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<H2><A NAME="SECTION00082000000000000000"></A><A NAME="sec:precset"></A>
<BR>
Subroutine mld_precset
</H2>
<P>
<DIV ALIGN="CENTER">
<code>call mld_precset(p,what,val,info)</code>
</DIV>
<P>
This routine sets the parameters defining the preconditioner. More
precisely, the parameter identified by <code>what</code> is assigned the value
contained in <code>val</code>.
<P>
The routine may also be invoked as a method
of the preconditioner object as in the following:
<DIV ALIGN="CENTER">
<code>call p%set(what,val,info [,ilev, pos])</code>
<BR>
</DIV>
In this case it is also possible to specify an optional <code>ilev</code>
argument that restricts the effect of
the call to the specified level.
<P>
Finally, if the user has developed a new type of smoother and/or
solver by extending one of the base MLD2P4 types, and has declared a
variable of the new type in the main program, it is possible to pass
the new smoother/solver variable to the setup routine as follows:
<DIV ALIGN="CENTER">
<code>call p%set(smoother,info [,ilev ,pos])</code>
<BR><code>call p%set(solver,info [,ilev ,pos])</code>
</DIV>
In this way, the variable will act as a <I>mold</I> to which the
preconditioner will conform, even though the MLD2P4 library is not
modified, and thus has no direct knowledge about the new type.
<P>
<FONT SIZE="+1"><B>Arguments</B></FONT>
<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must
be chosen according to the real/complex, single/double precision
version of MLD2P4 under use.</TD>
</TR>
<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>
</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
a predefined constant, or through its name; the string
is case-insensitive. See also
Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>val </code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer</code> <I>or</I> <code>character(len=*)</code> <I>or</I>
<code>real(psb_spk_)</code> <I>or</I> <code>real(psb_dpk_)</code>,
<code>intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The value of the parameter to be set. The list of allowed
values and the corresponding data types is given in
Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.
When the value is of type <code>character(len=*)</code>,
it is also treated as case insensitive.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>smoother</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>class(mld_x_base_smoother_type)</code></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The user-defined new smoother to be employed in the
preconditioner.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>solver</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>class(mld_x_base_solver_type)</code></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The user-defined new solver to be employed in the
preconditioner.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section&nbsp;<A HREF="node23.html#sec:errors">7</A>
for details.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>pos</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>charater(len=*), intent(in)</code>.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Whether the other arguments apply to the <code>'PRE'</code>
or to the <code>'POST'</code> smoothers.</TD>
</TR>
</TABLE>
<P>
<BR>
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
<OL>
<LI>the type of multi-level preconditioner;
</LI>
<LI>the one-level preconditioner used as smoother;
</LI>
<LI>the aggregation algorithm;
</LI>
<LI>the coarse-space correction at the coarsest level.
</LI>
</OL>
A list of the parameters that can be set, along with their allowed and
default values, is given in Tables&nbsp;<A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.
For a detailed description of the meaning of the parameters, please
refer to Section&nbsp;<A HREF="node11.html#sec:background">4</A>.
<P>
The smoother and solver objects are arranged in a hierarchical manner;
when specifying a smoother object, its parameters including the
contained solver are set to default values, and when a solver
object is specified its defaults are also set, overriding in both
cases any previous settings even if explicitly specified. Therefore if
the user sets a new smoother, and wishes to use a solver
different from the default one, the call to set the solver must come
<I>after</I> the call to set the smoother.
<P>
The combination of a Jacobi smoother with a Diagonal Scaling local
solver is equivalent to the strategy called Point Jacobi in the
literature; similarly, having a Jacobi smoother with a Gauss-Seidel
local solver is equivalent to a ``hybrid Gauss-Seidel'' solver.
<P>
Completely new smoother and/or solver class derived from the
base objects in the library may be used without recompiling the
library itself. Once the new smoother/solver class has been
developed, the user can declare a variable of that new type in the
application, and pass that variable to the <code>p%set(solver,info)</code>
call; the new solver object is then dynamically included in the
preconditioner structure.
