You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
207 lines
9.3 KiB
HTML
207 lines
9.3 KiB
HTML
<!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>General Overview</TITLE>
|
|
<META NAME="description" CONTENT="General Overview">
|
|
<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="node4.html">
|
|
<LINK REL="previous" HREF="node2.html">
|
|
<LINK REL="up" HREF="userhtml.html">
|
|
<LINK REL="next" HREF="node4.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html110"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html106"
|
|
HREF="userhtml.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html100"
|
|
HREF="node2.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html108"
|
|
HREF="node2.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html111"
|
|
HREF="node4.html">Code Distribution</A>
|
|
<B> Up:</B> <A NAME="tex2html107"
|
|
HREF="userhtml.html">userhtml</A>
|
|
<B> Previous:</B> <A NAME="tex2html101"
|
|
HREF="node2.html">Contents</A>
|
|
<B> <A NAME="tex2html109"
|
|
HREF="node2.html">Contents</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H1><A NAME="SECTION00030000000000000000"></A><A NAME="sec:overview"></A>
|
|
<BR>
|
|
General Overview
|
|
</H1>
|
|
|
|
<P>
|
|
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
|
|
</SMALL>PSBLAS (MLD2P4) provides parallel Algebraic MultiGrid (AMG) and Domain
|
|
Decomposition preconditioners (see, e.g., [<A
|
|
HREF="node27.html#Briggs2000">3</A>,<A
|
|
HREF="node27.html#Stuben_01">23</A>,<A
|
|
HREF="node27.html#dd2_96">21</A>]),
|
|
to be used in the iterative solution of linear systems,
|
|
<BR>
|
|
<DIV ALIGN="RIGHT">
|
|
|
|
<!-- MATH
|
|
\begin{equation}
|
|
Ax=b,
|
|
\end{equation}
|
|
-->
|
|
<TABLE WIDTH="100%" ALIGN="CENTER">
|
|
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="system1"></A><IMG
|
|
WIDTH="58" HEIGHT="30" BORDER="0"
|
|
SRC="img1.png"
|
|
ALT="\begin{displaymath}
|
|
Ax=b,
|
|
\end{displaymath}"></TD>
|
|
<TD WIDTH=10 ALIGN="RIGHT">
|
|
(1)</TD></TR>
|
|
</TABLE>
|
|
<BR CLEAR="ALL"></DIV><P></P>
|
|
where <IMG
|
|
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img2.png"
|
|
ALT="$A$"> is a square, real or complex, sparse matrix. The name of the package comes from its original implementation, containing
|
|
multi-level additive and hybrid Schwarz preconditioners, as well as one-level additive
|
|
Schwarz preconditioners. The current version extends the original plan by including
|
|
multi-level cycles and smoothers widely used in multigrid methods.
|
|
|
|
<P>
|
|
The multi-level preconditioners implemented in MLD2P4 are obtained by combining
|
|
AMG cycles with smoothers and coarsest-level solvers. The V-, W-, and
|
|
K-cycles [<A
|
|
HREF="node27.html#Briggs2000">3</A>,<A
|
|
HREF="node27.html#Notay2008">19</A>] are available, which allow to define
|
|
almost all the preconditioners in the package, including the multi-level hybrid
|
|
Schwarz ones; a specific cycle is implemented to obtain multi-level additive
|
|
Schwarz preconditioners. The Jacobi, hybridforward/backward Gauss-Seidel, block-Jacobi, and additive Schwarz methods
|
|
are available as smoothers. An algebraic approach is used to generate a hierarchy of
|
|
coarse-level matrices and operators, without explicitly using any information on the
|
|
geometry of the original problem, e.g., the discretization of a PDE. To this end,
|
|
the smoothed aggregation technique [<A
|
|
HREF="node27.html#BREZINA_VANEK">2</A>,<A
|
|
HREF="node27.html#VANEK_MANDEL_BREZINA">25</A>]
|
|
is applied. Either exact or approximate solvers can be used on the coarsest-level
|
|
system. Specifically, different sparse LU factorizations from external
|
|
packages, and native incomplete LU factorizations and Jacobi, hybrid Gauss-Seidel,
|
|
and block-Jacobi solvers are available. All smoothers can be also exploited as one-level
|
|
preconditioners.
|
|
|
|
<P>
|
|
MLD2P4 is written in Fortran 2003, following an
|
|
object-oriented design through the exploitation of features
|
|
such as abstract data type creation, type extension, functional overloading, and
|
|
dynamic memory management. The parallel implementation is based on a Single Program Multiple Data
|
|
(SPMD) paradigm. Single and
|
|
double precision implementations of MLD2P4 are available for both the
|
|
real and the complex case, which can be used through a single
|
|
interface.
