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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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<TITLE>Subroutine mld_precset</TITLE>
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HREF="node17.html">Subroutine mld_precinit</A>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00082000000000000000"></A><A NAME="sec:precset"></A>
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<BR>
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Subroutine mld_precset
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</H2>
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<P>
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<DIV ALIGN="CENTER">
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<code>call mld_precset(p,what,val,info)</code>
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</DIV>
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<P>
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This routine sets the parameters defining the preconditioner. More
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precisely, the parameter identified by <code>what</code> is assigned the value
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contained in <code>val</code>.
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<P>
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The routine may also be invoked as a method
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of the preconditioner object as in the following:
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<DIV ALIGN="CENTER">
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<code>call p%set(what,val,info [,ilev, pos])</code>
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<BR>
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</DIV>
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In this case it is also possible to specify an optional <code>ilev</code>
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argument that restricts the effect of
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the call to the specified level.
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<P>
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Finally, if the user has developed a new type of smoother and/or
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solver by extending one of the base MLD2P4 types, and has declared a
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variable of the new type in the main program, it is possible to pass
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the new smoother/solver variable to the setup routine as follows:
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<DIV ALIGN="CENTER">
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<code>call p%set(smoother,info [,ilev ,pos])</code>
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<BR><code>call p%set(solver,info [,ilev ,pos])</code>
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</DIV>
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In this way, the variable will act as a <I>mold</I> to which the
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preconditioner will conform, even though the MLD2P4 library is not
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modified, and thus has no direct knowledge about the new type.
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<P>
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<FONT SIZE="+1"><B>Arguments</B></FONT>
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<P>
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<TABLE CELLPADDING=3>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>p</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>type(mld_</code><I>x</I><code>prec_type), intent(inout)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The preconditioner data structure. Note that <I>x</I> must
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be chosen according to the real/complex, single/double precision
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version of MLD2P4 under use.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>what</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(in)</code> <I>or</I> <code>character(len=*)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The parameter to be set. It can be specified by
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a predefined constant, or through its name; the string
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is case-insensitive. See also
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Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>val </code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer</code> <I>or</I> <code>character(len=*)</code> <I>or</I>
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<code>real(psb_spk_)</code> <I>or</I> <code>real(psb_dpk_)</code>,
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<code>intent(in)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The value of the parameter to be set. The list of allowed
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values and the corresponding data types is given in
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Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.
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When the value is of type <code>character(len=*)</code>,
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it is also treated as case insensitive.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>smoother</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>class(mld_x_base_smoother_type)</code></TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The user-defined new smoother to be employed in the
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preconditioner.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>solver</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>class(mld_x_base_solver_type)</code></TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>The user-defined new solver to be employed in the
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preconditioner.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>info</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>integer, intent(out)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Error code. If no error, 0 is returned. See Section <A HREF="node23.html#sec:errors">7</A>
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for details.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34><code>pos</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340><code>charater(len=*), intent(in)</code>.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=34> </TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=340>Whether the other arguments apply to the <code>'PRE'</code>
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or to the <code>'POST'</code> smoothers.</TD>
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</TR>
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</TABLE>
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<P>
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<BR>
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A variety of (one-level and multi-level) preconditioners can be obtained
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by a suitable setting of the preconditioner parameters. These parameters
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can be logically divided into four groups, i.e. parameters defining
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<OL>
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<LI>the type of multi-level preconditioner;
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</LI>
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<LI>the one-level preconditioner used as smoother;
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</LI>
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<LI>the aggregation algorithm;
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</LI>
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<LI>the coarse-space correction at the coarsest level.
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</LI>
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</OL>
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A list of the parameters that can be set, along with their allowed and
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default values, is given in Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>.
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For a detailed description of the meaning of the parameters, please
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refer to Section <A HREF="node11.html#sec:background">4</A>.
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<P>
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The smoother and solver objects are arranged in a hierarchical manner;
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when specifying a smoother object, its parameters including the
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contained solver are set to default values, and when a solver
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object is specified its defaults are also set, overriding in both
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cases any previous settings even if explicitly specified. Therefore if
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the user sets a new smoother, and wishes to use a solver
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different from the default one, the call to set the solver must come
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<I>after</I> the call to set the smoother.
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<P>
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The combination of a Jacobi smoother with a Diagonal Scaling local
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solver is equivalent to the strategy called Point Jacobi in the
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literature; similarly, having a Jacobi smoother with a Gauss-Seidel
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local solver is equivalent to a ``hybrid Gauss-Seidel'' solver.
