Parallel implementation of sparse LU decomposition for chemical engineering applications

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 3-D 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 3-D grid graphs to make inferences regarding generalizations of these methods of flowsheeting applications.