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mld2p4-2:

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Docs updates.
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Salvatore Filippone
2017-04-21 13:37:08 +00:00
parent 05ab5f4d55
commit 597c6c58c7
3 changed files with 191 additions and 252 deletions
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docs/html/node17.html
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@@ -74,7 +74,7 @@ contained in <code>val</code>.
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>what</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in)</code> <I>or</I> <code>character(len=*)</code>.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>character(len=*)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The parameter to be set. It can be specified by
@@ -177,7 +177,7 @@ refer also to Section&nbsp;<A HREF="node11.html#sec:background">4</A>.
<BR>
<P>
<B>Remark 2.</B> A smoother is usually obtained by combining two objects:
a smoother (<code>mld_smoother_type_</code>) and a local solver (<code>mld_sub_solve_</code>),
a smoother (<code>SMOOTHER_TYPE</code>) and a local solver (<code>SUB_SOLVE</code>),
as specified in Tables&nbsp;<A HREF="#tab:p_smoother">7</A>-<A HREF="#tab:p_smoother_1">8</A>.
For example, the block-Jacobi smoother using
ILU(0) on the blocks is obtained by combining the block-Jacobi smoother
@@ -189,9 +189,9 @@ result of combining the block-Jacobi smoother object with a single sweep
of the pointwise-Jacobi solver object. However, for simplicity, shortcuts are
provided to set point-Jacobi, hybrid (forward) Gauss-Seidel, and
hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined
by setting only <code>mld_smoother_type_</code> to appropriate values (see
by setting only <code>SMOOTHER_TYPE</code> to appropriate values (see
Tables&nbsp;<A HREF="#tab:p_smoother">7</A>), i.e., without setting
<code>mld_sub_solve_</code> too.
<code>SUB_SOLVE</code> too.
<P>
The smoother and solver objects are arranged in a
@@ -241,7 +241,7 @@ solver is changed to the default sequential solver.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="963"></A>
<DIV ALIGN="CENTER"><A NAME="962"></A>
<TABLE>
<CAPTION><STRONG>Table 2:</STRONG>
Parameters defining the multi-level cycle and the number of cycles to
@@ -256,9 +256,7 @@ be applied.
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=204><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>mld_ml_cycle_</code>
<P>
<code>ML_CYCLE</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>ML_CYCLE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'VCYCLE'</TT>
<P>
@@ -276,9 +274,7 @@ be applied.
Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and
is included for compatibility with previous versions of MLD2P4.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>mld_outer_sweeps_</code>
<P>
<code>OUTER_SWEEPS</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><code>OUTER_SWEEPS</code></TD>
<TD ALIGN="LEFT"><TT>integer</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any integer
<P>
@@ -298,7 +294,7 @@ number <IMG
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="968"></A>
<DIV ALIGN="CENTER"><A NAME="967"></A>
<TABLE>
<CAPTION><STRONG>Table 3:</STRONG>
Parameters defining the aggregation algorithm.
@@ -312,9 +308,7 @@ Parameters defining the aggregation algorithm.
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_min_coarse_size_</code>
<P>
<code>MIN_COARSE_SIZE</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>MIN_COARSE_SIZE</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number
<P>
@@ -339,9 +333,7 @@ Parameters defining the aggregation algorithm.
is lower than or equal to this threshold
(see Note).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_min_cr_ratio_</code>
<P>
<code>MIN_CR_RATIO</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>MIN_CR_RATIO</code></TD>
<TD ALIGN="LEFT"><code>real</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any number
<P>
@@ -355,9 +347,7 @@ Parameters defining the aggregation algorithm.
