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Aztec User's Guide: Version 1.0

S. A. Hutchinson, J. N. Shadid, and R. S. Tuminaro

Sandia National Laboratories

Albuquerque, New Mexico 87185

Abstract

{\bf Aztec} is an iterative library that greatly simplifies the
parallelization process when solving the linear systems of equations $Ax
= b$ where $A$ is a user supplied $n \times n$ sparse matrix, $b$ is a
user supplied vector of length $n$ and $x$ is a vector of length $n$ to
be computed. {\bf Aztec} is intended as a software tool for users who
want to avoid cumbersome parallel programming details but who have large
sparse linear systems which require an efficiently utilized parallel
processing system. A collection of data transformation tools are
provided that allow for easy creation of distributed sparse unstructured
matrices for parallel solution. Once the distributed matrix is created,
computation can be performed on any of the parallel machines running
{\bf Aztec}: nCUBE 2, IBM SP2 and Intel Paragon, MPI platforms as well
as standard serial and vector platforms.

{\bf Aztec} includes a number of Krylov iterative methods such as
conjugate gradient (CG), generalized minimum residual (GMRES) and
stabilized biconjugate gradient (BiCGSTAB) to solve systems of
equations. These Krylov methods are used in conjunction with various
preconditioners such as polynomial or domain decomposition methods
using LU or incomplete LU factorizations within subdomains. Although
the matrix $A$ can be general, the package has been designed for
matrices arising from the approximation of partial differential
equations (PDEs).