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Added aggregation ordering option to docs.
This commit is contained in:
Salvatore Filippone
2016-05-09 16:04:33 +00:00
parent 875443efe7
commit c592733a8e
42 changed files with 2745 additions and 2539 deletions
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@@ -1,4 +1,4 @@
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@@ -25,31 +25,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
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<H1><A NAME="SECTION00030000000000000000"></A><A NAME="sec:overview"></A>
@@ -59,18 +58,17 @@ General Overview
<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 <SPAN CLASS="textit">multi-level Schwarz preconditioners</SPAN>&nbsp;[<A
HREF="node25.html#dd2_96">22</A>],
</SMALL>PSBLAS (MLD2P4) provides <I>multi-level Schwarz preconditioners</I>&nbsp;[<A
HREF="node25.html#dd2_96">23</A>],
to be used in the iterative solutions of sparse linear systems:
<BR>
<DIV ALIGN="RIGHT" CLASS="mathdisplay">
<DIV ALIGN="RIGHT">
<!-- MATH
\begin{equation}
Ax=b,
\end{equation}
-->
<A NAME="system1"></A>
<TABLE WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="system1"></A><IMG
WIDTH="58" HEIGHT="30" BORDER="0"
@@ -78,35 +76,35 @@ Ax=b,
ALT="\begin{displaymath}
Ax=b,
\end{displaymath}"></TD>
<TD CLASS="eqno" WIDTH=10 ALIGN="RIGHT">
(<SPAN CLASS="arabic">1</SPAN>)</TD></TR>
<TD WIDTH=10 ALIGN="RIGHT">
(1)</TD></TR>
</TABLE>
<BR CLEAR="ALL"></DIV><P></P>
where <SPAN CLASS="MATH"><IMG
where <IMG
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img2.png"
ALT="$A$"></SPAN> is a square, real or complex, sparse matrix with a symmetric
ALT="$A$"> is a square, real or complex, sparse matrix with a symmetric
sparsity pattern. These preconditioners have the following general features:
<UL>
<LI>both <SPAN CLASS="textit">additive and hybrid multilevel</SPAN> variants are implemented,
<LI>both <I>additive and hybrid multilevel</I> variants are implemented,
i.e. variants that are additive among the levels and inside each level, and variants
that are multiplicative among the levels and additive inside each level;
the basic Additive Schwarz (AS) preconditioners are obtained by considering only one level;
</LI>
<LI>a <SPAN CLASS="textit">purely algebraic</SPAN> approach is used to
<LI>a <I>purely algebraic</I> approach is used to
generate a sequence of coarse-level corrections to a basic AS preconditioner, without
explicitly using any information on the geometry of the original problem (e.g. the
discretization of a PDE). The <SPAN CLASS="textit">smoothed aggregation</SPAN> technique is applied
discretization of a PDE). The <I>smoothed aggregation</I> technique is applied
as algebraic coarsening strategy&nbsp;[<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#VANEK_MANDEL_BREZINA">26</A>].
HREF="node25.html#VANEK_MANDEL_BREZINA">27</A>].
</LI>
</UL>
<P>
Version 2.0 of the package is written in <SPAN CLASS="textit">Fortran&nbsp;2003</SPAN>, following an
<SPAN CLASS="textit">object-oriented design</SPAN> through the exploitation of features
Version 2.0 of the package is written in <I>Fortran&nbsp;2003</I>, following an
<I>object-oriented design</I> through the exploitation of features
such as abstract data type creation, functional overloading and
dynamic memory management. The parallel implementation is based on a Single Program Multiple Data
(SPMD) paradigm for distributed-memory architectures. Single and
@@ -116,10 +114,10 @@ interface.
<P>
MLD2P4 has been designed to implement scalable and easy-to-use
multilevel preconditioners in the context of the <SPAN CLASS="textit">PSBLAS
(Parallel Sparse BLAS) computational framework</SPAN>&nbsp;[<A
HREF="node25.html#psblas_00">17</A>,<A
HREF="node25.html#PSBLAS3">16</A>].
multilevel preconditioners in the context of the <I>PSBLAS
(Parallel Sparse BLAS) computational framework</I>&nbsp;[<A
HREF="node25.html#psblas_00">18</A>,<A
HREF="node25.html#PSBLAS3">17</A>].
PSBLAS is a library originally developed to address the parallel implementation of
iterative solvers for sparse linear system, by providing basic linear algebra
operators and data management facilities for distributed sparse matrices; it
@@ -132,10 +130,10 @@ portability, modularity ed extensibility in the development of the preconditione
package. On the other hand, the implementation of MLD2P4 has led to some
revisions and extentions of the PSBLAS kernels, leading to the
PSBLAS 2.0 version&nbsp;[<A
HREF="node25.html#PSBLASGUIDE">15</A>]. The inter-process comunication required
HREF="node25.html#PSBLASGUIDE">16</A>]. The inter-process comunication required
by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
MPI&nbsp;[<A
HREF="node25.html#MPI1">23</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
HREF="node25.html#MPI1">24</A>] is explicitly called. Therefore, MLD2P4 can be run on any parallel
machine where PSBLAS and MPI implementations are available.
<P>
@@ -172,30 +170,29 @@ in Section&nbsp;<A HREF="node23.html#sec:errors">7</A>. The copyright terms conc
of MLD2P4 are reported in Appendix&nbsp;<A HREF="node24.html#sec:license">A</A>.
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