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<head><title>Introduction</title>
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<!--l. 1--><div class="crosslinks"><p class="noindent">[<a
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href="userhtmlse2.html" >next</a>] [<a
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<h3 class="sectionHead"><span class="titlemark">1 </span> <a
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id="x3-20001"></a>Introduction</h3>
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<!--l. 3--><p class="noindent" >The PSBLAS library, developed with the aim to facilitate the parallelization of
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computationally intensive scientific applications, is designed to address parallel
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implementation of iterative solvers for sparse linear systems through the distributed
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memory paradigm. It includes routines for multiplying sparse matrices by dense
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matrices, solving block diagonal systems with triangular diagonal entries,
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preprocessing sparse matrices, and contains additional routines for dense matrix
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operations. The current implementation of PSBLAS addresses a distributed memory
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execution model operating with message passing.
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<!--l. 14--><p class="indent" > The PSBLAS library version 3 is implemented in the Fortran 2003 <span class="cite">[<a
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href="userhtmlli2.html#Xmetcalf">17</a>]</span>
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programming language, with reuse and/or adaptation of existing Fortran 77 and
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Fortran 95 software, plus a handful of C routines.
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<!--l. 19--><p class="indent" > The use of Fortran 2003 offers a number of advantages over Fortran 95, mostly in
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the handling of requirements for evolution and adaptation of the library to new
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computing architectures and integration of new algorithms. For a detailed discussion
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of our design see <span class="cite">[<a
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href="userhtmlli2.html#XSparse03">11</a>]</span>; other works discussing advanced programming in Fortran 2003
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include <span class="cite">[<a
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href="userhtmlli2.html#XDesPat:11">1</a>, <a
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href="userhtmlli2.html#XRouXiaXu:11">18</a>]</span>; sufficient support for Fortran 2003 is now available from many
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compilers, including the GNU Fortran compiler from the Free Software Foundation
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(as of version 4.8).
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<!--l. 30--><p class="indent" > Previous approaches have been based on mixing Fortran 95, with its support for
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object-based design, with other languages; these have been advocated by a number of
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authors, e.g. <span class="cite">[<a
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href="userhtmlli2.html#Xmachiels">16</a>]</span>. Moreover, the Fortran 95 facilities for dynamic memory
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management and interface overloading greatly enhance the usability of the PSBLAS
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subroutines. In this way, the library can take care of runtime memory requirements
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that are quite difficult or even impossible to predict at implementation or
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compilation time.
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<!--l. 40--><p class="indent" > The presentation of the PSBLAS library follows the general structure of the
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proposal for serial Sparse BLAS <span class="cite">[<a
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href="userhtmlli2.html#Xsblas97">8</a>, <a
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href="userhtmlli2.html#Xsblas02">9</a>]</span>, which in its turn is based on the proposal for
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BLAS on dense matrices <span class="cite">[<a
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href="userhtmlli2.html#XBLAS1">15</a>, <a
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href="userhtmlli2.html#XBLAS2">5</a>, <a
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href="userhtmlli2.html#XBLAS3">6</a>]</span>.
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<!--l. 45--><p class="indent" > The applicability of sparse iterative solvers to many different areas causes some
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terminology problems because the same concept may be denoted through different
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names depending on the application area. The PSBLAS features presented in this
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document will be discussed referring to a finite difference discretization of a Partial
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Differential Equation (PDE). However, the scope of the library is wider than that: for
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example, it can be applied to finite element discretizations of PDEs, and even to
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different classes of problems such as nonlinear optimization, for example in optimal
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control problems.
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<!--l. 55--><p class="indent" > The design of a solver for sparse linear systems is driven by many conflicting
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objectives, such as limiting occupation of storage resources, exploiting regularities in
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the input data, exploiting hardware characteristics of the parallel platform. To
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achieve an optimal communication to computation ratio on distributed memory
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machines it is essential to keep the <span
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class="cmti-10">data locality </span>as high as possible; this can be
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done through an appropriate data allocation strategy. The choice of the
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preconditioner is another very important factor that affects efficiency of the
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implemented application. Optimal data distribution requirements for a given
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preconditioner may conflict with distribution requirements of the rest of the solver.
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Finding the optimal trade-off may be very difficult because it is application
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dependent. Possible solutions to these problems and other important inputs to the
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development of the PSBLAS software package have come from an established
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experience in applying the PSBLAS solvers to computational fluid dynamics
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applications.
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href="userhtmlse2.html" >next</a>] [<a
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href="userhtmlse1.html" >front</a>] [<a
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href="userhtml.html#userhtmlse1.html" >up</a>] </p></div>
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