Parallel versions of Stone's strongly implicit algorithm
Parallel versions of Stone's strongly implicit algorithm
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.
strongly implicit methods, Stones algorithm, parallel numerical algorithms
1049-1062
Reeve, Jeff
dd909010-7d44-44ea-83fe-a09e4d492618
Scurr, Anthony
197fdeba-9dad-4992-bb6f-3fe7ce4690d5
Merlin, John
eef0301b-a984-46a7-af72-b0ab3d40bff7
2001
Reeve, Jeff
dd909010-7d44-44ea-83fe-a09e4d492618
Scurr, Anthony
197fdeba-9dad-4992-bb6f-3fe7ce4690d5
Merlin, John
eef0301b-a984-46a7-af72-b0ab3d40bff7
Reeve, Jeff, Scurr, Anthony and Merlin, John
(2001)
Parallel versions of Stone's strongly implicit algorithm.
Concurrency and Computation: Practice and Experience, 13, .
(doi:10.1002/cpe.590).
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.
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Published date: 2001
Keywords:
strongly implicit methods, Stones algorithm, parallel numerical algorithms
Organisations:
EEE
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Local EPrints ID: 257614
URI: http://eprints.soton.ac.uk/id/eprint/257614
ISSN: 1532-0626
PURE UUID: 6fbe2fd1-5993-4f83-8d48-a100dc8c1b4a
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Date deposited: 17 Jun 2003
Last modified: 14 Mar 2024 05:59
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Author:
Jeff Reeve
Author:
Anthony Scurr
Author:
John Merlin
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