PSPASES: Building a High Performance Scalable Parallel Direct Solver for Sparse Linear Systems

Abstract

Many problems in engineering and scientific domains require solving large sparse systems of linear equations, as a computationally intensive step towards the final solution. It has long been a challenge to develop efficient parallel formulations of sparse direct solvers due to several different complex steps involved in the process. In this paper, we describe PSPASES, one of the first efficient, portable, and robust scalable parallel solvers for sparse symmetric positive definite linear systems that we have developed. We discuss the algorithmic and implementation issues involved in its development; and present performance and scalability results on Cray T3E and SGI Origin 2000. PSPASES could solve the largest sparse system (1 million equations) ever solved by a direct method, with the highest performance (51 GFLOPS for Cholesky factorization) ever reported.