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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 version 3 is implemented in
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the Fortran 2003 [<A
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HREF="node137.html#metcalf">17</A>] programming language, with reuse and/or
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adaptation of existing Fortran 77 and Fortran 95 software, plus a
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handful of C routines.
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<P>
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The use of Fortran 2003 offers a number of advantages over Fortran 95,
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mostly in the handling of requirements for evolution and adaptation of
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the library to new computing architectures and integration of
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new algorithms.
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For a detailed discussion of our design see [<A
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HREF="node137.html#Sparse03">11</A>]; other
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works discussing advanced programming in Fortran 2003
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include [<A
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HREF="node137.html#DesPat:11">1</A>,<A
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HREF="node137.html#RouXiaXu:11">18</A>]; sufficient support for
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Fortran 2003 is now available from many compilers, including the GNU
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Fortran compiler from the Free Software Foundation (as of version 4.8).
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<P>
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Previous approaches have been based on mixing Fortran 95, with its
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support for object-based design, with other languages; these have
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been advocated by a number of authors,
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e.g. [<A
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HREF="node137.html#machiels">16</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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<P>
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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="node137.html#sblas97">8</A>,<A
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HREF="node137.html#sblas02">9</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="node137.html#BLAS1">15</A>,<A
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HREF="node137.html#BLAS2">5</A>,<A
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HREF="node137.html#BLAS3">6</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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