/matrices/index.html +young1r.mtx ! This (and others) from: http://math.nist.gov/MatrixMarket/ or +NONE ! http://www.cise.ufl.edu/research/sparse/matrices/index.html +MM ! File format: MM: Matrix Market HB: Harwell-Boeing. BICGSTAB ! Iterative method: BiCGSTAB BiCG CGS RGMRES BiCGSTABL CG CSR ! Storage format CSR COO JAD 0 ! IPART: Partition method 0: BLK 2: graph (with Metis) @@ -22,7 +23,7 @@ DEC ! Type of aggregation DEC SYMDEC GLB MULT ! Type of multilevel correction: ADD MULT POST ! Side of multiplicative correction PRE POST BOTH (ignored for ADD) DIST ! Coarse level: matrix distribution DIST REPL -UMF ! Coarse level: solver BJAC UMF SLU SLUDIST +BJAC ! Coarse level: solver BJAC UMF SLU SLUDIST ILU ! Coarse level: subsolver ILU UMF SLU SLUDIST 0 ! Coarse level: Level-set N for ILU(N) 1.d-4 ! Coarse level: Threshold T for ILU(T,P) diff --git a/test/fileread/runs/sfs.inp b/test/fileread/runs/sfs.inp index f9ff806f..347bdc6c 100644 --- a/test/fileread/runs/sfs.inp +++ b/test/fileread/runs/sfs.inp @@ -1,11 +1,12 @@ -thm1000x600.mtx ! les_t4.mtx ! young1r.mtx This (and others) from: http://math.nist.gov/MatrixMarket/ or -NONE !les_t4.rhs ! rhs.mtx http://www.cise.ufl.edu/research/sparse/matrices/index.html -RGMRES ! Iterative method: BiCGSTAB BiCG CGS RGMRES BiCGSTABL CG +young1r.mtx ! This (and others) from: http://math.nist.gov/MatrixMarket/ or +NONE ! http://www.cise.ufl.edu/research/sparse/matrices/index.html +MM ! File format: MM: Matrix Market HB: Harwell-Boeing. +BICGSTAB ! Iterative method: BiCGSTAB BiCG CGS RGMRES BiCGSTABL CG CSR ! Storage format CSR COO JAD 0 ! IPART: Partition method 0: BLK 2: graph (with Metis) 2 ! ISTOPC 01000 ! ITMAX -01 ! ITRACE +-1 ! ITRACE 30 ! IRST (restart for RGMRES and BiCGSTABL) 1.d-5 ! EPS 3L-M-RAS-I-D4 ! Longer descriptive name for preconditioner (up to 20 chars) @@ -22,10 +23,10 @@ DEC ! Type of aggregation DEC SYMDEC GLB MULT ! Type of multilevel correction: ADD MULT POST ! Side of multiplicative correction PRE POST BOTH (ignored for ADD) DIST ! Coarse level: matrix distribution DIST REPL -SLU ! Coarse level: solver BJAC SLU -ILU ! Coarse level: subsolver ILU SLU +BJAC ! Coarse level: solver BJAC UMF SLU SLUDIST +ILU ! Coarse level: subsolver ILU UMF SLU SLUDIST 0 ! Coarse level: Level-set N for ILU(N) 1.d-4 ! Coarse level: Threshold T for ILU(T,P) 4 ! Coarse level: Number of Jacobi sweeps -1.0d0 ! Smoother Omega: if < 0 means library choice. -0.01d0 ! Smoother Aggregation Threshold: >= 0.0 \ No newline at end of file +0.10d0 ! Smoother Aggregation Threshold: >= 0.0 diff --git a/test/fileread/runs/zfs.inp b/test/fileread/runs/zfs.inp index e0819748..09bcc374 100644 --- a/test/fileread/runs/zfs.inp +++ b/test/fileread/runs/zfs.inp @@ -1,11 +1,12 @@ -qc2534.mtx !This (and others) from: http://math.nist.gov/MatrixMarket/ or -NONE !http://www.cise.ufl.edu/research/sparse/matrices/index.html +qc2534.mtx ! This (and others) from: http://math.nist.gov/MatrixMarket/ or +NONE ! http://www.cise.ufl.edu/research/sparse/matrices/index.html +MM ! File format: MM: Matrix Market HB: Harwell-Boeing. BICGSTAB ! Iterative method: BiCGSTAB BiCG CGS RGMRES BiCGSTABL CG CSR ! Storage format CSR COO JAD 0 ! IPART: Partition method 0: BLK 2: graph (with Metis) 2 ! ISTOPC 01000 ! ITMAX -01 ! ITRACE +-1 ! ITRACE 30 ! IRST (restart for RGMRES and BiCGSTABL) 1.d-5 ! EPS 3L-M-RAS-I-D4 ! Longer descriptive name for preconditioner (up to 20 chars) @@ -22,7 +23,7 @@ DEC ! Type of aggregation DEC SYMDEC GLB MULT ! Type of multilevel correction: ADD MULT POST ! Side of multiplicative correction PRE POST BOTH (ignored for ADD) DIST ! Coarse level: matrix distribution DIST REPL -UMF ! Coarse level: solver BJAC UMF SLU SLUDIST +BJAC ! Coarse level: solver BJAC UMF SLU SLUDIST ILU ! Coarse level: subsolver ILU UMF SLU SLUDIST 0 ! Coarse level: Level-set N for ILU(N) 1.d-4 ! Coarse level: Threshold T for ILU(T,P) diff --git a/test/fileread/sf_sample.f90 b/test/fileread/sf_sample.f90 index 43c29ea3..f93144d7 100644 --- a/test/fileread/sf_sample.f90 +++ b/test/fileread/sf_sample.f90 @@ -47,6 +47,7 @@ program sf_sample ! input parameters character(len=40) :: kmethd, mtrx_file, rhs_file + character(len=2) :: filefmt type precdata character(len=20) :: descr ! verbose description of the prec character(len=10) :: prec ! overall prectype @@ -96,6 +97,7 @@ program sf_sample character(len=5) :: afmt character(len=20) :: name + integer, parameter :: iunit=12 integer :: iparm(20) ! other variables @@ -124,7 +126,7 @@ program sf_sample ! ! get parameters ! - call get_parms(ictxt,mtrx_file,rhs_file,kmethd,& + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,kmethd,& & prec_choice,ipart,afmt,istopc,itmax,itrace,irst,eps) call psb_barrier(ictxt) @@ -133,16 +135,35 @@ program sf_sample nrhs = 1 if (iam==psb_root_) then - call read_mat(mtrx_file, aux_a, ictxt) - + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) + end if + m_problem = aux_a%m call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) - end if - + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,dim=1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -347,14 +368,14 @@ contains ! ! get iteration parameters from standard input ! - subroutine get_parms(icontxt,mtrx,rhs,kmethd,& + subroutine get_parms(icontxt,mtrx,rhs,filefmt,kmethd,& & prec, ipart,afmt,istopc,itmax,itrace,irst,eps) use psb_base_mod implicit none integer :: icontxt - character(len=*) :: kmethd, mtrx, rhs, afmt + character(len=*) :: kmethd, mtrx, rhs, afmt,filefmt type(precdata) :: prec integer :: iret, istopc,itmax,itrace, ipart, irst real(psb_spk_) :: eps, omega,thr1,thr2 @@ -366,6 +387,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(kmethd,5) call read_data(afmt,5) call read_data(ipart,5) @@ -401,6 +423,7 @@ contains call psb_bcast(icontxt,mtrx) call psb_bcast(icontxt,rhs) + call psb_bcast(icontxt,filefmt) call psb_bcast(icontxt,kmethd) call psb_bcast(icontxt,afmt) call psb_bcast(icontxt,ipart) @@ -453,8 +476,3 @@ contains