at two consecutive levels is lower than or equal to this
threshold (see Note).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_max_levs_</code>
<P>
<code>MAX_LEVS</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>MAX_LEVS</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65>Any integer
<P>
@@ -369,9 +359,7 @@ number <IMG
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=196>Maximum number of levels. The aggregation stops
if the number of levels reaches this value (see Note).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_par_aggr_alg_</code>
<P>
<code>PAR_AGGR</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>PAR_AGGR</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'DEC'</TT>, <TT>'SYMDEC'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><TT>'DEC'</TT></TD>
@@ -386,9 +374,7 @@ Currently, only the
SRC="img22.png"
ALT="$A+A^T$">.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_aggr_type_</code>
<P>
<code>AGGR_TYPE</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>AGGR_TYPE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><B><TT>'VMB'</TT></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><B><TT>'VMB'</TT></B></TD>
@@ -397,9 +383,7 @@ Currently, only the
[<A
HREF="node27.html#VANEK_MANDEL_BREZINA">29</A>].</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_aggr_prol_</code>
<P>
<code>AGGR_PROL</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>AGGR_PROL</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'SMOOTHED'</TT>, <TT>'UNSMOOTHED'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=82><TT>'SMOOTHED'</TT></TD>
@@ -425,7 +409,7 @@ of levels.</TD>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="972"></A>
<DIV ALIGN="CENTER"><A NAME="971"></A>
<TABLE>
<CAPTION><STRONG>Table 4:</STRONG>
Parameters defining the aggregation algorithm (continued).
@@ -439,9 +423,7 @@ Parameters defining the aggregation algorithm (continued).
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=187><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>mld_aggr_ord_</code>
<P>
<code>AGGR_ORD</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>AGGR_ORD</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'NATURAL'</TT>
<P>
@@ -452,9 +434,7 @@ Parameters defining the aggregation algorithm (continued).
descending degrees of the nodes in the
matrix graph.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>mld_aggr_thresh_</code>
<P>
<code>AGGR_THRESH</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>AGGR_THRESH</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71>Any&nbsp;real
<P>
@@ -469,9 +449,7 @@ number&nbsp;<IMG
ALT="$\theta$"> in the aggregation algorithm
(see Note).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>mld_aggr_omega_alg_</code>
<P>
<code>AGGR_OMEGA_ALG</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>AGGR_OMEGA_ALG</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'EIG_EST'</TT>
<P>
@@ -500,9 +478,7 @@ number&nbsp;<IMG
ALT="$A$">, or explicily
specified by the user.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>mld_aggr_eig_</code>
<P>
<code>AGGR_EIG</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>AGGR_EIG</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'A_NORMI'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=65><TT>'A_NORMI'</TT></TD>
@@ -513,9 +489,7 @@ number&nbsp;<IMG
Currently only the infinity norm estimate
is available.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>mld_aggr_omega_val_</code>
<P>
<code>AGGR_OMEGA_VAL</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>AGGR_OMEGA_VAL</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71>Any real
<P>
@@ -547,9 +521,7 @@ number <IMG
SRC="img26.png"
ALT="$D^{-1}A$">.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>mld_aggr_filter_</code>
<P>
<code>AGGR_FILTER</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=108><code>AGGR_FILTER</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><TT>'FILTER'</TT>
<P>
@@ -575,7 +547,7 @@ the parameter <TT>ilev</TT>.</TD>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="977"></A>
<DIV ALIGN="CENTER"><A NAME="976"></A>
<TABLE>
<CAPTION><STRONG>Table 5:</STRONG>
Parameters defining the coarse-space correction at the coarsest
@@ -589,9 +561,7 @@ level.</CAPTION>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_coarse_mat_</code>
<P>
<code>COARSE_MAT</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>COARSE_MAT</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'DIST'</TT>
<P>
