|
|
|
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
|
|
|
|
|
|
|
|
|
<!--Converted with LaTeX2HTML 2012 (1.2)
|
|
|
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
|
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
|
|
|
* with significant contributions from:
|
|
|
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
|
|
|
<HTML>
|
|
|
|
|
<HEAD>
|
|
|
|
|
<TITLE>Getting Started</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="Getting Started">
|
|
|
|
|
<META NAME="keywords" CONTENT="userhtml">
|
|
|
|
|
<META NAME="resource-type" CONTENT="document">
|
|
|
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
|
|
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2012">
|
|
|
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
|
|
|
|
|
|
<LINK REL="STYLESHEET" HREF="userhtml.css">
|
|
|
|
|
|
|
|
|
|
<LINK REL="next" HREF="node18.html">
|
|
|
|
|
<LINK REL="previous" HREF="node12.html">
|
|
|
|
|
<LINK REL="up" HREF="userhtml.html">
|
|
|
|
|
<LINK REL="next" HREF="node17.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html276"
|
|
|
|
|
HREF="node17.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
|
|
|
<A NAME="tex2html272"
|
|
|
|
|
HREF="userhtml.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
|
|
|
<A NAME="tex2html266"
|
|
|
|
|
HREF="node15.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
|
|
|
<A NAME="tex2html274"
|
|
|
|
|
HREF="node2.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html277"
|
|
|
|
|
HREF="node17.html">Examples</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html273"
|
|
|
|
|
HREF="userhtml.html">userhtml</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html267"
|
|
|
|
|
HREF="node15.html">Smoothers and coarsest-level solvers</A>
|
|
|
|
|
<B> <A NAME="tex2html275"
|
|
|
|
|
HREF="node2.html">Contents</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
|
|
|
|
<H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A>
|
|
|
|
|
<BR>
|
|
|
|
|
Getting Started
|
|
|
|
|
</H1><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
|
|
|
|
|
<P>
|
|
|
|
|
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">We describe the basics for building and applying MLD2P4 one-level and multilevel
|
|
|
|
|
(i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS [<A
|
|
|
|
|
HREF="node30.html#PSBLASGUIDE">13</A>].
|
|
|
|
|
The following steps are required:
|
|
|
|
|
</FONT></FONT></FONT>
|
|
|
|
|
|
|
|
|
|
<OL>
|
|
|
|
|
<LI><I>Declare the preconditioner data structure</I>. It is a derived data type,
|
|
|
|
|
<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>
|
|
|
|
|
or <code>z</code>, according to the basic data type of the sparse matrix
|
|
|
|
|
(<code>s</code> = real single precision; <code>d</code> = real double precision;
|
|
|
|
|
<code>c</code> = complex single precision; <code>z</code> = complex double precision).
|
|
|
|
|
This data structure is accessed by the user only through the MLD2P4 routines,
|
|
|
|
|
following an object-oriented approach.
|
|
|
|
|
</LI>
|
|
|
|
|
<LI><I>Allocate and initialize the preconditioner data structure, according to
|
|
|
|
|
a preconditioner type chosen by the user</I>. This is performed by the routine
|
|
|
|
|
<code>init</code>, which also sets defaults for each preconditioner
|
|
|
|
|
type selected by the user. The preconditioner types and the defaults associated
|
|
|
|
|
with them are given in Table <A HREF="#tab:precinit">1</A>, where the strings used by
|
|
|
|
|
<code>init</code> to identify the preconditioner types are also given.
|
|
|
|
|
Note that these strings are valid also if uppercase letters are substituted by
|
|
|
|
|
corresponding lowercase ones.
|
|
|
|
|
</LI>
|
|
|
|
|
<LI><I>Modify the selected preconditioner type, by properly setting
|
|
|
|
|
preconditioner parameters.</I> This is performed by the routine <code>set</code>.