|
|
|
|
<P>
|
|
MLD2P4 has been designed to implement scalable and easy-to-use
|
|
multilevel preconditioners in the context of the PSBLAS (Parallel Sparse BLAS)
|
|
computational framework [<A
|
|
HREF="node27.html#psblas_00">15</A>,<A
|
|
HREF="node27.html#PSBLAS3">14</A>]. PSBLAS provides basic linear algebra
|
|
operators and data management facilities for distributed sparse matrices,
|
|
as well as parallel Krylov solvers which can be used with the MLD2P4 preconditioners.
|
|
The choice of PSBLAS has been mainly motivated by the need of having
|
|
a portable and efficient software infrastructure implementing ``de facto'' standard
|
|
parallel sparse linear algebra kernels, to pursue goals such as performance,
|
|
portability, modularity ed extensibility in the development of the preconditioner
|
|
package. On the other hand, the implementation of MLD2P4 has led to some
|
|
revisions and extentions of the original PSBLAS kernels.
|
|
The inter-process comunication required by MLD2P4 is encapsulated
|
|
in the PSBLAS routines;therefore, MLD2P4 can be run on any parallel machine where PSBLAS
|
|
implementations are available.
|
|
|
|
<P>
|
|
MLD2P4 has a layered and modular software architecture where three main layers can be
|
|
identified. The lower layer consists of the PSBLAS kernels, the middle one implements
|
|
the construction and application phases of the preconditioners, and the upper one
|
|
provides a uniform interface to all the preconditioners.
|
|
This architecture allows for different levels of use of the package:
|
|
few black-box routines at the upper layer allow all users to easily
|
|
build and apply any preconditioner available in MLD2P4;
|
|
facilities are also available allowing expert users to extend the set of smoothers
|
|
and solvers for building new versions of the preconditioners (see
|
|
Section <A HREF="node24.html#sec:adding">7</A>).
|
|
|
|
<P>
|
|
We note that the user interface of MLD2P4 2.1 has been extended with respect to the
|
|
previous versions in order to separate the construction of the multi-level hierarchy from
|
|
the construction of the smoothers and solvers, and to allow for more flexibility
|
|
at each level. The software architecture described in [<A
|
|
HREF="node27.html#MLD2P4_TOMS">8</A>] has significantly
|
|
evolved too, in order to fully exploit the Fortran 2003 features implemented in PSBLAS 3.
|
|
However, compatibility with previous versions has been preserved.
|
|
|
|
<P>
|
|
This guide is organized as follows. General information on the distribution of the source
|
|
code is reported in Section <A HREF="node4.html#sec:distribution">2</A>, while details on the configuration
|
|
and installation of the package are given in Section <A HREF="node5.html#sec:building">3</A>. A short description
|
|
of the preconditioners implemented in MLD2P4 is provided in Section <A HREF="node11.html#sec:background">4</A>,
|
|
to help the users in choosing among them. The basics for building and applying the
|
|
preconditioners with the Krylov solvers implemented in PSBLAS are reported
|
|
in Section <A HREF="node13.html#sec:started">5</A>, where the Fortran codes of a few sample programs
|
|
are also shown. A reference guide for the user interface routines is provided
|
|
in Section <A HREF="node15.html#sec:userinterface">6</A>. Information on the extension of the package
|
|
through the addition of new smoothers and solvers is reported in Section <A HREF="node24.html#sec:adding">7</A>.
|
|
The error handling mechanism used by the package
|
|
is briefly described in Section <A HREF="node25.html#sec:errors">8</A>. The copyright terms concerning the
|
|
distribution and modification of MLD2P4 are reported in Appendix <A HREF="node26.html#sec:license">A</A>.
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html110"
|
|
HREF="node4.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>
|
|
<A NAME="tex2html106"
|
|
HREF="userhtml.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>
|
|
<A NAME="tex2html100"
|
|
HREF="node2.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>
|
|
<A NAME="tex2html108"
|
|
HREF="node2.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html111"
|
|
HREF="node4.html">Code Distribution</A>
|
|
<B> Up:</B> <A NAME="tex2html107"
|
|
HREF="userhtml.html">userhtml</A>
|
|
<B> Previous:</B> <A NAME="tex2html101"
|
|
HREF="node2.html">Contents</A>
|
|
<B> <A NAME="tex2html109"
|
|
HREF="node2.html">Contents</A></B>
|
|
<!--End of Navigation Panel-->
|
|
|
|
</BODY>
|
|
</HTML>
|