@@ -600,9 +570,7 @@ level.</CAPTION>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=244>Coarsest matrix layout: distributed among the processes or
replicated on each of them.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_coarse_solve_</code>
<P>
<code>COARSE_SOLVE</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>COARSE_SOLVE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'MUMPS'</TT>
<P>
@@ -636,9 +604,7 @@ Note that <TT>UMF</TT> and <TT>SLU</TT> require the coarsest
value UMFPACK and SuperLU_Dist
are available only in double precision.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_coarse_subsolve_</code>
<P>
<code>COARSE_SUBSOLVE</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>COARSE_SUBSOLVE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=48><TT>'ILU'</TT>
<P>
@@ -669,8 +635,8 @@ Note that <TT>UMF</TT> and <TT>SLU</TT> require the coarsest
Note that UMFPACK and SuperLU_Dist
are available only in double precision.</TD>
</TR>
<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> Defaults for <TT>mld_coarse_solve_</TT> and
<TT>mld_coarse_subsolve_</TT> are chosen in the following order:</TD>
<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note.</B> Defaults for <TT>COARSE_SOLVE</TT> and
<TT>COARSE_SUBSOLVE</TT> are chosen in the following order:</TD>
</TR>
<TR><TD ALIGN="LEFT" COLSPAN=5>single precision version - <TT>MUMPS</TT> if installed,
then <TT>SLU</TT> if installed,
@@ -689,7 +655,7 @@ Note that <TT>UMF</TT> and <TT>SLU</TT> require the coarsest
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="979"></A>
<DIV ALIGN="CENTER"><A NAME="978"></A>
<TABLE>
<CAPTION><STRONG>Table 6:</STRONG>
Parameters defining the coarse-space correction at the coarsest
@@ -703,9 +669,7 @@ level (continued).</CAPTION>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_coarse_sweeps_</code>
<P>
<code>COARSE_SWEEPS</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>COARSE_SWEEPS</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any integer
<P>
@@ -717,9 +681,7 @@ number <IMG
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=213>Number of sweeps when <code>JACOBI</code>, <code>GS</code> or <code>BJAC</code>
is chosen as coarsest-level solver.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_coarse_fillin_</code>
<P>
<code>COARSE_FILLIN</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>COARSE_FILLIN</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any integer
<P>
@@ -733,9 +695,7 @@ number <IMG
SRC="img30.png"
ALT="$p$"> of the ILU factorizations.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>mld_coarse_iluthrs_</code>
<P>
<code>COARSE_ILUTHRS</code></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=111><code>COARSE_ILUTHRS</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57>Any real
<P>
@@ -761,7 +721,7 @@ number <IMG
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="981"></A>
<DIV ALIGN="CENTER"><A NAME="980"></A>
<TABLE>
<CAPTION><STRONG>Table 7:</STRONG>
Parameters defining the smoother or the details of the one-level preconditioner.
@@ -777,9 +737,7 @@ Parameters defining the smoother or the details of the one-level preconditioner.
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=184><FONT SIZE="-1">
<SMALL>COMMENTS</SMALL> </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>mld_smoother_type_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SMOOTHER_TYPE</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>SMOOTHER_TYPE</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> <code>'JACOBI'</code> </FONT>
@@ -802,10 +760,7 @@ Parameters defining the smoother or the details of the one-level preconditioner.
<P>
<FONT SIZE="-1">It is ignored by one-level preconditioners. </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">
<code>mld_sub_solve_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SUB_SOLVE</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>SUB_SOLVE</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> <TT>'JACOBI'</TT> </FONT>
@@ -849,10 +804,7 @@ Parameters defining the smoother or the details of the one-level preconditioner.
(plus triangular solve). See Note for details on hybrid
Gauss-Seidel. </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">
<code>mld_moother_sweeps_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SMOOTHER_SWEEPS</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>SMOOTHER_SWEEPS</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> Any integer </FONT>
@@ -870,10 +822,7 @@ Parameters defining the smoother or the details of the one-level preconditioner.
