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mld2p4:
config/pac.m4 configure docs/html/WARNINGS docs/html/images.log docs/html/images.pl docs/html/images.tex docs/html/img100.png docs/html/img101.png docs/html/img92.png docs/html/img93.png docs/html/img94.png docs/html/img95.png docs/html/img96.png docs/html/img97.png docs/html/img98.png docs/html/img99.png docs/html/index.html docs/html/internals.pl docs/html/labels.pl docs/html/node1.html docs/html/node10.html docs/html/node11.html docs/html/node12.html docs/html/node13.html docs/html/node14.html docs/html/node15.html docs/html/node16.html docs/html/node17.html docs/html/node18.html docs/html/node19.html docs/html/node2.html docs/html/node20.html docs/html/node21.html docs/html/node22.html docs/html/node23.html docs/html/node24.html docs/html/node25.html docs/html/node26.html docs/html/node27.html docs/html/node28.html docs/html/node29.html docs/html/node3.html docs/html/node30.html docs/html/node31.html docs/html/node4.html docs/html/node5.html docs/html/node6.html docs/html/node7.html docs/html/node8.html docs/html/node9.html docs/html/userhtml.html docs/pdf/Makefile docs/pdf/abstract.tex docs/pdf/background.tex docs/pdf/bibliography.tex docs/pdf/building.tex docs/pdf/conventions.tex docs/pdf/distribution.tex docs/pdf/errors.tex docs/pdf/gettingstarted.tex docs/pdf/overview.tex docs/pdf/title.tex docs/pdf/userguide.tex docs/pdf/userhtml.tex docs/pdf/userinterface.tex Configure minro fix: require psblas 2.3 Doc fixes: dual version of title for pdf/html, fixed tables.
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Salvatore Filippone
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
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original version by: Nikos Drakos, CBLU, University of Leeds
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@@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
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<HTML>
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<HEAD>
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<TITLE>Notational Conventions</TITLE>
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<META NAME="description" CONTENT="Notational Conventions">
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<TITLE>General Overview</TITLE>
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<META NAME="description" CONTENT="General Overview">
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<META NAME="keywords" CONTENT="userhtml">
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<META NAME="resource-type" CONTENT="document">
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<META NAME="distribution" CONTENT="global">
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@@ -25,51 +25,182 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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</HEAD>
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<BODY >
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<B> Up:</B> <A NAME="tex2html98"
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<B> Up:</B> <A NAME="tex2html97"
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HREF="userhtml.html">userhtml</A>
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<B> Previous:</B> <A NAME="tex2html92"
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HREF="node2.html">General Overview</A>
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<B> <A NAME="tex2html100"
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HREF="node1.html">Contents</A></B>
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<BR>
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<B> Previous:</B> <A NAME="tex2html91"
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HREF="node2.html">Contents</A>
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<B> <A NAME="tex2html99"
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HREF="node2.html">Contents</A></B>
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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="SECTION00030000000000000000"></A><A NAME="sec:conventions"></A>
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<H1><A NAME="SECTION00030000000000000000"></A><A NAME="sec:overview"></A>
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<BR>
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Notational Conventions
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General Overview
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</H1>
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<P>
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- caratteri tipografici usati nella guida (vedi guida ML recente e guida Aztec)
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<BR> - convenzioni sui nomi di routine (anche differenza nei nomi tra high-level e
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medium-level?), strutture dati, moduli, costanti, etc. (vedi guida psblas)
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<BR> - versione reale e complessa, singola e doppia precisione
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The M<SMALL>ULTI-</SMALL>L<SMALL>EVEL </SMALL>D<SMALL>OMAIN </SMALL>D<SMALL>ECOMPOSITION </SMALL>P<SMALL>ARALLEL </SMALL>P<SMALL>RECONDITIONERS </SMALL>P<SMALL>ACKAGE BASED ON
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</SMALL>PSBLAS (MLD2P4) provides <SPAN CLASS="textit">multi-level Schwarz preconditioners</SPAN> [<A
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HREF="node30.html#dd2_96">20</A>],
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to be used in the iterative solutions of sparse linear systems:
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<BR>
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<BR><HR>
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<DIV ALIGN="RIGHT" CLASS="mathdisplay">
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<!-- MATH
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\begin{equation}
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Ax=b,
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\end{equation}
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-->
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<A NAME="system1"></A>
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<TABLE WIDTH="100%" ALIGN="CENTER">
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<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="system1"></A><IMG
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WIDTH="57" HEIGHT="30" BORDER="0"
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SRC="img1.png"
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ALT="\begin{displaymath}
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Ax=b,
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\end{displaymath}"></TD>
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<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
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(<SPAN CLASS="arabic">1</SPAN>)</TD></TR>
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</TABLE>
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<BR CLEAR="ALL"></DIV><P></P>
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where <SPAN CLASS="MATH"><IMG
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WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img2.png"
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ALT="$A$"></SPAN> is a square, real or complex, sparse matrix with a symmetric sparsity pattern.