<P>
The <code>what,val</code> pairs described here are those of the predefined
smoother/solver objects; newly developed solvers may define new pairs
according to their needs.
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1312"></A>
<TABLE>
<CAPTION><STRONG>Table 2:</STRONG>
Parameters defining the type of multi-level preconditioner.
</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>what</code></TD>
<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><code>val</code></TD>
<TD ALIGN="LEFT"><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_ml_type_</code> <BR><code>ML_TYPE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><TT>'ADD'</TT> <TT>'MULT'</TT></TD>
<TD ALIGN="LEFT"><TT>'MULT'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>Basic multi-level framework: additive or multiplicative
among the levels (always additive inside a level).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_smoother_type_</code> <BR><code>SMOOTHER_TYPE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><TT>'JACOBI'</TT> <TT>'BJAC'</TT> <TT>'AS'</TT></TD>
<TD ALIGN="LEFT"><TT>'AS'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>Basic predefined one-level preconditioner
(i.e. smoother): Jacobi, block Jacobi, AS.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_smoother_pos_</code> <BR><code>SMOOTHER_POS</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><TT>'PRE'</TT> <TT>'POST'</TT> <TT>'TWOSIDE'</TT></TD>
<TD ALIGN="LEFT"><TT>'TWOSIDE'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>``Position'' of the smoother: pre-smoother, post-smoother,
pre- and post-smoother.</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1314"></A>
<TABLE>
<CAPTION><STRONG>Table 3:</STRONG>
Parameters defining the one-level preconditioner used as smoother.
</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>what</code></TD>
<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><code>val</code></TD>
<TD ALIGN="LEFT"><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_ovr_</code> <BR><code>SUB_OVR</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any&nbsp;int.&nbsp;num.&nbsp;<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img90.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">1</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Number of overlap layers.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_restr_</code> <BR><code>SUB_RESTR</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'HALO'</TT> <TT>'NONE'</TT></TD>
<TD ALIGN="LEFT"><TT>'HALO'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Type of restriction operator:
<TT>'HALO'</TT> for taking into account the overlap, <TT>'NONE'</TT>
for neglecting it.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_prol_</code> <BR><code>SUB_PROL</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'SUM'</TT> <TT>'NONE'</TT></TD>
<TD ALIGN="LEFT"><TT>'NONE'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Type of prolongation operator:
<TT>'SUM'</TT> for adding the contributions from the overlap, <TT>'NONE'</TT>
for neglecting them.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_solve_</code> <BR><code>SUB_SOLVE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'DIAG'</TT>
<TT>'GS'</TT> <TT>'BWGS'</TT>
<TT>'ILU'</TT>
<TT>'MILU'</TT> <TT>'ILUT'</TT>
<TT>'UMF'</TT>
<TT>'SLU'</TT>
<TT>'MUMPS'</TT></TD>
<TD ALIGN="LEFT"><TT>'ILU'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Predefined local solver: pointwise Jacobi
(diagonal scaling),
(forward) Gauss-Seidel, Backward
Gauss-Seidel, ILU(<IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p$">), MILU(<IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p$">),
ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$p,t$">), LU from UMFPACK, LU from
SuperLU (plus triangular solve), LU from MUMPS.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_fillin_</code> <BR><code>SUB_FILLIN</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img90.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p$"> of the incomplete LU factorizations.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_iluthrs_</code> <BR><code>SUB_ILUTHRS</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;real&nbsp;num.&nbsp;<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img90.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <IMG
WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img91.png"
ALT="$t$"> in the ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$p,t$">) factorization.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_ren_</code> <BR><code>SUB_REN</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'RENUM_NONE'</TT> <TT>'RENUM_GLOBAL'</TT> </TD>
<TD ALIGN="LEFT"><TT>'RENUM_NONE'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>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.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_solver_sweeps_</code> <BR><code>SOLVER_SWEEPS</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img92.png"
ALT="$\ge 1$"></TD>
<TD ALIGN="LEFT">1</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Number of sweeps for iterative local solver
(currently only Gauss-Seidel).</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1316"></A>
<TABLE>
<CAPTION><STRONG>Table 4:</STRONG>
Parameters defining the aggregation algorithm.
