Parallel versions of Stone's strongly implicit algorithm

• Published in: Concurrency and computation Vol. 13; no. 12; pp. 1049 - 1062
• Main Authors: Reeve, J. S., Scurr, A. D., Merlin, J. H.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2001
• Subjects: parallel numerical algorithms; Stones algorithm; strongly implicit methods
• ISSN: 1532-0626; 1532-0634
• DOI: 10.1002/cpe.590

In this paper, we describe various methods of deriving a parallel version of Stone's Strongly Implicit Procedure (SIP) for solving sparse linear equations arising from finite difference approximation to partial differential equations (PDEs). Sequential versions of this algorithm have been very successful in solving semi‐conductor, heat conduction and flow simulation problems and an efficient parallel version would enable much larger simulations to be run. An initial investigation of various parallelizing strategies was undertaken using a version of high performance Fortran (HPF) and the best methods were reprogrammed using the MPI message passing libraries for increased efficiency. Early attempts concentrated on developing a parallel version of the characteristic wavefront computation pattern of the existing sequential SIP code. However, a red‐black ordering of grid points, similar to that used in parallel versions of the Gauss–Seidel algorithm, is shown to be far more efficient. The results of both the wavefront and red‐black MPI based algorithms are reported for various size problems and number of processors on a sixteen node IBM SP2. Copyright © 2001 John Wiley & Sons, Ltd.