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mld2p4:
config/pac.m4 configure docs/html/WARNINGS docs/html/images.log docs/html/images.pl docs/html/images.tex docs/html/img100.png docs/html/img101.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.html docs/pdf/Makefile docs/pdf/abstract.tex docs/pdf/background.tex docs/pdf/bibliography.tex docs/pdf/building.tex docs/pdf/conventions.tex docs/pdf/distribution.tex docs/pdf/errors.tex docs/pdf/gettingstarted.tex docs/pdf/overview.tex docs/pdf/title.tex docs/pdf/userguide.tex docs/pdf/userhtml.tex docs/pdf/userinterface.tex Configure minro fix: require psblas 2.3 Doc fixes: dual version of title for pdf/html, fixed tables.
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Salvatore Filippone
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@@ -1,4 +1,4 @@
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//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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@@ -24,34 +24,35 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> <A NAME="tex2html233"
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HREF="node1.html">Contents</A></B>
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<BR>
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<B> <A NAME="tex2html232"
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HREF="node2.html">Contents</A></B>
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<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
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@@ -60,11 +61,9 @@ Examples
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</H2>
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<P>
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The code reported in Figure <A HREF="#fig:ex_default"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A> shows how to set and apply the default
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The code reported in Figure <A HREF="#fig:ex_default">2</A> shows how to set and apply the default
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multi-level preconditioner available in the real double precision version
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of MLD2P4 (see Table <A HREF="#tab:precinit"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>). This preconditioner is chosen
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of MLD2P4 (see Table <A HREF="node13.html#tab:precinit">1</A>). This preconditioner is chosen
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by simply specifying <code>'ML'</code> as second argument of <code>mld_precinit</code>
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(a call to <code>mld_precset</code> is not needed) and is applied with the BiCGSTAB
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solver provided by PSBLAS. As previously observed, the modules <code>psb_base_mod</code>,
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@@ -78,25 +77,23 @@ here for brevity; the statements concerning the deallocation of the PSBLAS
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data structure are neglected too.
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The complete code can be found in the example program file <code>mld_dexample_ml.f90</code>,
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in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
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Section <A HREF="node5.html#sec:building"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>).
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Section <A HREF="node9.html#sec:ex_and_test">3.4</A>).
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For details on the use of the PSBLAS routines, see the PSBLAS User's
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Guide [<A
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HREF="node30.html#PSBLASGUIDE">11</A>].
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HREF="node30.html#PSBLASGUIDE">14</A>].
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<P>
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The setup and application of the default multi-level
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preconditioners for the real single precision and the complex, single and double
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precision, versions are obtained with straightforward modifications of the previous
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example (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> for details). If these versions are installed,
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example (see Section <A HREF="node15.html#sec:userinterface">6</A> for details). If these versions are installed,
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the corresponding Fortran 95 codes are available in <code>examples/fileread/</code>.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="975"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="926"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure:</STRONG>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
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Setup and application of the default multi-level Schwarz preconditioner.
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</CAPTION>
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<TR><TD>
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@@ -165,8 +162,7 @@ Setup and application of the default multi-level Schwarz preconditioner.
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<P>
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Different versions of multi-level preconditioners can be obtained by changing
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the default values of the preconditioner parameters. The code reported in
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Figure <A HREF="#fig:ex_3lh"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A> shows how to set a three-level hybrid Schwarz
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Figure <A HREF="#fig:ex_3lh">3</A> shows how to set a three-level hybrid Schwarz
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preconditioner, which uses block Jacobi with ILU(0) on the
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local blocks as post-smoother, has a coarsest matrix replicated on the processors,
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and solves the coarsest-level system with the LU factorization from UMFPACK [<A
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@@ -178,28 +174,22 @@ with post-smoothing only) is not specified since it is the default
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set by <code>mld_precinit</code>.
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<P>
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Figure <A HREF="#fig:ex_3la"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A> shows how to
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Figure <A HREF="#fig:ex_3la">4</A> shows how to
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set a three-level additive Schwarz preconditioner,
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which uses RAS, with overlap 1 and ILU(0) on the blocks,
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as pre- and post-smoother, and applies five block-Jacobi sweeps, with
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the UMFPACK LU factorization on the blocks, as distributed coarsest-level
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solver. Again, <code>mld_precset</code> is used only to set
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non-default values of the parameters (see 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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non-default values of the parameters (see Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>).
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In both cases, the construction and the application of the preconditioner
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are carried out as for the default multi-level preconditioner.
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The code fragments shown in in Figures <A HREF="#fig:ex_3lh"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A>-<A HREF="#fig:ex_3la"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A> are
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The code fragments shown in in Figures <A HREF="#fig:ex_3lh">3</A>-<A HREF="#fig:ex_3la">4</A> are
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included in the example program file <code>mld_dexample_ml.f90</code> too.
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<P>
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Finally, Figure <A HREF="#fig:ex_1l"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/share/latex2html/icons/crossref.png"></A> shows the setup of a one-level
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Finally, Figure <A HREF="#fig:ex_1l">5</A> shows the setup of a one-level
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additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding
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example program is available in <code>mld_dexample_1lev.f90</code>.
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example program is available in <code>mld_dexample_</code> <code>1lev.f90</code>.
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<P>
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For all the previous preconditioners, example programs where the sparse matrix and
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@@ -207,10 +197,20 @@ the right-hand side are generated by discretizing a PDE with Dirichlet
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boundary conditions are also available in the directory <code>examples/pdegen</code>.
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<P>
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<BR><SPAN CLASS="textbf">Remark 3.</SPAN> Any PSBLAS-based program using the basic preconditioners
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implemented in PSBLAS 2.0, i.e. the diagonal and block-Jacobi ones,
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can use the diagonal and block-Jacobi preconditioners
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implemented in MLD2P4 without any change in the code.
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The PSBLAS-based program must be only recompiled
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and linked to the MLD2P4 library.
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="977"></A>
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<BR>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="928"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure:</STRONG>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
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Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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@@ -240,9 +240,9 @@ Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="979"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="930"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure:</STRONG>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
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Setup of an additive three-level Schwarz preconditioner.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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@@ -272,9 +272,9 @@ Setup of an additive three-level Schwarz preconditioner.</CAPTION>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="981"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="932"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure:</STRONG>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
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Setup of a one-level Schwarz preconditioner.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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@@ -296,46 +296,38 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
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</DIV>
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<P>
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<BR><B>Remark 3.</B> Any PSBLAS-based program using the basic preconditioners
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implemented in PSBLAS 2.0, i.e. the diagonal and block-Jacobi ones,
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can use the diagonal and block-Jacobi preconditioners
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implemented in MLD2P4 without any change in the code.
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The PSBLAS-based program must be only recompiled
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and linked to the MLD2P4 library.
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<P>
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<ADDRESS>
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Salvatore Filippone
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2008-07-22
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2008-07-23
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