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mld2p4-2:
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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -24,31 +24,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<B> Up:</B> <A NAME="tex2html240"
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HREF="node14.html">Getting Started</A>
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HREF="node14.html">Getting Started</A>
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<B> <A NAME="tex2html241"
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<B> <A NAME="tex2html242"
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR></DIV>
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<BR>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
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@@ -76,7 +75,7 @@ in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
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Section <A HREF="node10.html#sec:ex_and_test">3.5</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="node25.html#PSBLASGUIDE">15</A>].
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HREF="node25.html#PSBLASGUIDE">16</A>].
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<P>
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The setup and application of the default multi-level
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@@ -87,7 +86,7 @@ the corresponding Fortran 95 codes are available in <code>examples/fileread/</co
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="930"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="946"></A>
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<TABLE>
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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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@@ -164,6 +163,10 @@ 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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HREF="node25.html#UMFPACK">9</A>].
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Figure <A HREF="#fig:ex_3lhm">4</A> shows how to set a three-level preconditioner similar to the one of <A HREF="#fig:ex_3lh">3</A>, but the coarsest-level systems is solved with the multifrontal factorization from MUMPS [<A
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HREF="node25.html#UMFPACK">9</A>].
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Note that MUMPS can be used on both replicated and distributed coarsest level matrices,
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as a global and local solver respectively.
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The number of levels is specified by using <code>mld_precinit</code>; the other
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preconditioner parameters are set by calling <code>mld_precset</code>. Note that
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the type of multilevel framework (i.e. multiplicative among the levels
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@@ -171,7 +174,7 @@ 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">4</A> shows how to
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Figure <A HREF="#fig:ex_3la">5</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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@@ -180,11 +183,11 @@ 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">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">3</A>-<A HREF="#fig:ex_3la">4</A> are
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The code fragments shown in in Figures <A HREF="#fig:ex_3lh">3</A> <A HREF="#fig:ex_3lhm">4</A>-<A HREF="#fig:ex_3la">5</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">5</A> shows the setup of a one-level
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Finally, Figure <A HREF="#fig:ex_1l">6</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_</code> <code>1lev.f90</code>.
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@@ -195,7 +198,7 @@ boundary conditions are also available in the directory <code>examples/pdegen</c
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="932"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="948"></A>
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<TABLE>
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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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@@ -228,9 +231,43 @@ 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="934"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3lhm"></A><A NAME="950"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</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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</DIV><TABLE WIDTH="90%">
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<TR><TD>
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<PRE>
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... ...
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! set a three-level hybrid Schwarz preconditioner, which uses
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! block Jacobi (with ILU(0) on the blocks) as post-smoother,
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! a coarsest matrix replicated on the processors, and the
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! multifrontal solver in MUMPS as coarse-level solver
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call mld_precinit(P,'ML',info,nlev=3)
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call mld_precset(P,mld_smoother_type_,'BJAC',info)
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call mld_precset(P,mld_coarse_mat_,'REPL',info)
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call mld_precset(P,mld_coarse_solve_,'MUMPS',info)
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... ...
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</PRE>
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</TD></TR>
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</TABLE>
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<DIV ALIGN="CENTER">
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</DIV>
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<P>
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<DIV ALIGN="CENTER">
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="952"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</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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@@ -260,9 +297,9 @@ 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="936"></A>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="954"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6:</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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@@ -284,30 +321,29 @@ Setup of a one-level Schwarz preconditioner.</CAPTION>
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</DIV>
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