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Salvatore Filippone
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@@ -16,33 +16,34 @@ href="userhtmlli1.html" >prev</a>] [<a
href="userhtmlli1.html#tailuserhtmlli1.html" >prev-tail</a>] [<a
href="#tailuserhtmlse1.html">tail</a>] [<a
href="userhtml.html#userhtmlse1.html" >up</a>] </p></div>
<h3 class="sectionHead"><span class="titlemark">1 </span> <a
<h3 class="sectionHead"><span class="titlemark">1 </span> <a
id="x3-20001"></a>Introduction</h3>
<!--l. 3--><p class="noindent" >The PSBLAS library, developed with the aim to facilitate the parallelization of
computationally intensive scientific applications, is designed to address parallel
implementation of iterative solvers for sparse linear systems through the distributed
memory paradigm. It includes routines for multiplying sparse matrices by dense
matrices, solving block diagonal systems with triangular diagonal entries,
preprocessing sparse matrices, and contains additional routines for dense matrix
operations. The current implementation of PSBLAS addresses a distributed memory
execution model operating with message passing.
implementation of iterative solvers for sparse linear systems through the
distributed memory paradigm. It includes routines for multiplying sparse
matrices by dense matrices, solving block diagonal systems with triangular
diagonal entries, preprocessing sparse matrices, and contains additional
routines for dense matrix operations. The current implementation of PSBLAS
addresses a distributed memory execution model operating with message
passing.
<!--l. 14--><p class="indent" > The PSBLAS library version 3 is implemented in the Fortran&#x00A0;2003&#x00A0;<span class="cite">[<a
href="userhtmlli2.html#Xmetcalf">16</a>]</span>
programming language, with reuse and/or adaptation of existing Fortran&#x00A0;77 and
Fortran&#x00A0;95 software, plus a handful of C routines.
<!--l. 19--><p class="indent" > The use of Fortran&#x00A0;2003 offers a number of advantages over Fortran&#x00A0;95, mostly in
the handling of requirements for evolution and adaptation of the library to new
computing architectures and integration of new algorithms. For a detailed discussion
of our design see&#x00A0;<span class="cite">[<a
href="userhtmlli2.html#XSparse03">10</a>]</span>; other works discussing advanced programming in Fortran&#x00A0;2003
include&#x00A0;<span class="cite">[<a
<!--l. 19--><p class="indent" > The use of Fortran&#x00A0;2003 offers a number of advantages over Fortran&#x00A0;95, mostly
in the handling of requirements for evolution and adaptation of the library to new
computing architectures and integration of new algorithms. For a detailed
discussion of our design see&#x00A0;<span class="cite">[<a
href="userhtmlli2.html#XSparse03">10</a>]</span>; other works discussing advanced programming in
Fortran&#x00A0;2003 include&#x00A0;<span class="cite">[<a
href="userhtmlli2.html#XDesPat:11">20</a>,&#x00A0;<a
href="userhtmlli2.html#XRouXiaXu:11">18</a>]</span>; sufficient support for Fortran&#x00A0;2003 is now available from many
compilers, including the GNU Fortran compiler from the Free Software Foundation
(as of version 4.8).
href="userhtmlli2.html#XRouXiaXu:11">18</a>]</span>; sufficient support for Fortran&#x00A0;2003 is now available
from many compilers, including the GNU Fortran compiler from the Free Software
Foundation (as of version 4.8).
<!--l. 30--><p class="indent" > Previous approaches have been based on mixing Fortran&#x00A0;95, with its support for
object-based design, with other languages; these have been advocated by a number of
authors, e.g.&#x00A0;<span class="cite">[<a
object-based design, with other languages; these have been advocated by a number
of authors, e.g.&#x00A0;<span class="cite">[<a
href="userhtmlli2.html#Xmachiels">15</a>]</span>. Moreover, the Fortran&#x00A0;95 facilities for dynamic memory
management and interface overloading greatly enhance the usability of the PSBLAS
subroutines. In this way, the library can take care of runtime memory requirements
@@ -56,24 +57,25 @@ BLAS on dense matrices&#x00A0;<span class="cite">[<a
href="userhtmlli2.html#XBLAS1">14</a>,&#x00A0;<a
href="userhtmlli2.html#XBLAS2">4</a>,&#x00A0;<a
href="userhtmlli2.html#XBLAS3">5</a>]</span>.
<!--l. 45--><p class="indent" > The applicability of sparse iterative solvers to many different areas causes some
terminology problems because the same concept may be denoted through different
names depending on the application area. The PSBLAS features presented in this
document will be discussed referring to a finite difference discretization of a Partial
Differential Equation (PDE). However, the scope of the library is wider than that: for
example, it can be applied to finite element discretizations of PDEs, and even to
different classes of problems such as nonlinear optimization, for example in optimal
control problems.
<!--l. 45--><p class="indent" > The applicability of sparse iterative solvers to many different areas causes
some terminology problems because the same concept may be denoted
through different names depending on the application area. The PSBLAS
features presented in this document will be discussed referring to a finite
difference discretization of a Partial Differential Equation (PDE). However,
the scope of the library is wider than that: for example, it can be applied
to finite element discretizations of PDEs, and even to different classes of
problems such as nonlinear optimization, for example in optimal control
problems.
<!--l. 55--><p class="indent" > The design of a solver for sparse linear systems is driven by many conflicting
objectives, such as limiting occupation of storage resources, exploiting regularities in
the input data, exploiting hardware characteristics of the parallel platform. To
achieve an optimal communication to computation ratio on distributed memory
machines it is essential to keep the <span
class="cmti-10">data locality </span>as high as possible; this can be
done through an appropriate data allocation strategy. The choice of the
machines it is essential to keep the <span
class="pplri7t-">data locality </span>as high as possible; this can
be done through an appropriate data allocation strategy. The choice of the
preconditioner is another very important factor that affects efficiency of the
implemented application. Optimal data distribution requirements for a given
preconditioner may conflict with distribution requirements of the rest of the solver.