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<P>
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Completely new smoother and/or solver class derived from the
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base objects in the library may be used without recompiling the
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library itself. Once the new smoother/solver class has been
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developed, the user can declare a variable of that new type in the
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application, and pass that variable to the <code>p%set(solver,info)</code>
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call; the new solver object is then dynamically included in the
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preconditioner structure.
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<P>
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The <code>what,val</code> pairs described here are those of the predefined
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smoother/solver objects; newly developed solvers may define new pairs
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according to their needs.
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="1312"></A>
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<TABLE>
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<CAPTION><STRONG>Table 2:</STRONG>
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Parameters defining the type of multi-level preconditioner.
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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" VALIGN="TOP" WIDTH=142><code>what</code></TD>
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<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><code>val</code></TD>
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<TD ALIGN="LEFT"><SMALL>DEFAULT</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198><SMALL>COMMENTS</SMALL></TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_ml_type_</code> <BR><code>ML_TYPE</code></TD>
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<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><TT>'ADD'</TT> <TT>'MULT'</TT></TD>
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<TD ALIGN="LEFT"><TT>'MULT'</TT></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>Basic multi-level framework: additive or multiplicative
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among the levels (always additive inside a level).</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_smoother_type_</code> <BR><code>SMOOTHER_TYPE</code></TD>
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<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><TT>'JACOBI'</TT> <TT>'BJAC'</TT> <TT>'AS'</TT></TD>
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<TD ALIGN="LEFT"><TT>'AS'</TT></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>Basic predefined one-level preconditioner
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(i.e. smoother): Jacobi, block Jacobi, AS.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_smoother_pos_</code> <BR><code>SMOOTHER_POS</code></TD>
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<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=57><TT>'PRE'</TT> <TT>'POST'</TT> <TT>'TWOSIDE'</TT></TD>
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<TD ALIGN="LEFT"><TT>'TWOSIDE'</TT></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=198>``Position'' of the smoother: pre-smoother, post-smoother,
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pre- and post-smoother.</TD>
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</TR>
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</TABLE>
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</DIV>
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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><P></P>
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<DIV ALIGN="CENTER"><A NAME="1314"></A>
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<TABLE>
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<CAPTION><STRONG>Table 3:</STRONG>
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Parameters defining the one-level preconditioner used as smoother.
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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" VALIGN="TOP" WIDTH=99><code>what</code></TD>
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<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><code>val</code></TD>
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<TD ALIGN="LEFT"><SMALL>DEFAULT</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><SMALL>COMMENTS</SMALL></TD>
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</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_sub_ovr_</code> <BR><code>SUB_OVR</code></TD>
|
|
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|
|
<TD ALIGN="LEFT"><code>integer</code></TD>
|
|
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|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>any int. num. <IMG
|
|
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|
|
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img90.png"
|
|
|
|
|
ALT="$\ge 0$"></TD>
|
|
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|
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<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>
|
|
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|
|
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
|
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|
<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:
|
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|
|
<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>
|
|
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|
|
<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
|
|
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|
|
<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>
|
|
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|
|
<TT>'MILU'</TT> <TT>'ILUT'</TT>
|
|
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|
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|
|
<TT>'UMF'</TT>
|
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|
|
<TT>'SLU'</TT>
|
|
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|
|
<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
|
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|
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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|
|
SRC="img35.png"
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|
|
ALT="$p$">), MILU(<IMG
|
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|
|
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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|
|
SRC="img35.png"
|
|
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|
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ALT="$p$">),
|
|
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|
ILU(<IMG
|
|
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|
|
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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|
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|
|
SRC="img36.png"
|
|
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|
|
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 int. num. <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 real num. <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 int. num. <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 real 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 real 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>
|
|
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>How to estimate the spectral radius of <IMG
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SRC="img87.png"
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ALT="$D^{-1}A$">.
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Currently only the infinity norm estimate
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is available.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><code>mld_aggr_omega_val_</code> <BR><code>AGGR_OMEGA_VAL</code></TD>
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<TD ALIGN="LEFT"><code>real(</code><I>kind_parameter</I><code>)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68>Any nonnegative real num.</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=68><!-- MATH
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$4/(3\rho(D^{-1}A))$
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-->
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<IMG
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WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img98.png"
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ALT="$4/(3\rho(D^{-1}A))$"></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=170>Damping parameter <IMG
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SRC="img86.png"
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ALT="$\omega$"> in the smoothed aggregation algorithm.
