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D.J. Grey* and M.H.B.M. Shariff#

*School of Computing and Information Systems, University of Sunderland, Sunderland, United Kingdom
#School of Computing and Mathematics, University of Teesside, Middlesbrough, United Kingdom

doi:10.4203/ccp.38.8.3

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D.J. Grey, M.H.B.M. Shariff, "Parallel Inversion of Finite Element Matrices via a Direct Method", in B.H.V. Topping, (Editor), "Advances in Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, pp 359-364, 1996. doi:10.4203/ccp.38.8.3

Abstract

A direct method and its variants, based on matrix multiplications, to invert square non-singular matrices(need not be positive definite) are developed. Theoretical background, analysis of the proposed method and the complexity of the algorithm for sparse and dense matrices are given. Two significantly different parallel algorithms for dense and sparse (finite element) matrices are developed. In the case of the dense matrix standard parallelisation of matrix multiplications was undertaken. However, for sparse matrices the standard parallel matrix multiplication is not effective which leads us to develop a parallel algorithm different from that for the dense matrix. Numerical examples are given to test our method.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 38 ADVANCES IN COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping Paper VIII.3 Parallel Inversion of Finite Element Matrices via a Direct Method D.J. Grey* and M.H.B.M. Shariff# *School of Computing and Information Systems, University of Sunderland, Sunderland, United Kingdom #School of Computing and Mathematics, University of Teesside, Middlesbrough, United Kingdom doi:10.4203/ccp.38.8.3 purchase the full-text of this paper Full Bibliographic Reference for this paper D.J. Grey, M.H.B.M. Shariff, "Parallel Inversion of Finite Element Matrices via a Direct Method", in B.H.V. Topping, (Editor), "Advances in Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, pp 359-364, 1996. doi:10.4203/ccp.38.8.3 Abstract A direct method and its variants, based on matrix multiplications, to invert square non-singular matrices(need not be positive definite) are developed. Theoretical background, analysis of the proposed method and the complexity of the algorithm for sparse and dense matrices are given. Two significantly different parallel algorithms for dense and sparse (finite element) matrices are developed. In the case of the dense matrix standard parallelisation of matrix multiplications was undertaken. However, for sparse matrices the standard parallel matrix multiplication is not effective which leads us to develop a parallel algorithm different from that for the dense matrix. Numerical examples are given to test our method. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £82 +P&P)
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