<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <!--Converted with LaTeX2HTML 2018 (Released Feb 1, 2018) --> <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 v2018"> <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 > <DIV CLASS="navigation"><!--Navigation Panel--> <A NAME="tex2html283" HREF="node17.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html279" HREF="userhtml.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html273" HREF="node15.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html281" HREF="node2.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <BR> <B> Next:</B> <A NAME="tex2html284" HREF="node17.html">Examples</A> <B> Up:</B> <A NAME="tex2html280" HREF="userhtml.html">userhtml</A> <B> Previous:</B> <A NAME="tex2html274" HREF="node15.html">Smoothers and coarsest-level solvers</A> <B> <A NAME="tex2html282" HREF="node2.html">Contents</A></B> <BR> <BR></DIV> <!--End of Navigation Panel--> <H1><A NAME="SECTION00070000000000000000"></A><A NAME="sec:started"></A> <BR> Getting Started </H1><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG> <P> <BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">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="node36.html#PSBLASGUIDE">13</A>]. The following steps are required: </BIG></BIG></BIG> <OL> <LI><SPAN CLASS="textit">Declare the preconditioner data structure</SPAN>. It is a derived data type, <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> 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><SPAN CLASS="textit">Allocate and initialize the preconditioner data structure, according to a preconditioner type chosen by the user</SPAN>. 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><SPAN CLASS="textit">Modify the selected preconditioner type, by properly setting preconditioner parameters.</SPAN> 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><SPAN CLASS="textit">Build the preconditioner for a given matrix</SPAN>. If the selected preconditioner is multilevel, then two steps must be performed, as specified next. <DL COMPACT> <DT>4.1</DT> <DD><SPAN CLASS="textit">Build the aggregation hierarchy for a given matrix.</SPAN> This is performed by the routine <code>hierarchy_build</code>. </DD> <DT>4.2</DT> <DD><SPAN CLASS="textit">Build the preconditioner for a given matrix.</SPAN> 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><SPAN CLASS="textit">Apply the preconditioner at each iteration of a Krylov solver.</SPAN> This is performed by the method <code>apply</code>. When using the PSBLAS Krylov solvers, this step is completely transparent to the user, since <code>apply</code> is called by the PSBLAS routine implementing the Krylov solver (<code>psb_krylov</code>). </LI> <LI><SPAN CLASS="textit">Free the preconditioner data structure</SPAN>. 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><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG> <P> <BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">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>. </BIG></BIG></BIG> <P> <BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG> <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>'NONE'</code></TD> <TD ALIGN="LEFT" VALIGN="TOP" WIDTH=232>Considered 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><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG> <P> <BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">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></BIG></BIG></BIG> <P> <BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE"><SPAN CLASS="textbf">Remark 1.</SPAN> 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. </BIG></BIG></BIG> <P> <BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG> <BR><HR> <!--Table of Child-Links--> <A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A> <UL CLASS="ChildLinks"> <LI><A NAME="tex2html285" HREF="node17.html">Examples</A> </UL> <!--End of Table of Child-Links--> <DIV CLASS="navigation"><HR> <!--Navigation Panel--> <A NAME="tex2html283" HREF="node17.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html279" HREF="userhtml.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html273" HREF="node15.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html281" HREF="node2.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <BR> <B> Next:</B> <A NAME="tex2html284" HREF="node17.html">Examples</A> <B> Up:</B> <A NAME="tex2html280" HREF="userhtml.html">userhtml</A> <B> Previous:</B> <A NAME="tex2html274" HREF="node15.html">Smoothers and coarsest-level solvers</A> <B> <A NAME="tex2html282" HREF="node2.html">Contents</A></B> </DIV> <!--End of Navigation Panel--> </BODY> </HTML>