together with <code>pos='PRE'</code> or <code>pos='POST</code>,
respectively. </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1">
<code>mld_sub_ovr_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SUB_OVR</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=102><FONT SIZE="-1"> <code>SUB_OVR</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><FONT SIZE="-1"> Any integer </FONT>
@@ -895,7 +844,7 @@ Parameters defining the smoother or the details of the one-level preconditioner.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="983"></A>
<DIV ALIGN="CENTER"><A NAME="982"></A>
<TABLE>
<CAPTION><STRONG>Table 8:</STRONG>
Parameters defining the smoother or the details of the one-level preconditioner
@@ -911,10 +860,7 @@ Parameters defining the smoother or the details of the one-level preconditioner
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=201><FONT SIZE="-1">
<SMALL>COMMENTS</SMALL> </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">
<code>mld_sub_restr_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SUB_RESTR</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1"> <code>SUB_RESTR</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> <TT>'HALO'</TT> </FONT>
@@ -930,10 +876,7 @@ Parameters defining the smoother or the details of the one-level preconditioner
<FONT SIZE="-1">Note that <TT>HALO</TT> must be chosen for
the classical Addditive Schwarz smoother and its RAS variant.</FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">
<code>mld_sub_prol_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SUB_PROL</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1"> <code>SUB_PROL</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>character(len=*)</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> <TT>'SUM'</TT> </FONT>
@@ -949,10 +892,7 @@ Parameters defining the smoother or the details of the one-level preconditioner
<FONT SIZE="-1">Note that <TT>SUM</TT> must be chosen for the classical Additive
Schwarz smoother, and <TT>NONE</TT> for its RAS variant. </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">
<code>mld_sub_fillin_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SUB_FILLIN</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1"> <code>SUB_FILLIN</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>integer</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> Any integer </FONT>
@@ -969,10 +909,7 @@ Parameters defining the smoother or the details of the one-level preconditioner
SRC="img30.png"
ALT="$p$"> of the incomplete LU factorizations. </FONT></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1">
<code>mld_sub_iluthrs_</code> </FONT>
<P>
<FONT SIZE="-1"><code>SUB_ILUTHRS</code> </FONT></TD>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=85><FONT SIZE="-1"> <code>SUB_ILUTHRS</code> </FONT></TD>
<TD ALIGN="LEFT"><FONT SIZE="-1"> <code>real(</code><I>kind_parameter</I><code>)</code>
</FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=71><FONT SIZE="-1"> Any real number&nbsp;<IMG
docs/mld2p4-2.1-guide.pdf
+86 -113
View File
@@ -3280,7 +3280,7 @@ endstream
endobj
447 0 obj
<<
/Length 7248
/Length 7147
>>
stream
0 g 0 G
@@ -3293,7 +3293,7 @@ BT
/F17 11.9552 Tf -401.542 -35.866 Td [(6.2)-1125(Subroutine)-375(set)]TJ
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docs/src/userinterface.tex
+64 -35
View File
@@ -99,7 +99,7 @@ contained in \verb|val|.
% & The preconditioner data structure. Note that \emph{x} must
% be chosen according to the real/complex, single/double precision
% version of MLD2P4 under use.\\
\verb|what| & \verb|integer, intent(in)| \emph{or} \verb|character(len=*)|. \\
\verb|what| & \verb|character(len=*)|. \\
& The parameter to be set. It can be specified by
a predefined constant, or through its name; the string
is case-insensitive. See also
@@ -169,7 +169,7 @@ For a description of the meaning of the parameters, please
refer also to Section~\ref{sec:background}. \\
\textbf{Remark 2.} A smoother is usually obtained by combining two objects:
a smoother (\verb|mld_smoother_type_|) and a local solver (\verb|mld_sub_solve_|),
a smoother (\verb|SMOOTHER_TYPE|) and a local solver (\verb|SUB_SOLVE|),
as specified in Tables~\ref{tab:p_smoother}-\ref{tab:p_smoother_1}.
For example, the block-Jacobi smoother using
ILU(0) on the blocks is obtained by combining the block-Jacobi smoother
@@ -181,9 +181,9 @@ result of combining the block-Jacobi smoother object with a single sweep
of the pointwise-Jacobi solver object. However, for simplicity, shortcuts are
provided to set point-Jacobi, hybrid (forward) Gauss-Seidel, and
hybrid backward Gauss-Seidel, i.e., the previous smoothers can be defined
by setting only \verb|mld_smoother_type_| to appropriate values (see
by setting only \verb|SMOOTHER_TYPE| to appropriate values (see
Tables~\ref{tab:p_smoother}), i.e., without setting
\verb|mld_sub_solve_| too.
\verb|SUB_SOLVE| too.
The smoother and solver objects are arranged in a
hierarchical manner. When specifying a smoother object, its parameters,
@@ -239,7 +239,8 @@ solver is changed to the default sequential solver.