</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>what</code></TD>
<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><code>val</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_coarse_aggr_size_</code> <BR><code>COARSE_AGGR_SIZE</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>A positive number</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>The cubic root of
the matrix size at the fine level.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Coarse size threshold. Aggregation will
proceed until either the global number of
variables is below this threshold, or the
aggregation does not reduce the size any
longer, or the maximum number of levels is
reached.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_min_aggr_ratio</code> <BR><code>MIN_AGGR_RATIO</code></TD>
<TD ALIGN="LEFT"><code>real</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>A number greater than one</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>1.5</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Minimum aggregation ratio. Aggregation will
stop if the ratio between the matrix sizes
at two consecutive levels drops below this
threshold.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_n_prec_levs_</code> <BR><code>N_PREC_LEVS</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>A number greater than 1, or -1.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>-1</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Number of levels; if set to a positive
number greater than 1, it will force the
aggregation algorithm to use this many
levels (unless there is no reduction in the
coarse matrix size).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_max_prec_levs_</code> <BR><code>MAX_PREC_LEVS</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>A positive number</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>20</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Maximum number of levels: irrespective of
the other settings, do not use more than
this many levels.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_alg_</code> <BR><code>AGGR_ALG</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'DEC'</TT>, <TT>'SYMDEC'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'DEC'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Aggregation algorithm. Currently, only the
decoupled aggregation is available; the
<code>SYMDEC</code> option applies decoupled
aggregation to the sparsity pattern
of <IMG
WIDTH="62" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="img93.png"
ALT="$A+A^T$">.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_ord_</code> <BR><code>AGGR_ORD</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'NATURAL'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'DEGREE'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Initial ordering of indices for aggregation
algorithm: natural ordering or sorted by
descending degree of the node in the
matrix graph. Since aggregation is
heuristics, results will be different.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_kind_</code> <BR><code>AGGR_KIND</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'SMOOTHED'</TT> <TT>'NONSMOOTHED'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'SMOOTHED'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Type of aggregation: smoothed, nonsmoothed
(i.e. using the tentative prolongator).</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_thresh_</code> <BR><code>AGGR_THRESH</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any&nbsp;real&nbsp;num. <IMG
WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="img94.png"
ALT="$\in [0, 1]$"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>0.05</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Threshold <IMG
WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img95.png"
ALT="$\theta$"> in the aggregation algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_scale_</code> <BR><code>AGGR_SCALE</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any&nbsp;real&nbsp;num. <IMG
WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
SRC="img94.png"
ALT="$\in [0, 1]$"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>1.0</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Scale factor applied to the threshold going
from level <IMG
WIDTH="33" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img96.png"
ALT="$ilev$"> to level <IMG
WIDTH="63" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="img97.png"
ALT="$ilev+1$">.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_omega_alg_</code> <BR><code>AGGR_OMEGA_ALG</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'EIG_EST'</TT> <TT>'USER_CHOICE'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'EIG_EST'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How the damping parameter <IMG
WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$\omega$"> in the
smoothed aggregation should be computed:
either via an estimate of the spectral radius of
<IMG
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img87.png"
ALT="$D^{-1}A$">, or explicily
specified by the user.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_eig_</code> <BR><code>AGGR_EIG</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'A_NORMI'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><TT>'A_NORMI'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How to estimate the spectral radius of <IMG
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img87.png"
ALT="$D^{-1}A$">.
Currently only the infinity norm estimate
is available.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_omega_val_</code> <BR><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=68>Any&nbsp;nonnegative&nbsp;real&nbsp;num.</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><!-- MATH
$4/(3\rho(D^{-1}A))$
-->
<IMG
WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img98.png"
ALT="$4/(3\rho(D^{-1}A))$"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Damping parameter <IMG
WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img86.png"
ALT="$\omega$"> in the smoothed aggregation algorithm.
