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126 lines
6.9 KiB
HTML
126 lines
6.9 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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"http://www.w3.org/TR/html4/loose.dtd">
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<html >
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<head><title>General overview</title>
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)">
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</head><body
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>
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<!--l. 72--><div class="crosslinks"><p class="noindent">[<a
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href="userhtmlsu7.html" >next</a>] [<a
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href="userhtmlse1.html" >prev</a>] [<a
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href="userhtmlse1.html#tailuserhtmlse1.html" >prev-tail</a>] [<a
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href="#tailuserhtmlse2.html">tail</a>] [<a
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<h3 class="sectionHead"><span class="titlemark">2 </span> <a
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id="x4-30002"></a>General overview</h3>
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<!--l. 74--><p class="noindent" >The PSBLAS library is designed to handle the implementation of iterative solvers for
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sparse linear systems on distributed memory parallel computers. The system
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coefficient matrix <span
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class="cmmi-10">A </span>must be square; it may be real or complex, nonsymmetric, and
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its sparsity pattern needs not to be symmetric. The serial computation parts are
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based on the serial sparse BLAS, so that any extension made to the data structures
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of the serial kernels is available to the parallel version. The overall design and
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parallelization strategy have been influenced by the structure of the ScaLAPACK
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parallel library. The layered structure of the PSBLAS library is shown in figure <a
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href="#x4-30011">1<!--tex4ht:ref: fig:psblas --></a>;
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lower layers of the library indicate an encapsulation relationship with upper
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layers. The ongoing discussion focuses on the Fortran 2003 layer immediately
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below the application layer. The serial parts of the computation on each
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process are executed through calls to the serial sparse BLAS subroutines. In a
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similar way, the inter-process message exchanges are encapsulated in an
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applicaiton layer that has been strongly inspired by the Basic Linear Algebra
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Communication Subroutines (BLACS) library <span class="cite">[<a
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href="userhtmlli2.html#XBLACS">7</a>]</span>. Usually there is no need to deal
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directly with MPI; however, in some cases, MPI routines are used directly
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to improve efficiency. For further details on our communication layer see
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Sec. <a
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href="userhtmlse7.html#x68-1050007">7<!--tex4ht:ref: sec:parenv --></a>.
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<!--l. 101--><p class="indent" > <hr class="figure"><div class="figure"
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>
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<a
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id="x4-30011"></a>
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<div class="center"
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>
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<!--l. 102--><p class="noindent" >
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<!--l. 104--><p class="noindent" ><img
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src="psblas.png" alt="PIC"
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></div>
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<br /> <div class="caption"
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><span class="id">Figure 1: </span><span
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class="content">PSBLAS library components hierarchy.</span></div><!--tex4ht:label?: x4-30011 -->
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<!--l. 110--><p class="indent" > </div><hr class="endfigure">
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<!--l. 113--><p class="indent" > The type of linear system matrices that we address typically arise in
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the numerical solution of PDEs; in such a context, it is necessary to pay
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special attention to the structure of the problem from which the application
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originates. The nonzero pattern of a matrix arising from the discretization of a
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PDE is influenced by various factors, such as the shape of the domain, the
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discretization strategy, and the equation/unknown ordering. The matrix itself can be
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interpreted as the adjacency matrix of the graph associated with the discretization
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mesh.
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<!--l. 124--><p class="indent" > The distribution of the coefficient matrix for the linear system is based on the
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“owner computes” rule: the variable associated to each mesh point is assigned to a
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process that will own the corresponding row in the coefficient matrix and will
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carry out all related computations. This allocation strategy is equivalent to a
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partition of the discretization mesh into <span
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class="cmti-10">sub-domains</span>. Our library supports any
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distribution that keeps together the coefficients of each matrix row; there are no
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other constraints on the variable assignment. This choice is consistent with
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simple data distributions such as <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">CYCLIC(N)</span></span></span> and <span class="obeylines-h"><span class="verb"><span
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class="cmtt-10">BLOCK</span></span></span>, as well as completely
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arbitrary assignments of equation indices to processes. In particular it is
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consistent with the usage of graph partitioning tools commonly available in
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the literature, e.g. METIS <span class="cite">[<a
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href="userhtmlli2.html#XMETIS">14</a>]</span>. Dense vectors conform to sparse matrices,
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that is, the entries of a vector follow the same distribution of the matrix
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rows.
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<!--l. 146--><p class="indent" > We assume that the sparse matrix is built in parallel, where each process generates
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its own portion. We never require that the entire matrix be available on a single
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node. However, it is possible to hold the entire matrix in one process and distribute it
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explicitly<span class="footnote-mark"><a
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href="userhtml5.html#fn1x0"><sup class="textsuperscript">1</sup></a></span><a
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id="x4-3002f1"></a> ,
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even though the resulting memory bottleneck would make this option unattractive in
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most cases.
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<div class="subsectionTOCS">
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 <span class="subsectionToc" >2.1 <a
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href="userhtmlsu1.html#x6-40002.1">Basic Nomenclature</a></span>
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<br />  <span class="subsectionToc" >2.2 <a
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href="userhtmlsu2.html#x8-50002.2">Library contents</a></span>
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<br />  <span class="subsectionToc" >2.3 <a
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href="userhtmlsu3.html#x9-60002.3">Application structure</a></span>
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<br />   <span class="subsubsectionToc" >2.3.1 <a
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href="userhtmlsu3.html#x9-70002.3.1">User-defined index mappings</a></span>
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<br />  <span class="subsectionToc" >2.4 <a
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href="userhtmlsu4.html#x11-80002.4">Programming model</a></span>
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</div>
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href="userhtmlsu7.html" >next</a>] [<a
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href="userhtmlse1.html#tailuserhtmlse1.html" >prev-tail</a>] [<a
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href="userhtmlse2.html" >front</a>] [<a
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href="userhtml.html#userhtmlse2.html" >up</a>] </p></div>
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id="tailuserhtmlse2.html"></a>
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