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201 lines
7.4 KiB
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201 lines
7.4 KiB
HTML
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original version by: Nikos Drakos, CBLU, University of Leeds
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<TITLE>General overview</TITLE>
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HREF="node2.html">Introduction</A>
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<H1><A NAME="SECTION00030000000000000000"></A>
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<A NAME="sec:overview"></A>
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<BR>
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General overview
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</H1>
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The PSBLAS library is designed to handle the implementation of
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iterative solvers for sparse linear systems on distributed memory
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parallel computers. The system coefficient matrix <IMG
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WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img1.png"
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ALT="$A$"> must be square;
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it may be real or complex, nonsymmetric, and its sparsity pattern
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needs not to be symmetric. The serial computation parts are based on
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the serial sparse BLAS, so that any extension made to the data
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structures of the serial kernels is available to the parallel
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version. The overall design and parallelization strategy have been
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influenced by the structure of the ScaLAPACK parallel
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library. The layered structure of the PSBLAS library
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is shown in figure <A HREF="#fig:psblas">1</A>; lower layers of the library
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indicate an encapsulation relationship with upper layers. The ongoing
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discussion focuses on the Fortran 95 layer immediately below the
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application layer.
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The serial parts of the computation on each process are executed through
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calls to the serial sparse BLAS subroutines. In a similar way, the
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inter-process message exchanges are implemented through the Basic
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Linear Algebra Communication Subroutines (BLACS) library [<A
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HREF="node105.html#BLACS">6</A>]
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that guarantees a portable and efficient communication layer. The
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Message Passing Interface code is encapsulated within the BLACS
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layer. However, in some cases, MPI routines are directly used either
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to improve efficiency or to implement communication patterns for which
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the BLACS package doesn't provide any method.
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<P>
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In any case we provide wrappers around the BLACS routines so that the
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user does not need to delve into their details (see Sec. <A HREF="node70.html#sec:parenv">7</A>).
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:psblas"></A><A NAME="224"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
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PSBLAS library components hierarchy.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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<IMG
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WIDTH="204" HEIGHT="294" ALIGN="BOTTOM" BORDER="0"
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SRC="img3.png"
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ALT="\includegraphics[scale=0.65]{figures/psblas.eps}">
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<!-- MATH
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$\rotatebox{-90}{\includegraphics[scale=0.65]{figures/psblas}}$
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-->
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<IMG
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WIDTH="37" HEIGHT="2" ALIGN="BOTTOM" BORDER="0"
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SRC="img2.png"
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ALT="\rotatebox{-90}{\includegraphics[scale=0.65]{figures/psblas}}">
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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The type of linear system matrices that we address typically arise in the
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numerical solution of PDEs; in such a context,
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it is necessary to pay special attention to the
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structure of the problem from which the application originates.
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The nonzero pattern of a matrix arising from the
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discretization of a PDE is influenced by various factors, such as the
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shape of the domain, the discretization strategy, and
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the equation/unknown ordering. The matrix itself can be interpreted as
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the adjacency matrix of the graph associated with the discretization
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mesh.
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<P>
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The distribution of the coefficient matrix for the linear system is
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based on the ``owner computes'' rule:
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the variable associated to each mesh point is assigned to a process
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that will own the corresponding row in the coefficient matrix and
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will carry out all related computations. This allocation strategy
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is equivalent to a partition of the discretization mesh into <EM>sub-domains</EM>.
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Our library supports any distribution that keeps together
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the coefficients of each matrix row; there are no other constraints on
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the variable assignment.
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This choice is consistent with data distributions commonly used in
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ScaLAPACK such as <code>CYCLIC(N)</code> and <code>BLOCK</code>,
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as well as completely arbitrary assignments of
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equation indices to processes. In particular it is consistent with the
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usage of graph partitioning tools commonly available in the
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literature, e.g. METIS [<A
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HREF="node105.html#METIS">11</A>].
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Dense vectors conform to sparse
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matrices, that is, the entries of a vector follow the same distribution
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of the matrix rows.
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<P>
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We assume that the sparse matrix is built in parallel, where each
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process generates its own portion. We never require that the entire
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matrix be available on a single node. However, it is possible
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to hold the entire matrix in one process and distribute it
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explicitly<A NAME="tex2html2"
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HREF="footnode.html#foot165"><SUP>1</SUP></A>, even though the resulting
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bottleneck would make this option unattractive in most cases.
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<P>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html193"
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HREF="node4.html">Basic Nomenclature</A>
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<LI><A NAME="tex2html194"
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HREF="node5.html">Library contents</A>
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<LI><A NAME="tex2html195"
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HREF="node6.html">Application structure</A>
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<LI><A NAME="tex2html196"
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HREF="node7.html">Programming model</A>
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</UL>
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<BR>
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<B> Next:</B> <A NAME="tex2html192"
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HREF="node4.html">Basic Nomenclature</A>
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HREF="userhtml.html">userhtml</A>
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<B> Previous:</B> <A NAME="tex2html182"
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HREF="node2.html">Introduction</A>
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<B> <A NAME="tex2html190"
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HREF="node1.html">Contents</A></B>
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