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{type of the multi-level preconditioner}}\\ \hline
\verb|mld_ml_cycle_| \par \verb|ML_CYCLE| & \verb|character(len=*)|
%\verb|mld_ml_cycle_| \par
\verb|ML_CYCLE| & \verb|character(len=*)|
& \texttt{'VCYCLE'} \par \texttt{'WCYCLE'} \par \texttt{'KCYCLE'} \par
\texttt{'MULT'} \par \texttt{'ADD'}
& \texttt{'VCYCLE'}
@@ -247,7 +248,8 @@ solver is changed to the default sequential solver.
and Additive Schwarz. \par
Note that hybrid Multiplicative Schwarz is equivalent to V-cycle and
is included for compatibility with previous versions of MLD2P4. \\ \hline
\verb|mld_outer_sweeps_| \par \verb|OUTER_SWEEPS| & \texttt{integer} &
%\verb|mld_outer_sweeps_| \par
\verb|OUTER_SWEEPS| & \texttt{integer} &
Any integer \par number $\ge 1$ & 1 &
Number of multi-level cycles. \\ \hline
%\verb|mld_smoother_type_| \par \verb|SMOOTHER_TYPE| & \verb|character(len=*)|
@@ -276,7 +278,8 @@ be applied.
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{aggregation algorithm}} \\ \hline
\verb|mld_min_coarse_size_| \par \verb|MIN_COARSE_SIZE| & \verb|integer|
%\verb|mld_min_coarse_size_| \par
\verb|MIN_COARSE_SIZE| & \verb|integer|
& Any number \par $> 0$
& $\lfloor 40 \sqrt[3]{n} \rfloor$, where $n$ is the dimension
of the matrix at the finest level
@@ -291,19 +294,22 @@ be applied.
% the maximum number of levels is reached
% (see \verb|mld_n_prec_levs_|).
\\ \hline
\verb|mld_min_cr_ratio_| \par \verb|MIN_CR_RATIO| & \verb|real|
%\verb|mld_min_cr_ratio_| \par
\verb|MIN_CR_RATIO| & \verb|real|
& Any number \par $> 1$
& 1.5
& Minimum coarsening ratio. The aggregation stops
if the ratio between the matrix dimensions
at two consecutive levels is lower than or equal to this
threshold (see Note).\\ \hline
\verb|mld_max_levs_| \par \verb|MAX_LEVS| & \verb|integer|
%\verb|mld_max_levs_| \par
\verb|MAX_LEVS| & \verb|integer|
& Any integer \par number $> 1$
& 20
& Maximum number of levels. The aggregation stops
if the number of levels reaches this value (see Note). \\ \hline
\verb|mld_par_aggr_alg_| \par \verb|PAR_AGGR| & \verb|character(len=*)| \hspace*{-3mm}
%\verb|mld_par_aggr_alg_| \par
\verb|PAR_AGGR| & \verb|character(len=*)| \hspace*{-3mm}
& \texttt{'DEC'}, \texttt{'SYMDEC'}
& \texttt{'DEC'}
& Parallel aggregation algorithm. \par Currently, only the
@@ -311,12 +317,14 @@ be applied.
\verb|SYMDEC| option applies decoupled
aggregation to the sparsity pattern
of $A+A^T$.\\ \hline
\verb|mld_aggr_type_| \par \verb|AGGR_TYPE| & \verb|character(len=*)| \hspace*{-3mm}
%\verb|mld_aggr_type_| \par
\verb|AGGR_TYPE| & \verb|character(len=*)| \hspace*{-3mm}
& \textbf{\texttt{'VMB'}} & \textbf{\texttt{'VMB'}}
& Type of aggregation algorithm: currently, the scalar aggregation
algorithm by Van\v{e}k, Mandel and Brezina is implemented
\cite{VANEK_MANDEL_BREZINA}. \\ \hline
\verb|mld_aggr_prol_| \par \verb|AGGR_PROL| & \verb|character(len=*)| \hspace*{-3mm}
%\verb|mld_aggr_prol_| \par
\verb|AGGR_PROL| & \verb|character(len=*)| \hspace*{-3mm}
& \texttt{'SMOOTHED'}, \texttt{'UNSMOOTHED'} & \texttt{'SMOOTHED'}
& Prolongator used by the aggregation algorithm: smoothed or unsmoothed
(i.e., tentative prolongator). \\
@@ -342,7 +350,8 @@ of levels. } \\
\hline
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
\verb|mld_aggr_ord_| \par \verb|AGGR_ORD| & \verb|character(len=*)|
%\verb|mld_aggr_ord_| \par
\verb|AGGR_ORD| & \verb|character(len=*)|
& \texttt{'NATURAL'} \par \texttt{'DEGREE'}
& \texttt{'NATURAL'}
& Initial ordering of indices for the aggregation
@@ -351,17 +360,20 @@ of levels. } \\
matrix graph. \\ \hline
%Since aggregation is
%heuristic, results will be different.
