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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.
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Salvatore Filippone
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
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<TITLE>Getting Started</TITLE>
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HREF="node12.html">Smoothed Aggregation</A>
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<B> <A NAME="tex2html222"
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HREF="node1.html">Contents</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A>
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<BR>
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Getting Started
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</H1>
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<P>
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We describe the basics for building and applying MLD2P4 one-level and multi-level
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Schwarz preconditioners with the Krylov solvers included in PSBLAS [<A
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HREF="node30.html#PSBLASGUIDE">11</A>].
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The following steps are required:
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<OL>
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<LI><I>Declare the preconditioner data structure</I>. It is a derived data type,
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<code>mld_</code><I>x</I><code>prec_type</code>, where <I>x</I> may be <code>s</code>, <code>d</code>, <code>c</code>
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or <code>z</code>, according to the basic data type of the sparse matrix
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(<code>s</code> = real single precision; <code>d</code> = real double precision;
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<code>c</code> = complex single precision; <code>z</code> = complex double precision).
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This data structure is accessed by the user only through the MLD2P4 routines,
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following an object-oriented approach.
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</LI>
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<LI><I>Allocate and initialize the preconditioner data structure, according to
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a preconditioner type chosen by the user</I>. This is performed by the routine
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<code>mld_precinit</code>, which also sets defaults for each preconditioner
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type selected by the user. The defaults associated to each preconditioner
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type are given in Table <A HREF="#tab:precinit"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>, where the strings used by
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<code>mld_precinit</code> to identify the preconditioner types are also given.
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Note that these strings are valid also if uppercase letters are substituted by
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corresponding lowercase ones.
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</LI>
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<LI><I>Modify the selected preconditioner type, by properly setting
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preconditioner parameters.</I> This is performed by the routine <code>mld_precset</code>.
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This routine must be called only if the user wants to modify the default values
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of the parameters associated to the selected preconditioner type, to obtain a variant
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of the preconditioner. Examples of use of <code>mld_precset</code> are given in
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Section <A HREF="node14.html#sec:examples"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>; a complete list of all the
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preconditioner parameters and their allowed and default values is provided in
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Section <A HREF="node15.html#sec:userinterface"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>, Tables <A HREF="#tab:p_type"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>-<A HREF="#tab:p_coarse"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>.
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</LI>
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<LI><I>Build the preconditioner for a given matrix.</I> This is performed by
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the routine <code>mld_precbld</code>.
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</LI>
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<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
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This is performed by the routine <code>mld_precaply</code>. When using the PSBLAS Krylov solvers,
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this step is completely transparent to the user, since <code>mld_precaply</code> is called
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by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
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</LI>
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<LI><I>Free the preconditioner data structure</I>. This is performed by
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the routine <code>mld_precfree</code>. This step is complementary to step 1 and should
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be performed when the preconditioner is no more used.
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</LI>
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</OL>
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A detailed description of the above routines is given in Section <A HREF="node15.html#sec:userinterface"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>.
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Examples showing the basic use of MLD2P4 are reported in Section <A HREF="node14.html#sec:examples"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>.
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<P>
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Note that the Fortran 95 module <code>mld_prec_mod</code>, containing the definition of the
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preconditioner data type and the interfaces to the routines of MLD2P4,
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must be used in any program calling such routines.
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The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
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data types, and <code>psb_krylov_mod</code>, for interfacing with the
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Krylov solvers, must be also used (see Section <A HREF="node14.html#sec:examples"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>).
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<P>
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<BR><B>Remark 1.</B> The coarsest-level solver used by the default two-level
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preconditioner has been chosen by taking into account that, on parallel
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machines, it often leads to the smallest execution time when applied to
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linear systems coming from finite-difference discretizations of basic
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elliptic PDE problems, considered as standard tests for multi-level Schwarz
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preconditioners [<A
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HREF="node30.html#aaecc_07">3</A>,<A
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HREF="node30.html#apnum_07">4</A>]. However, this solver does
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not necessarily correspond to the smallest number of iterations of the
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preconditioned Krylov method, which is usually obtained by applying
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a direct solver to the coarsest-level system, e.g. based on the LU
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factorization (see Section <A HREF="node15.html#sec:userinterface"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>
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for the coarsest-level solvers available in MLD2P4).
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<P>
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<BR><B>Remark 2.</B> The include path for MLD2P4 must override
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those for PSBLAS, e.g. the latter must come first in the sequence
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passed to the compiler, as the MLD2P4 version of the Krylov solver
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interfaces must override that of PSBLAS. This will change in the future
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when the support for the <code>class</code> statement becomes widespread in Fortran
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compilers.
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="972"></A>
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<TABLE>
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<CAPTION><STRONG>Table:</STRONG>
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Preconditioner types, corresponding strings and default choices.
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</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
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<TR><TD ALIGN="LEFT"><SMALL>TYPE</SMALL></TD>
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<TD ALIGN="LEFT"><SMALL>STRING</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=181><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
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</TR>
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<TR><TD ALIGN="LEFT">No preconditioner</TD>
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<TD ALIGN="LEFT"><code>'NOPREC'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=181>Considered only to use the PSBLAS
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Krylov solvers with no preconditioner.</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Diagonal</TD>
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<TD ALIGN="LEFT"><code>'DIAG'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=181>--</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Block Jacobi</TD>
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<TD ALIGN="LEFT"><code>'BJAC'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=181>Block Jacobi with ILU(0) on the local blocks.</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Additive Schwarz</TD>
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<TD ALIGN="LEFT"><code>'AS'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=181>Restricted Additive Schwarz (RAS),
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with overlap 1 and ILU(0) on the local blocks.</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Multilevel</TD>
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<TD ALIGN="LEFT"><code>'ML'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=181>Multi-level hybrid preconditioner (additive on the
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same level and multiplicative through the levels),
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with post-smoothing only.
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Number of levels: 2.
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Post-smoother: RAS with overlap 1 and ILU(0)
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on the local blocks.
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Aggregation: smoothed aggregation with
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threshold <IMG
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WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img86.png"
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ALT="$\theta = 0$">.
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Coarsest matrix: distributed among the processors.
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Coarsest-level solver:
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4 sweeps of the block-Jacobi solver,
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with LU factorization of the blocks
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(UMFPACK for the double precision versions and
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SuperLU for the single precision ones)</TD>
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</TR>
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</TABLE>
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</DIV>
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<P>
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</TD></TR>
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</TABLE>
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</DIV><P></P>
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<BR>
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<P>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html225"
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HREF="node14.html">Examples</A>
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HREF="userhtml.html">userhtml</A>
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<B> Previous:</B> <A NAME="tex2html214"
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HREF="node12.html">Smoothed Aggregation</A>
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HREF="node1.html">Contents</A></B>
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<ADDRESS>
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Salvatore Filippone
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2008-07-22
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</ADDRESS>
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