*
Tom Cwik ^{*}, Daniel S. Katz^{1}, Cinzia Zuffada,
Vahraz Jamnejad*

*
*
Jet Propulsion Laboratory

California Institute of Technology

Pasadena, CA 91109

^{1}Cray Research, Inc.

El Segundo, CA 90245

In this work an iterative solver for use with out finite element codes
was developed for the Cray T3D massively parallel processor located at
the Jet Propulsion Laboratory. This development was completed in two
stages. First, a matrix decomposition algorithm was constructed,
properly decomposing the sparse *matrix entries* into data sets
that were read by the T3D processing elements (PEs). It is noted that
this a different strategy that the usual *mesh* decomposition
algorithms developed in the past. The second stage was the
construction of a scalable iterative solver on the T3D that efficiently
computes a solution of the sparse system. The initial sparse matrix
decomposition algorithm was originally developed for a YMP processor
and then ported to the T3D.

In this talk we will present an overview of sparse matrix methods for distributed memory machines, as well as the specific implementation of the iterative solver. Example solutions have been obtained for systems with over one-half million unknowns.