\verb|mld_aggr_thresh_| \par \verb|AGGR_THRESH| & \verb|real(|\emph{kind\_parameter}\verb|)|
%\verb|mld_aggr_thresh_| \par
\verb|AGGR_THRESH| & \verb|real(|\emph{kind\_parameter}\verb|)|
& Any~real \par number~$\in [0, 1]$
& 0.05
& The threshold $\theta$ in the aggregation algorithm
(see Note). \\ \hline
%\verb|mld_aggr_scale_| \par \verb|AGGR_SCALE| & \verb|real(|\emph{kind\_parameter}\verb|)|
%%\verb|mld_aggr_scale_| \par
% \verb|AGGR_SCALE| & \verb|real(|\emph{kind\_parameter}\verb|)|
% & Any~real \par number~$\in [0, 1]$
% & 1.0
% & Scale factor applied to the threshold in going
% from level $ilev$ to level $ilev+1$. \\ \hline
\verb|mld_aggr_omega_alg_| \par \verb|AGGR_OMEGA_ALG|& \verb|character(len=*)|
%\verb|mld_aggr_omega_alg_| \par
\verb|AGGR_OMEGA_ALG|& \verb|character(len=*)|
& \texttt{'EIG\_EST'} \par \texttt{'USER\_CHOICE'}
& \texttt{'EIG\_EST'}
& How the damping parameter $\omega$ in the
@@ -371,13 +383,15 @@ of levels. } \\
level and $D$ is the diagonal matrix with
the same diagonal entires as $A$, or explicily
specified by the user. \\ \hline
\verb|mld_aggr_eig_| \par \verb|AGGR_EIG| & \verb|character(len=*)|
%\verb|mld_aggr_eig_| \par
\verb|AGGR_EIG| & \verb|character(len=*)|
& \texttt{'A\_NORMI'}
& \texttt{'A\_NORMI'}
& How to estimate the spectral radius of $D^{-1}A$.
Currently only the infinity norm estimate
is available. \\ \hline
\verb|mld_aggr_omega_val_| \par \verb|AGGR_OMEGA_VAL| & \verb|real(|\emph{kind\_parameter}\verb|)|
%\verb|mld_aggr_omega_val_| \par
\verb|AGGR_OMEGA_VAL| & \verb|real(|\emph{kind\_parameter}\verb|)|
& Any real \par number $>0$
& $4/(3\rho(D^{-1}A))$
& Damping parameter $\omega$ in the smoothed aggregation algorithm.
