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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 <SPAN CLASS="MATH"><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="$A$"></SPAN> 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 2003 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.
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In a similar way, the inter-process message exchanges are encapsulated
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in an applicaiton layer that has been strongly inspired by the Basic
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Linear Algebra Communication Subroutines (BLACS) library [<A
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HREF="node133.html#BLACS">7</A>].
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Usually there is no need to deal directly with MPI; however, in some
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cases, MPI routines are used directly to improve efficiency. For
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further details on our communication layer see Sec. <A HREF="node99.html#sec:parenv">7</A>.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:psblas"></A><A NAME="272"></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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<DIV ALIGN="CENTER">
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ALT="\includegraphics[scale=0.65]{figures/psblas.eps}">
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<IMG
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ALT="\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 simple data distributions
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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.
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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="node133.html#METIS">14</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#foot201"><SUP><SPAN CLASS="arabic">1</SPAN></SUP></A>, even though the resulting memory
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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 CLASS="ChildLinks">
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<LI><A NAME="tex2html226"
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HREF="node4.html">Basic Nomenclature</A>
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<LI><A NAME="tex2html227"
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HREF="node5.html">Library contents</A>
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<LI><A NAME="tex2html228"
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HREF="node6.html">Application structure</A>
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<UL>
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<LI><A NAME="tex2html229"
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HREF="node7.html">User-defined index mappings</A>
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</UL>
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<BR>
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<LI><A NAME="tex2html230"
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HREF="node8.html">Programming model</A>
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</UL>
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