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158 lines
6.4 KiB
HTML
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<H1><A NAME="SECTION00020000000000000000"></A><A NAME="sec:intro"></A>
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<BR>
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Introduction
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</H1>
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<P>
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The PSBLAS library, developed with the aim to facilitate the
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parallelization of computationally intensive scientific applications,
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is designed to address parallel implementation of iterative solvers
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for sparse linear systems through the distributed memory paradigm. It
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includes routines for multiplying sparse matrices by dense matrices,
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solving block diagonal systems with triangular diagonal entries,
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preprocessing sparse matrices, and contains additional routines for
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dense matrix operations. The current implementation of PSBLAS
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addresses a distributed memory execution model operating with message
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passing.
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<P>
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The PSBLAS library is internally implemented in
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the Fortran 95 [<A
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HREF="node105.html#metcalf">14</A>] programming language, with reuse and/or
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adaptation of some existing Fortran 77 software, and a handful of C
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routines.
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A similar approach has been advocated by a number of authors,
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e.g. [<A
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HREF="node105.html#machiels">13</A>]. Moreover, the Fortran 95 facilities for dynamic
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memory management and interface overloading greatly enhance the
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usability of the PSBLAS
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subroutines. In this way, the library can take care of runtime memory
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requirements that are quite difficult or even impossible to predict at
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implementation or compilation time.
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In the current release we rely on the availability of the so-called
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allocatable extensions, specified in TR 15581. Strictly speaking they
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are outside the Fortran 95 standard; however they have been included
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in the Fortran 2003 language standard, and are available in
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practically all Fortran 95 compilers on the market, including the GNU
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Fortran compiler from the Free Software Foundation (as of version 4.2).
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The presentation of the
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PSBLAS library follows the general structure of the proposal for
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serial Sparse BLAS [<A
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HREF="node105.html#sblas97">7</A>,<A
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HREF="node105.html#sblas02">8</A>], which in its turn is based on the
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proposal for BLAS on dense matrices [<A
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HREF="node105.html#BLAS1">12</A>,<A
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HREF="node105.html#BLAS2">4</A>,<A
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HREF="node105.html#BLAS3">5</A>].
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<P>
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The applicability of sparse iterative solvers to many different areas
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causes some terminology problems because the same concept may be
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denoted through different names depending on the application area. The
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PSBLAS features presented in this document will be discussed referring
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to a finite difference discretization of a Partial Differential
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Equation (PDE). However, the scope of the library is wider than
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that: for example, it can be applied to finite element discretizations
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of PDEs, and even to different classes of problems such as nonlinear
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optimization, for example in optimal control problems.
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<P>
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The design of a solver for sparse linear systems is driven by many
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conflicting objectives, such as limiting occupation of storage
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resources, exploiting regularities in the input data, exploiting
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hardware characteristics of the parallel platform. To achieve an
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optimal communication to computation ratio on distributed memory
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machines it is essential to keep the <EM>data locality</EM> as high as
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possible; this can be done through an appropriate data allocation
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strategy. The choice of the preconditioner is another very important
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factor that affects efficiency of the implemented application. Optimal
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data distribution requirements for a given preconditioner may conflict
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with distribution requirements of the rest of the solver. Finding the
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optimal trade-off may be very difficult because it is application
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dependent. Possible solutions to these problems and other important
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inputs to the development of the PSBLAS software package have come from
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an established experience in applying the PSBLAS solvers to
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computational fluid dynamics applications.
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