|
|
|
|
|
This routine must be called only if the user wants to modify the default values
|
|
|
|
|
of the parameters associated with the selected preconditioner type, to obtain a variant
|
|
|
|
|
of that preconditioner. Examples of use of <code>set</code> are given in
|
|
|
|
|
Section <A HREF="node17.html#sec:examples">5.1</A>; a complete list of all the
|
|
|
|
|
preconditioner parameters and their allowed and default values is provided in
|
|
|
|
|
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>.
|
|
|
|
|
</LI>
|
|
|
|
|
<LI><I>Build the preconditioner for a given matrix</I>. If the selected preconditioner
|
|
|
|
|
is multilevel, then two steps must be performed, as specified next.
|
|
|
|
|
<DL COMPACT>
|
|
|
|
|
<DT>4.1</DT>
|
|
|
|
|
<DD><I>Build the aggregation hierarchy for a given matrix.</I> This is
|
|
|
|
|
performed by the routine <code>hierarchy_build</code>.
|
|
|
|
|
</DD>
|
|
|
|
|
<DT>4.2</DT>
|
|
|
|
|
<DD><I>Build the preconditioner for a given matrix.</I> This is performed
|
|
|
|
|
by the routine <code>smoothers_build</code>.
|
|
|
|
|
</DD>
|
|
|
|
|
</DL>
|
|
|
|
|
If the selected preconditioner is one-level, it is built in a single step,
|
|
|
|
|
performed by the routine <code>bld</code>.
|
|
|
|
|
</LI>
|
|
|
|
|
<LI><I>Apply the preconditioner at each iteration of a Krylov solver.</I>
|
|
|
|
|
This is performed by the routine <code>aply</code>. When using the PSBLAS Krylov solvers,
|
|
|
|
|
this step is completely transparent to the user, since <code>aply</code> is called
|
|
|
|
|
by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>).
|
|
|
|
|
</LI>
|
|
|
|
|
<LI><I>Free the preconditioner data structure</I>. This is performed by
|
|
|
|
|
the routine <code>free</code>. This step is complementary to step 1 and should
|
|
|
|
|
be performed when the preconditioner is no more used.
|
|
|
|
|
</LI>
|
|
|
|
|
</OL><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
|
|
|
|
|
<P>
|
|
|
|
|
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">All the previous routines are available as methods of the preconditioner object.
|
|
|
|
|
A detailed description of them is given in Section <A HREF="node18.html#sec:userinterface">6</A>.
|
|
|
|
|
Examples showing the basic use of MLD2P4 are reported in Section <A HREF="node17.html#sec:examples">5.1</A>.
|
|
|
|
|
</FONT></FONT></FONT>
|
|
|
|
|
<P>
|
|
|
|
|
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
|
|
|
|
|
<BR><P></P>
|
|
|
|
|
<DIV ALIGN="CENTER"><A NAME="904"></A>
|
|
|
|
|
<TABLE>
|
|
|
|
|
<CAPTION><STRONG>Table 1:</STRONG>
|
|
|
|
|
Preconditioner types, corresponding strings and default choices.
|
|
|
|
|
</CAPTION>
|
|
|
|
|
<TR><TD>
|
|
|
|
|
<DIV ALIGN="CENTER">
|
|
|
|
|
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
|
|
|
|
|
<TR><TD ALIGN="LEFT"><SMALL>TYPE</SMALL></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><SMALL>STRING</SMALL></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232><SMALL>DEFAULT PRECONDITIONER</SMALL></TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">No preconditioner</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'NOPREC'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered only to use the PSBLAS
|
|
|
|
|
Krylov solvers with no preconditioner.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">Diagonal</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'DIAG'</code> or <code>'JACOBI'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Diagonal preconditioner.