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These preconditioners have the following general features:
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<UL>
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<LI>both <SPAN CLASS="textit">additive and hybrid multilevel</SPAN> variants are implemented,
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i.e. variants that are additive among the levels and inside each level, and variants
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that are multiplicative among the levels and additive inside each level;
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the basic Additive Schwarz (AS) preconditioners are obtained by considering only one level;
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</LI>
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<LI>a <SPAN CLASS="textit">purely algebraic</SPAN> approach is used to
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generate a sequence of coarse-level corrections to a basic AS preconditioner, without
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explicitly using any information on the geometry of the original problem (e.g. the
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discretization of a PDE). The <SPAN CLASS="textit">smoothed aggregation</SPAN> technique is applied
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as algebraic coarsening strategy [<A
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HREF="node30.html#BREZINA_VANEK">1</A>,<A
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HREF="node30.html#VANEK_MANDEL_BREZINA">24</A>].
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</LI>
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</UL>
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<P>
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The package is written in <SPAN CLASS="textit">Fortran 95</SPAN>, following an
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<SPAN CLASS="textit">object-oriented approach</SPAN> through the exploitation of features
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such as abstract data type creation, functional
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overloading and dynamic memory management.
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The parallel implementation is based
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on a Single Program Multiple Data (SPMD) paradigm for distributed-memory architectures.
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Single and double precision implementations of MLD2P4 are available for both the
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real and the complex case, that can be used through a single interface.
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<P>
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MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
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in the context of the <SPAN CLASS="textit">PSBLAS (Parallel Sparse BLAS)
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computational framework</SPAN> [<A
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HREF="node30.html#psblas_00">15</A>].
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PSBLAS is a library originally developed to address the parallel implementation of
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iterative solvers for sparse linear system, by providing basic linear algebra
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operators and data management facilities for distributed sparse matrices; it
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also includes parallel Krylov solvers, built on the top of the basic PSBLAS kernels.
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The preconditioners available in MLD2P4 can be used with these Krylov solvers.
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The choice of PSBLAS has been mainly motivated by the need of having
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a portable and efficient software infrastructure implementing ``de facto'' standard
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parallel sparse linear algebra kernels, to pursue goals such as performance,
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portability, modularity ed extensibility in the development of the preconditioner
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package. On the other hand, the implementation of MLD2P4 has led to some
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revisions and extentions of the PSBLAS kernels, leading to the
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recent PSBLAS 2.0 version [<A
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HREF="node30.html#PSBLASGUIDE">14</A>]. The inter-process comunication required
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by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
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MPI [<A
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HREF="node30.html#MPI1">21</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
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machine where PSBLAS and MPI implementations are available.
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<P>
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MLD2P4 has a layered and modular software architecture where three main layers can be identified.
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The lower layer consists of the PSBLAS kernels, the middle one implements
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the construction and application phases of the preconditioners, and the upper one
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provides a uniform and easy-to-use interface to all the preconditioners.
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This architecture allows for different levels of use of the package:
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few black-box routines at the upper layer allow non-expert users to easily
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build any preconditioner available in MLD2P4 and to apply it within a PSBLAS Krylov solver.
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On the other hand, the routines of the middle and lower layer can be used and extended
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by expert users to build new versions of multi-level Schwarz preconditioners.
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We provide here a description of the upper-layer routines, but not of the
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medium-layer ones.
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<P>
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This guide is organized as follows. General information on the distribution of the source code
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is reported in Section <A HREF="node4.html#sec:distribution">2</A>, while details on the configuration
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and installation of the package are given in Section <A HREF="node5.html#sec:building">3</A>. A description of
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multi-level Schwarz preconditioners based on smoothed aggregation is provided
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in Section <A HREF="node10.html#sec:background">4</A>, to help the users in choosing among the different preconditioners
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implemented in MLD2P4. The basics for building and applying the preconditioners
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with the Krylov solvers implemented in PSBLAS are reported in Section <A HREF="node13.html#sec:started">5</A>, where the
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Fortran 95 codes of a few sample programs are also shown. A reference guide for
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the upper-layer routines of MLD2P4, that are the user interface, is provided
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in Section <A HREF="node15.html#sec:userinterface">6</A>. The error handling mechanism used by the package is briefly described
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in Section <A HREF="node28.html#sec:errors">7</A>. The copyright terms concerning the distribution and modification
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of MLD2P4 are reported in Appendix <A HREF="node29.html#sec:license">A</A>.
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<P>
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<DIV CLASS="navigation"><HR>
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HREF="node4.html">Code Distribution</A>
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<B> Up:</B> <A NAME="tex2html97"
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HREF="userhtml.html">userhtml</A>
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<B> Previous:</B> <A NAME="tex2html91"
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HREF="node2.html">Contents</A>
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<B> <A NAME="tex2html99"
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HREF="node2.html">Contents</A></B> </DIV>
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<!--End of Navigation Panel-->
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<ADDRESS>
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Salvatore Filippone
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2008-07-22
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2008-07-23
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</ADDRESS>
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</HTML>
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