Multifrontal Parallel Distributed Symmetric and Unsymmetric Solvers

Abstract

We consider the solution of both symmetric and unsymmetric systems of sparse linear equations. A new parallel distributed memory multifrontal approach is described. To handle numerical pivoting efficiently, a parallel asynchronous algorithm with dynamic scheduling of the computing tasks has been developed. We discuss some of the main algorithmic choices and compare both implementation issues and the performance of the LDL T and LU factorizations. Performance analysis on an IBM SP2 shows the efficiency and the potential of the method. The test problems used are from the Rutherford-Boeing collection and from the PARASOL end users. Keywords: MPI, distributed memory architecture, sparse matrices, multifrontal direct methods. AMS(MOS) subject classifications: 65F05, 65F50. 1 This work has been partially supported by the PARASOL project (EU ESPRIT IV LTR project 20160). Also appeared as Technical Report RAL-TR-1998-051 from Rutherford Appleton Laboratory, Oxfordshire. Current reports av...