|
|
|
|
|
For any zero diagonal entry of the matrix to be preconditioned,
|
|
|
|
|
the corresponding entry of the preconditioner is set to 1.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">Gauss-Seidel</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'GS'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Hybrid Gauss-Seidel (forward), that is,
|
|
|
|
|
global block Jacobi with
|
|
|
|
|
Gauss-Seidel as local solver.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">Symmetrized Gauss-Seidel</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'FBGS'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Symmetrized hybrid Gauss-Seidel,that is,
|
|
|
|
|
forward Gauss-Seidel followed by
|
|
|
|
|
backward Gauss-Seidel.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">Block Jacobi</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'BJAC'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Block-Jacobi with ILU(0) on the local blocks.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">Additive Schwarz</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'AS'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Additive Schwarz (AS),
|
|
|
|
|
with overlap 1 and ILU(0) on the local blocks.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
<TR><TD ALIGN="LEFT">Multilevel</TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=51><code>'ML'</code></TD>
|
|
|
|
|
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>V-cycle with one hybrid forward Gauss-Seidel
|
|
|
|
|
(GS) sweep as pre-smoother and one hybrid backward
|
|
|
|
|
GS sweep as post-smoother, basic smoothed aggregation
|
|
|
|
|
as coarsening algorithm, and LU (plus triangular solve)
|
|
|
|
|
as coarsest-level solver. See the default values in
|
|
|
|
|
Tables <A HREF="#tab:p_cycle">2</A>-<A HREF="#tab:p_smoother_1">8</A>
|
|
|
|
|
for further details of the preconditioner.</TD>
|
|
|
|
|
</TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV></TD></TR>
|
|
|
|
|
</TABLE>
|
|
|
|
|
</DIV><P></P>
|
|
|
|
|
<BR><FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
|
|
|
|
|
<P>
|
|
|
|
|
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1">Note that the module <code>mld_prec_mod</code>, containing the definition of the
|
|
|
|
|
preconditioner data type and the interfaces to the routines of MLD2P4,
|
|
|
|
|
must be used in any program calling such routines.
|
|
|
|
|
The modules <code>psb_base_mod</code>, for the sparse matrix and communication descriptor
|
|
|
|
|
data types, and <code>psb_krylov_mod</code>, for interfacing with the
|
|
|
|
|
Krylov solvers, must be also used (see Section <A HREF="node17.html#sec:examples">5.1</A>).
|
|
|
|
|
<BR></FONT></FONT></FONT>
|
|
|
|
|
<P>
|
|
|
|
|
<FONT SIZE="+1"><FONT SIZE="+1"><FONT SIZE="+1"><B>Remark 1.</B> Coarsest-level solvers based on the LU factorization,
|
|
|
|
|
such as those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU_Dist,
|
|
|
|
|
usually lead to smaller numbers of preconditioned Krylov
|
|
|
|
|
iterations than inexact solvers, when the linear system comes from
|
|
|
|
|
a standard discretization of basic scalar elliptic PDE problems. However,
|
|
|
|
|
this does not necessarily correspond to the smallest execution time
|
|
|
|
|
on parallel computers. </FONT></FONT></FONT>
|
|
|
|
|
<P>
|
|
|
|
|
<FONT SIZE="+1"><FONT SIZE="+1"></FONT></FONT>
|
|
|
|
|
<BR><HR>
|
|
|
|
|
<!--Table of Child-Links-->
|
|
|
|
|
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
|
|
|
|
|
|
|
|
|
<UL>
|
|
|
|
|
<LI><A NAME="tex2html278"
|
|
|
|
|
HREF="node17.html">Examples</A>
|
|
|
|
|
</UL>
|
|
|
|
|
<!--End of Table of Child-Links-->
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html276"
|
|
|
|
|
HREF="node17.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
|
|
|
<A NAME="tex2html272"
|
|
|
|
|
HREF="userhtml.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
|
|
|
<A NAME="tex2html266"
|
|
|
|
|
HREF="node15.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
|
|
|
<A NAME="tex2html274"
|
|
|
|
|
HREF="node2.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html277"
|
|
|
|
|
HREF="node17.html">Examples</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html273"
|
|
|
|
|
HREF="userhtml.html">userhtml</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html267"
|
|
|
|
|
HREF="node15.html">Smoothers and coarsest-level solvers</A>
|
|
|
|
|
<B> <A NAME="tex2html275"
|
|
|
|
|
HREF="node2.html">Contents</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