@@ -387,7 +401,8 @@ of levels. } \\
otherwise it is computed by the library, using the
selected estimate of the spectral radius $\rho(D^{-1}A)$ of
$D^{-1}A$.\\ \hline
\verb|mld_aggr_filter_| \par \verb|AGGR_FILTER|
%\verb|mld_aggr_filter_| \par
\verb|AGGR_FILTER|
& \verb|character(len=*)|
& \texttt{'FILTER'} \par \texttt{'NOFILTER'}
& \texttt{'NOFILTER'} & Matrix used in computing the smoothed
@@ -412,12 +427,14 @@ the parameter \texttt{ilev}.} \\
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline
\verb|mld_coarse_mat_| \par \verb|COARSE_MAT| & \verb|character(len=*)|
%\verb|mld_coarse_mat_| \par
\verb|COARSE_MAT| & \verb|character(len=*)|
& \texttt{'DIST'} \par \texttt{'REPL'}
& \texttt{'REPL'}
& Coarsest matrix layout: distributed among the processes or
replicated on each of them. \\ \hline
\verb|mld_coarse_solve_| \par \verb|COARSE_SOLVE| & \verb|character(len=*)|
%\verb|mld_coarse_solve_| \par
\verb|COARSE_SOLVE| & \verb|character(len=*)|
& \texttt{'MUMPS'} \par \texttt{'UMF'} \par
\texttt{'SLU'} \par \texttt{'SLUDIST'} \par
\texttt{'JACOBI'} \par \texttt{'GS'} \par \texttt{'BJAC'}
@@ -438,7 +455,8 @@ the parameter \texttt{ilev}.} \\
which allows the use
value UMFPACK and SuperLU\_Dist
are available only in double precision. \\ \hline
\verb|mld_coarse_subsolve_| \par \verb|COARSE_SUBSOLVE| & \verb|character(len=*)|
%\verb|mld_coarse_subsolve_| \par
\verb|COARSE_SUBSOLVE| & \verb|character(len=*)|
& \texttt{'ILU'} \par \texttt{'ILUT'} \par \texttt{'MILU'} \par
\texttt{'MUMPS'} \par \texttt{'SLU'} \par \texttt{'UMF'}
& See~Note.
@@ -450,8 +468,8 @@ the parameter \texttt{ilev}.} \\
Note that UMFPACK and SuperLU\_Dist
are available only in double precision. \\
\hline
\multicolumn{5}{|l|}{{\bfseries Note.} Defaults for \texttt{mld\_coarse\_solve\_} and
\texttt{mld\_coarse\_subsolve\_} are chosen in the following order:} \\
\multicolumn{5}{|l|}{{\bfseries Note.} Defaults for \texttt{COARSE\_SOLVE} and
\texttt{COARSE\_SUBSOLVE} are chosen in the following order:} \\
\multicolumn{5}{|l|}{single precision version -- \texttt{MUMPS} if installed,
then \texttt{SLU} if installed,
\texttt{ILU} otherwise;}\\
@@ -472,16 +490,19 @@ level.\label{tab:p_coarse}}
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{coarse-space correction at the coarsest level}}\\ \hline
\verb|mld_coarse_sweeps_| \par \verb|COARSE_SWEEPS| & \verb|integer|
%\verb|mld_coarse_sweeps_| \par
\verb|COARSE_SWEEPS| & \verb|integer|
& Any integer \par number $> 0$
& 10
& Number of sweeps when \verb|JACOBI|, \verb|GS| or \verb|BJAC|
is chosen as coarsest-level solver. \\ \hline
\verb|mld_coarse_fillin_| \par \verb|COARSE_FILLIN| & \verb|integer|
%\verb|mld_coarse_fillin_| \par
\verb|COARSE_FILLIN| & \verb|integer|
& Any integer \par number $\ge 0$
& 0
& Fill-in level $p$ of the ILU factorizations. \\ \hline
\verb|mld_coarse_iluthrs_| \par \verb|COARSE_ILUTHRS|
%\verb|mld_coarse_iluthrs_| \par
\verb|COARSE_ILUTHRS|
& \verb|real(|\emph{kind\_parameter}\verb|)|
& Any real \par number $\ge 0$
& 0
@@ -501,7 +522,8 @@ level (continued).\label{tab:p_coarse_1}}
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
%\multicolumn{5}{|c|}{\emph{basic one-level preconditioner (smoother)}} \\ \hline
