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Changes to docs to highlight new stuff in MLD internals.
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Salvatore Filippone
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!--Converted with LaTeX2HTML 2012 (1.2)
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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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* with significant contributions from:
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<!--Converted with LaTeX2HTML 2017.2 (Released Jan 23, 2017) -->
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<HTML>
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<HEAD>
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<TITLE>Getting Started</TITLE>
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@@ -13,7 +9,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -25,54 +21,55 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<BODY >
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HREF="node15.html">Smoothers and coarsest-level solvers</A>
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<B> <A NAME="tex2html275"
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<B> <A NAME="tex2html282"
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR>
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<BR></DIV>
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<!--End of Navigation Panel-->
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<H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A>
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<BR>
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Getting Started
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</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
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</H1><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We describe the basics for building and applying MLD2P4 one-level and multilevel
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">We describe the basics for building and applying MLD2P4 one-level and multilevel
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(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
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HREF="node30.html#PSBLASGUIDE">13</A>].
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HREF="node36.html#PSBLASGUIDE">13</A>].
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The following steps are required:
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</FONT></FONT></FONT>
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</BIG></BIG></BIG>
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<OL>
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<LI><I>Declare the preconditioner data structure</I>. It is a derived data type,
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<code>mld_</code><I>x</I><code>prec_</code> <code>type</code>, where <I>x</I> may be <code>s</code>, <code>d</code>, <code>c</code>
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<LI><SPAN CLASS="textit">Declare the preconditioner data structure</SPAN>. It is a derived data type,
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<code>mld_</code><SPAN CLASS="textit">x</SPAN><code>prec_</code> <code>type</code>, where <SPAN CLASS="textit">x</SPAN> may be <code>s</code>, <code>d</code>, <code>c</code>
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or <code>z</code>, according to the basic data type of the sparse matrix
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(<code>s</code> = real single precision; <code>d</code> = real double precision;
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<code>c</code> = complex single precision; <code>z</code> = complex double precision).
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This data structure is accessed by the user only through the MLD2P4 routines,
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following an object-oriented approach.
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</LI>
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<LI><I>Allocate and initialize the preconditioner data structure, according to
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a preconditioner type chosen by the user</I>. This is performed by the routine
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<LI><SPAN CLASS="textit">Allocate and initialize the preconditioner data structure, according to
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a preconditioner type chosen by the user</SPAN>. This is performed by the routine
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<code>init</code>, which also sets defaults for each preconditioner
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type selected by the user. The preconditioner types and the defaults associated
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with them are given in Table <A HREF="#tab:precinit">1</A>, where the strings used by
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@@ -80,8 +77,8 @@ The following steps are required:
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Note that these strings are valid also if uppercase letters are substituted by
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corresponding lowercase ones.
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</LI>
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<LI><I>Modify the selected preconditioner type, by properly setting
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preconditioner parameters.</I> This is performed by the routine <code>set</code>.
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<LI><SPAN CLASS="textit">Modify the selected preconditioner type, by properly setting
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preconditioner parameters.</SPAN> This is performed by the routine <code>set</code>.
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This routine must be called only if the user wants to modify the default values
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of the parameters associated with the selected preconditioner type, to obtain a variant
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of that preconditioner. Examples of use of <code>set</code> are given in
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@@ -89,38 +86,38 @@ The following steps are required:
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preconditioner parameters and their allowed and default values is provided in
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Section <A HREF="node18.html#sec:userinterface">6</A>, Tables <A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>.
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</LI>
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<LI><I>Build the preconditioner for a given matrix</I>. If the selected preconditioner
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<LI><SPAN CLASS="textit">Build the preconditioner for a given matrix</SPAN>. If the selected preconditioner
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is multilevel, then two steps must be performed, as specified next.
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<DL COMPACT>
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<DT>4.1</DT>
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<DD><I>Build the aggregation hierarchy for a given matrix.</I> This is
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<DD><SPAN CLASS="textit">Build the aggregation hierarchy for a given matrix.</SPAN> This is
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performed by the routine <code>hierarchy_build</code>.
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</DD>
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<DT>4.2</DT>
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<DD><I>Build the preconditioner for a given matrix.</I> This is performed
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<DD><SPAN CLASS="textit">Build the preconditioner for a given matrix.</SPAN> This is performed
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by the routine <code>smoothers_build</code>.
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</DD>
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</DL>
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If the selected preconditioner is one-level, it is built in a single step,
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performed by the routine <code>bld</code>.
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</LI>
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<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
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This is performed by the routine <code>aply</code>. When using the PSBLAS Krylov solvers,
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this step is completely transparent to the user, since <code>aply</code> is called
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<LI><SPAN CLASS="textit">Apply the preconditioner at each iteration of a Krylov solver.</SPAN>
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This is performed by the method <code>apply</code>. When using the PSBLAS Krylov solvers,
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this step is completely transparent to the user, since <code>apply</code> is called
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by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
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</LI>
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<LI><I>Free the preconditioner data structure</I>. This is performed by
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<LI><SPAN CLASS="textit">Free the preconditioner data structure</SPAN>. This is performed by
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the routine <code>free</code>. This step is complementary to step 1 and should
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be performed when the preconditioner is no more used.
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</LI>
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</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
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</OL><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the previous routines are available as methods of the preconditioner object.
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">All the previous routines are available as methods of the preconditioner object.
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A detailed description of them is given in Section <A HREF="node18.html#sec:userinterface">6</A>.
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Examples showing the basic use of MLD2P4 are reported in Section <A HREF="node17.html#sec:examples">5.1</A>.
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</FONT></FONT></FONT>
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</BIG></BIG></BIG>
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<P>
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<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="904"></A>
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<TABLE>
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@@ -135,8 +132,8 @@ Preconditioner types, corresponding strings and default choices.
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
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</TR>
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<TR><TD ALIGN="LEFT">No preconditioner</TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NOPREC'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered only to use the PSBLAS
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NONE'</code></TD>
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<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered to use the PSBLAS
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Krylov solvers with no preconditioner.</TD>
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</TR>
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<TR><TD ALIGN="LEFT">Diagonal</TD>
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@@ -177,60 +174,63 @@ Preconditioner types, corresponding strings and default choices.
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for further details of the preconditioner.</TD>
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</TR>
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</TABLE>
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</DIV></TD></TR>
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</TABLE>
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</DIV><P></P>
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<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
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<BR><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Note that the module <code>mld_prec_mod</code>, containing the definition of the
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">Note that the module <code>mld_prec_mod</code>, containing the definition of the
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preconditioner data type and the interfaces to the routines of MLD2P4,
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must be used in any program calling such routines.
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The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
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data types, and <code>psb_krylov_mod</code>, for interfacing with the
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Krylov solvers, must be also used (see Section <A HREF="node17.html#sec:examples">5.1</A>).
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<BR></FONT></FONT></FONT>
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<BR></BIG></BIG></BIG>
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<P>
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<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 1.</B> Coarsest-level solvers based on the LU factorization,
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><SPAN CLASS="textbf">Remark 1.</SPAN> Coarsest-level solvers based on the LU factorization,
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such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist,
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usually lead to smaller numbers of preconditioned Krylov
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iterations than inexact solvers, when the linear system comes from
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a standard discretization of basic scalar elliptic PDE problems. However,
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this does not necessarily correspond to the smallest execution time
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on parallel computers. </FONT></FONT></FONT>
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on parallel computers.
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</BIG></BIG></BIG>
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<P>
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<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html278"
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<UL CLASS="ChildLinks">
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