Parallel Versions of Stone's Strongly Implicit Algorithm

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Description/Abstract

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 (PDE's). 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 parallelising 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.