\verb|mld_smoother_type_| \par \verb|SMOOTHER_TYPE| & \verb|character(len=*)|
%\verb|mld_smoother_type_| \par
\verb|SMOOTHER_TYPE| & \verb|character(len=*)|
& \verb|'JACOBI'| \par \verb|'GS'| \par \verb|'BGS'| \par \verb|'BJAC'|
\par \verb|'AS'|
& \verb|'FBGS'|
@@ -510,7 +532,8 @@ level (continued).\label{tab:p_coarse_1}}
hybrid backward Gauss-Seidel, block-Jacobi, and
Additive Schwarz. \par
It is ignored by one-level preconditioners. \\ \hline
\verb|mld_sub_solve_| \par \verb|SUB_SOLVE| & \verb|character(len=*)|
%\verb|mld_sub_solve_| \par
\verb|SUB_SOLVE| & \verb|character(len=*)|
& \texttt{'JACOBI'} \par
\texttt{'GS'} \par \texttt{'BGS'} \par \texttt{'ILU'} \par
\texttt{'ILUT'} \par \texttt{'MILU'} \par
@@ -526,7 +549,8 @@ level (continued).\label{tab:p_coarse_1}}
LU from MUMPS, SuperLU or UMFPACK
(plus triangular solve). See Note for details on hybrid
Gauss-Seidel. \\ \hline
\verb|mld_moother_sweeps_| \par \verb|SMOOTHER_SWEEPS| & \verb|integer|
%\verb|mld_moother_sweeps_| \par
\verb|SMOOTHER_SWEEPS| & \verb|integer|
& Any integer \par number~$\ge 0$
& 1
& Number of sweeps of the smoother or one-level preconditioner.
@@ -534,7 +558,8 @@ level (continued).\label{tab:p_coarse_1}}
post-smoother is used if this parameter is set to 0
together with \verb|pos='PRE'| or \verb|pos='POST|,
respectively. \\ \hline
\verb|mld_sub_ovr_| \par \verb|SUB_OVR| & \verb|integer|
%\verb|mld_sub_ovr_| \par
\verb|SUB_OVR| & \verb|integer|
& Any integer \par number~$\ge 0$
& 1
& Number of overlap layers, for Additive Schwarz only. \\
@@ -552,7 +577,8 @@ level (continued).\label{tab:p_coarse_1}}
\hline
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
\textsc{comments} \\ \hline
\verb|mld_sub_restr_| \par \verb|SUB_RESTR| & \verb|character(len=*)|
%\verb|mld_sub_restr_| \par
\verb|SUB_RESTR| & \verb|character(len=*)|
& \texttt{'HALO'} \par \texttt{'NONE'}
& \texttt{'HALO'}
& Type of restriction operator, for Additive Schwarz only:
@@ -560,7 +586,8 @@ level (continued).\label{tab:p_coarse_1}}
for neglecting it. \par
Note that \texttt{HALO} must be chosen for
the classical Addditive Schwarz smoother and its RAS variant.\\ \hline
\verb|mld_sub_prol_| \par \verb|SUB_PROL| & \verb|character(len=*)|
%\verb|mld_sub_prol_| \par
\verb|SUB_PROL| & \verb|character(len=*)|
& \texttt{'SUM'} \par \texttt{'NONE'}
& \texttt{'NONE'}
& Type of prolongation operator, for Additive Schwarz only:
@@ -568,11 +595,13 @@ level (continued).\label{tab:p_coarse_1}}
for neglecting them. \par
Note that \texttt{SUM} must be chosen for the classical Additive
Schwarz smoother, and \texttt{NONE} for its RAS variant. \\ \hline
\verb|mld_sub_fillin_| \par \verb|SUB_FILLIN| & \verb|integer|
%\verb|mld_sub_fillin_| \par
\verb|SUB_FILLIN| & \verb|integer|
& Any integer \par number~$\ge 0$
& 0
& Fill-in level $p$ of the incomplete LU factorizations. \\ \hline
\verb|mld_sub_iluthrs_| \par \verb|SUB_ILUTHRS| & \verb|real(|\emph{kind\_parameter}\verb|)|
%\verb|mld_sub_iluthrs_| \par
\verb|SUB_ILUTHRS| & \verb|real(|\emph{kind\_parameter}\verb|)|
& Any real number~$\ge 0$
& 0
& Drop tolerance $t$ in the ILU($p,t$) factorization. \\ %\hline