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It must be set by the user if
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<code>USER_CHOICE</code> was specified for
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<code>mld_aggr_omega_alg_</code>,
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otherwise it is computed by the library, using the
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selected estimate of the spectral radius <IMG
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WIDTH="73" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
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SRC="img99.png"
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ALT="$\rho(D^{-1}A)$"> of
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<IMG
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WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
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ALT="$D^{-1}A$">.</TD>
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</TR>
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</TABLE>
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</DIV>
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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><P></P>
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<DIV ALIGN="CENTER"><A NAME="1319"></A>
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<TABLE>
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<CAPTION><STRONG>Table 5:</STRONG>
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Parameters defining the coarse-space correction at the coarsest
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level.</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" VALIGN="TOP" WIDTH=99><code>what</code></TD>
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<TD ALIGN="LEFT"><SMALL>DATA TYPE</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><code>val</code></TD>
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<TD ALIGN="LEFT"><SMALL>DEFAULT</SMALL></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142><SMALL>COMMENTS</SMALL></TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_mat_</code> <BR><code>COARSE_MAT</code></TD>
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<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'DISTR'</TT> <TT>'REPL'</TT></TD>
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<TD ALIGN="LEFT"><TT>'DISTR'</TT></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Coarsest matrix: distributed among the processors or
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replicated on each of them.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_solve_</code> <BR><code>COARSE_SOLVE</code></TD>
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<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'BJAC'</TT>
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<TT>'UMF'</TT> <TT>'MUMPS'</TT>
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<TT>'SLU'</TT> <TT>'SLUDIST'</TT></TD>
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<TD ALIGN="LEFT"><TT>'BJAC'</TT></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Solver used at the coarsest level: block Jacobi, sequential
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LU from UMFPACK, sequential LU from SuperLU,
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distributed LU from SuperLU_Dist or MUMPS.
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<TT>'SLUDIST'</TT> and <TT>'MUMPS'</TT>
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require the coarsest matrix to be distributed, while
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<TT>'UMF'</TT> and <TT>'SLU'</TT> require
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it to be replicated.</TD>
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</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_subsolve_</code> <BR><code>COARSE_SUBSOLVE</code></TD>
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<TD ALIGN="LEFT"><code>character(len=*)</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91><TT>'ILU'</TT> <TT>'MILU'</TT>
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<TT>'ILUT'</TT>
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<TT>'UMF'</TT>
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<TT>'SLU'</TT>
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<TT>'MUMPS'</TT></TD>
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<TD ALIGN="LEFT">See note</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Solver for the diagonal blocks of the coarse matrix,
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in case the block Jacobi solver
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is chosen as coarsest-level solver: ILU(<IMG
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ALT="$p$">), MILU(<IMG
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SRC="img35.png"
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ALT="$p$">),
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ILU(<IMG
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SRC="img36.png"
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ALT="$p,t$">), LU from UMFPACK,
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LU from SuperLU, plus triangular solve.</TD>
|
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|
</TR>
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<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_sweeps_</code> <BR><code>COARSE_SWEEPS</code></TD>
|
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<TD ALIGN="LEFT"><code>integer</code></TD>
|
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <IMG
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WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img100.png"
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ALT="$> 0$"></TD>
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<TD ALIGN="LEFT">4</TD>
|
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|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Number of Block-Jacobi sweeps when 'BJAC' is used as
|
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|
|
|
coarsest-level solver.</TD>
|
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|
|
|
</TR>
|
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|
<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=99><code>mld_coarse_fillin_</code> <BR><code>COARSE_FILLIN</code></TD>
|
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|
|
<TD ALIGN="LEFT"><code>integer</code></TD>
|
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|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=91>Any int. num. <IMG
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WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img90.png"
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ALT="$\ge 0$"></TD>
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<TD ALIGN="LEFT">0</TD>
|
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|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Fill-in level <IMG
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WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img35.png"
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ALT="$p$"> of the incomplete LU factorizations.</TD>
|
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|
|
</TR>
|
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|
|
<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 real. num. <IMG
|
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WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
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SRC="img90.png"
|
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ALT="$\ge 0$"></TD>
|
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<TD ALIGN="LEFT">0</TD>
|
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|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=142>Drop tolerance <IMG
|
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WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
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SRC="img91.png"
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ALT="$t$"> in the ILU(<IMG
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WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img36.png"
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ALT="$p,t$">) factorization.</TD>
|
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|
|
</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>
|
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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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<P>
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