write(iout, *) ' 0: block partition ' end subroutine pr_usage end program sf_sample - - - - - diff --git a/test/fileread/zf_sample.f90 b/test/fileread/zf_sample.f90 index 949071cc..5deb225e 100644 --- a/test/fileread/zf_sample.f90 +++ b/test/fileread/zf_sample.f90 @@ -47,6 +47,7 @@ program zf_sample ! input parameters character(len=40) :: kmethd, mtrx_file, rhs_file + character(len=2) :: filefmt type precdata character(len=20) :: descr ! verbose description of the prec character(len=10) :: prec ! overall prectype @@ -96,6 +97,7 @@ program zf_sample character(len=5) :: afmt character(len=20) :: name + integer, parameter :: iunit=12 integer :: iparm(20) ! other variables @@ -124,7 +126,7 @@ program zf_sample ! ! get parameters ! - call get_parms(ictxt,mtrx_file,rhs_file,kmethd,& + call get_parms(ictxt,mtrx_file,rhs_file,filefmt,kmethd,& & prec_choice,ipart,afmt,istopc,itmax,itrace,irst,eps) call psb_barrier(ictxt) @@ -133,16 +135,35 @@ program zf_sample nrhs = 1 if (iam==psb_root_) then - call read_mat(mtrx_file, aux_a, ictxt) - + select case(psb_toupper(filefmt)) + case('MM') + ! For Matrix Market we have an input file for the matrix + ! and an (optional) second file for the RHS. + call mm_mat_read(aux_a,info,iunit=iunit,filename=mtrx_file) + if (info == 0) then + if (rhs_file /= 'NONE') then + call mm_vet_read(aux_b,info,iunit=iunit,filename=rhs_file) + end if + end if + + case ('HB') + ! For Harwell-Boeing we have a single file which may or may not + ! contain an RHS. + call hb_read(aux_a,info,iunit=iunit,b=aux_b,filename=mtrx_file) + + case default + info = -1 + write(0,*) 'Wrong choice for fileformat ', filefmt + end select + if (info /= 0) then + write(0,*) 'Error while reading input matrix ' + call psb_abort(ictxt) + end if + m_problem = aux_a%m call psb_bcast(ictxt,m_problem) - - if(rhs_file /= 'NONE') then - ! reading an rhs - call read_rhs(rhs_file,aux_b,ictxt) - end if - + + ! At this point aux_b may still be unallocated if (psb_size(aux_b,dim=1)==m_problem) then ! if any rhs were present, broadcast the first one write(0,'("Ok, got an rhs ")') @@ -347,14 +368,14 @@ contains ! ! get iteration parameters from standard input ! - subroutine get_parms(icontxt,mtrx,rhs,kmethd,& + subroutine get_parms(icontxt,mtrx,rhs,filefmt,kmethd,& & prec, ipart,afmt,istopc,itmax,itrace,irst,eps) use psb_base_mod implicit none integer :: icontxt - character(len=*) :: kmethd, mtrx, rhs, afmt + character(len=*) :: kmethd, mtrx, rhs, afmt,filefmt type(precdata) :: prec integer :: iret, istopc,itmax,itrace, ipart, irst real(psb_dpk_) :: eps, omega,thr1,thr2 @@ -366,6 +387,7 @@ contains ! read input parameters call read_data(mtrx,5) call read_data(rhs,5) + call read_data(filefmt,5) call read_data(kmethd,5) call read_data(afmt,5) call read_data(ipart,5) @@ -401,6 +423,7 @@ contains call psb_bcast(icontxt,mtrx) call psb_bcast(icontxt,rhs) + call psb_bcast(icontxt,filefmt) call psb_bcast(icontxt,kmethd) call psb_bcast(icontxt,afmt) call psb_bcast(icontxt,ipart)