It must be set by the user if
<code>USER_CHOICE</code> was specified for
<code>mld_aggr_omega_alg_</code>,
otherwise it is computed by the library, using the
selected estimate of the spectral radius <IMG
WIDTH="73" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="img99.png"
ALT="$\rho(D^{-1}A)$"> of
<IMG
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
SRC="img87.png"
ALT="$D^{-1}A$">.</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="1319"></A>
<TABLE>
<CAPTION><STRONG>Table 5:</STRONG>
Parameters defining the coarse-space correction at the coarsest
level.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>what</code></TD>
<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><code>val</code></TD>
<TD ALIGN="LEFT"><SMALL>DEFAULT</SMALL></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><SMALL>COMMENTS</SMALL></TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_mat_</code> <BR><code>COARSE_MAT</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'DISTR'</TT> <TT>'REPL'</TT></TD>
<TD ALIGN="LEFT"><TT>'DISTR'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Coarsest matrix: distributed among the processors or
replicated on each of them.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_solve_</code> <BR><code>COARSE_SOLVE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'BJAC'</TT>
<TT>'UMF'</TT> <TT>'MUMPS'</TT>
<TT>'SLU'</TT> <TT>'SLUDIST'</TT></TD>
<TD ALIGN="LEFT"><TT>'BJAC'</TT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Solver used at the coarsest level: block Jacobi, sequential
LU from UMFPACK, sequential LU from SuperLU,
distributed LU from SuperLU_Dist or MUMPS.
<TT>'SLUDIST'</TT> and <TT>'MUMPS'</TT>
require the coarsest matrix to be distributed, while
<TT>'UMF'</TT> and <TT>'SLU'</TT> require
it to be replicated.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_subsolve_</code> <BR><code>COARSE_SUBSOLVE</code></TD>
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'ILU'</TT> <TT>'MILU'</TT>
<TT>'ILUT'</TT>
<TT>'UMF'</TT>
<TT>'SLU'</TT>
<TT>'MUMPS'</TT></TD>
<TD ALIGN="LEFT">See note</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Solver for the diagonal blocks of the coarse matrix,
in case the block Jacobi solver
is chosen as coarsest-level solver: ILU(<IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p$">), MILU(<IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p$">),
ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$p,t$">), LU from UMFPACK,
LU from SuperLU, plus triangular solve.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_sweeps_</code> <BR><code>COARSE_SWEEPS</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img100.png"
ALT="$&gt; 0$"></TD>
<TD ALIGN="LEFT">4</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Number of Block-Jacobi sweeps when 'BJAC' is used as
coarsest-level solver.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_fillin_</code> <BR><code>COARSE_FILLIN</code></TD>
<TD ALIGN="LEFT"><code>integer</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;int.&nbsp;num.&nbsp;<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img90.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <IMG
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p$"> of the incomplete LU factorizations.</TD>
</TR>
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_iluthrs_</code> <BR><code>COARSE_ILUTHRS</code></TD>
<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any&nbsp;real.&nbsp;num.&nbsp;<IMG
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img90.png"
ALT="$\ge 0$"></TD>
<TD ALIGN="LEFT">0</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <IMG
WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img91.png"
ALT="$t$"> in the ILU(<IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img36.png"
ALT="$p,t$">) factorization.</TD>
</TR>
<TR><TD ALIGN="LEFT" COLSPAN=5><B>Note:</B> defaults for
<TT>m</TT>ld_coarse_subsolve_ are chosen as</TD>
</TR>
<TR><TD ALIGN="LEFT" COLSPAN=5>single precision version: 'MUMPS' if installed, 'SLU' if installed, 'ILU' otherwise</TD>
</TR>
<TR><TD ALIGN="LEFT" COLSPAN=5>double precision version: 'MUMPS' if installed, 'UMF' if installed,
else 'SLU' if installed, 'ILU' otherwise</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>
<P>
<P>
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