### Parallel Implementation of Sparse LU Decomposition for
Chemical Engineering Applications

by

Alan B. Coon and Mark A. Stadtherr

#### ABSTRACT

Parallel, shared-memory computer architectures can provide enormous
computational resources for numerical simulations in many chemical engineering
applications. The efficient solution of large, sparse sets of linear equations
is often a critical requirement in these applications; thus, the parallel
implementation of a sparse linear solver is crucial. We examine methods
for the parallel LU decomposition of sparse matrices arising from three-dimensional
grid graphs (typically associated with finite difference discretizations
in three dimensions). Parallel performance of the decomposition is significantly
enhanced by the use of a new diagonal variant of nested dissection, in
conjunction with a parallel dense solver at certain stages. The overall
parallel efficiency exceeds that of the parallel dense solver. We also
consider the extension of such methods to the less structured graphs that
arise from sparse linear systems in equation-based process flowsheeting.
We use performance results from the three-dimensional grid graphs to make
inferences regarding generalizations of these methods to flowsheeting applications.

Comput. Chem. Eng., 13, 899-914 (1989)