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<H1><A NAME="SECTION00030000000000000000"></A>
<A NAME="sec:overview"></A>
<BR>
General overview
</H1> 
The PSBLAS library is designed to handle the implementation of
iterative solvers for sparse linear systems on distributed memory
parallel computers.  The system coefficient matrix <IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$A$"> must be square;
it may be real or complex, nonsymmetric, and its sparsity pattern
needs not to be symmetric.  The serial computation parts are based on
the serial sparse BLAS, so that any extension made to the data
structures of the serial kernels is available to the parallel
version. The overall design and parallelization strategy have been
influenced by the structure of the ScaLAPACK parallel
library.  The layered structure of the PSBLAS library
is shown in figure&nbsp;<A HREF="#fig:psblas">1</A>; lower layers of the library
indicate an encapsulation relationship with upper layers. The ongoing
discussion focuses on the Fortran&nbsp;2003 layer immediately below the
application layer.
The serial parts of the computation on each process are executed through
calls to the serial sparse BLAS subroutines. 
In a similar way, the inter-process message exchanges are encapsulated
in an applicaiton layer that has been strongly inspired by the  Basic
Linear Algebra Communication Subroutines (BLACS) library&nbsp;[<A
 HREF="node132.html#BLACS">7</A>].  
Usually  there is no need to deal directly with MPI;  however, in some
cases, MPI routines are used directly to improve efficiency. For
further details on our communication layer see Sec.&nbsp;<A HREF="node98.html#sec:parenv">7</A>.
<P>

<DIV ALIGN="CENTER"><A NAME="fig:psblas"></A><A NAME="270"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
PSBLAS library components hierarchy.</CAPTION>
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 SRC="img3.png"
 ALT="\includegraphics[scale=0.65]{figures/psblas}">

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</DIV>

<P>
The type of linear system matrices that we address  typically arise in the
numerical solution of PDEs;  in such a context,
it is necessary to pay special attention to the
structure of the problem from which the application originates. 
The nonzero pattern of a matrix arising from the
discretization of a PDE is influenced by various factors, such as the
shape of the  domain, the discretization strategy, and
the equation/unknown ordering. The matrix itself can be interpreted as
the  adjacency matrix of the graph associated with the discretization
mesh. 

<P>
The distribution of the coefficient matrix for the linear system is
based on the ``owner computes'' rule: 
the variable associated to each mesh point is assigned to a process
that will  own the corresponding row in the coefficient matrix and
will  carry out all related computations. This allocation strategy 
is equivalent to a partition of the discretization mesh into <EM>sub-domains</EM>. 
Our library  supports any distribution that keeps together 
the coefficients of each matrix row; there are no other constraints on
the variable assignment. 
This choice is consistent with simple  data distributions such as  <code>CYCLIC(N)</code> and <code>BLOCK</code>, 
as well as completely arbitrary assignments of
equation indices to processes. 
In particular it is consistent with the
usage of graph partitioning tools commonly available in the
literature, e.g. METIS&nbsp;[<A
 HREF="node132.html#METIS">14</A>].
Dense vectors  conform  to sparse
matrices, that is, the entries of a vector follow the same distribution
of the matrix rows.  

<P>
We assume that the sparse matrix is built in parallel, where each
process generates its own portion. We never require that the entire
matrix be available on a single node. However, it is possible
to hold the entire matrix in one process and distribute it
explicitly<A NAME="tex2html2"
  HREF="footnode.html#foot201"><SUP>1</SUP></A>, even though  the resulting memory 
bottleneck would make this option unattractive in most  cases. 

<P>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>

<UL>
<LI><A NAME="tex2html224"
  HREF="node4.html">Basic Nomenclature</A>
<LI><A NAME="tex2html225"
  HREF="node5.html">Library contents</A>
<LI><A NAME="tex2html226"
  HREF="node6.html">Application structure</A>
<UL>
<LI><A NAME="tex2html227"
  HREF="node7.html">User-defined index mappings</A>
</UL>
<BR>
<LI><A NAME="tex2html228"
  HREF="node8.html">Programming model</A>
</UL>
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