An efficient parallel discrete PDE solver
We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently deve...
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| Veröffentlicht in: | Parallel computing Jg. 21; H. 11; S. 1725 - 1748 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
1995
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| ISSN: | 0167-8191, 1872-7336 |
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| Abstract | We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently developed parallelization technique to avoid communication bottleneck for the computation associated to the internal boundary nodes. Numerical results are given for a transputer network with up to 512 processors and a few workstation cluster. |
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| AbstractList | We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently developed parallelization technique to avoid communication bottleneck for the computation associated to the internal boundary nodes. Numerical results are given for a transputer network with up to 512 processors and a few workstation cluster. |
| Author | Notay, Y. |
| Author_xml | – sequence: 1 givenname: Y. surname: Notay fullname: Notay, Y. email: ynotay@ulb.ac.be organization: Service de Métrologie Nucléaire Université Libre de Bruxelles (C.P. 165) 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium |
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| Cites_doi | 10.1007/BF01389447 10.1137/0801034 10.1137/0912079 10.1016/0024-3795(91)90401-H 10.1137/0906018 10.1016/0167-8191(89)90030-6 10.1016/0377-0427(89)90298-7 10.1016/0010-4655(89)90163-X 10.1007/BF01932738 10.1016/0010-4655(89)90164-1 10.1002/nla.1680010602 |
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| Issue | 11 |
| Keywords | Incomplete factorization Distributed memory multiprocessor Preconditioning Partial differential equation Conjugate gradient algorithm |
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| References | Clauss (BIB7) 1993 Filippone, Marrone, di Brozolo (BIB12) 1992 Ortega (BIB23) 1990; 1 Notay (BIB18) 1993; vol. 41 Concus, Golub, Meurant (BIB8) 1985; 6 Axelsson, Barker (BIB2) 1984 Eijkhout (BIB10) 1991; 154–156 Di Brozolo, Robert (BIB24) 1989; 11 Nakamura (BIB16) 1977 Notay (BIB20) 1994; 1 Beauwens, Wilmet (BIB5) 1989; 26 Manneback, Qin (BIB14) 1992 Bastian, Horton (BIB4) 1991; 12 Meijerink, Van Der Vorst (BIB15) 1977; 31 Notay (BIB19) 1993 Magolu (BIB13) 1995; 11 Notay, Van De Velde (BIB22) 1995 Ashby, Holst, Manteuffel, Ṡaylor (BIB1) 1992 Notay (BIB21) 1995 Axelsson, Lindskog (BIB3) 1986; 48 Duff, Meurant (BIB9) 1989; 29 Notay (BIB17) 1991 Elman, Agrón (BIB11) 1989; 53 Chan, Kuo, Tong (BIB6) 1989; 53 Manneback (10.1016/0167-8191(96)80005-6_BIB14) 1992 Bastian (10.1016/0167-8191(96)80005-6_BIB4) 1991; 12 Nakamura (10.1016/0167-8191(96)80005-6_BIB16) 1977 Magolu (10.1016/0167-8191(96)80005-6_BIB13) 1995; 11 Ortega (10.1016/0167-8191(96)80005-6_BIB23) 1990; 1 Ashby (10.1016/0167-8191(96)80005-6_BIB1) 1992 Meijerink (10.1016/0167-8191(96)80005-6_BIB15) 1977; 31 Notay (10.1016/0167-8191(96)80005-6_BIB20) 1994; 1 Notay (10.1016/0167-8191(96)80005-6_BIB18) 1993; vol. 41 Beauwens (10.1016/0167-8191(96)80005-6_BIB5) 1989; 26 Elman (10.1016/0167-8191(96)80005-6_BIB11) 1989; 53 Chan (10.1016/0167-8191(96)80005-6_BIB6) 1989; 53 Di Brozolo (10.1016/0167-8191(96)80005-6_BIB24) 1989; 11 Notay (10.1016/0167-8191(96)80005-6_BIB22) 1995 Filippone (10.1016/0167-8191(96)80005-6_BIB12) 1992 Clauss (10.1016/0167-8191(96)80005-6_BIB7) 1993 Duff (10.1016/0167-8191(96)80005-6_BIB9) 1989; 29 Notay (10.1016/0167-8191(96)80005-6_BIB17) 1991 Notay (10.1016/0167-8191(96)80005-6_BIB19) 1993 Axelsson (10.1016/0167-8191(96)80005-6_BIB3) 1986; 48 Eijkhout (10.1016/0167-8191(96)80005-6_BIB10) 1991; 154–156 Concus (10.1016/0167-8191(96)80005-6_BIB8) 1985; 6 Notay (10.1016/0167-8191(96)80005-6_BIB21) 1995 Axelsson (10.1016/0167-8191(96)80005-6_BIB2) 1984 |
| References_xml | – year: 1977 ident: BIB16 article-title: Computational Methods in Engineering and Science – volume: 53 start-page: 237 year: 1989 end-page: 252 ident: BIB6 article-title: Parallel elliptic preconditioners: Fourier analysis and performance on the Connection Machine publication-title: Comput. Phys. Comm. – year: 1993 ident: BIB7 article-title: PARIX 1.2, Software Documentation – volume: 11 year: 1995 ident: BIB13 article-title: Implementation of parallel block preconditionings on a transputer-based multiprocessor publication-title: Future Generation Computer Systems – volume: 6 start-page: 220 year: 1985 end-page: 252 ident: BIB8 article-title: Block preconditioning for the conjugate gradient method publication-title: SIAM J. Sci. Statist. 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Comm. doi: 10.1016/0010-4655(89)90163-X – year: 1995 ident: 10.1016/0167-8191(96)80005-6_BIB22 – year: 1984 ident: 10.1016/0167-8191(96)80005-6_BIB2 – volume: 31 start-page: 148 year: 1977 ident: 10.1016/0167-8191(96)80005-6_BIB15 article-title: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix publication-title: Math. Comp. – volume: 29 start-page: 635 year: 1989 ident: 10.1016/0167-8191(96)80005-6_BIB9 article-title: The effect of ordering on preconditioned conjugate gradients publication-title: BIT doi: 10.1007/BF01932738 – year: 1992 ident: 10.1016/0167-8191(96)80005-6_BIB12 article-title: Parallel preconditioned conjugate-gradient type algorithms for general sparsity structures publication-title: Journal of Computer Mathematics – start-page: 172 year: 1992 ident: 10.1016/0167-8191(96)80005-6_BIB14 article-title: Algorithmic on a distributed memory mimd computer: a case study – volume: vol. 41 start-page: 103 year: 1993 ident: 10.1016/0167-8191(96)80005-6_BIB18 article-title: A new incomplete factorization method, in Incomplete Decomposition (ILU)-Algorithms, Theory and Applications – year: 1993 ident: 10.1016/0167-8191(96)80005-6_BIB19 article-title: Ordering methods for approximate factorization preconditioning – volume: 53 start-page: 253 year: 1989 ident: 10.1016/0167-8191(96)80005-6_BIB11 article-title: Ordering techniques for the preconditioned conjugate gradient method on parallel computers publication-title: Comput. Phys. Comm. doi: 10.1016/0010-4655(89)90164-1 – year: 1993 ident: 10.1016/0167-8191(96)80005-6_BIB7 – volume: 11 year: 1995 ident: 10.1016/0167-8191(96)80005-6_BIB13 article-title: Implementation of parallel block preconditionings on a transputer-based multiprocessor publication-title: Future Generation Computer Systems – volume: 1 start-page: 511 year: 1994 ident: 10.1016/0167-8191(96)80005-6_BIB20 article-title: DRIC: a dynamic version of the RIC method publication-title: Journ. Num. Lin. Alg. with Appl. doi: 10.1002/nla.1680010602 |
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| SubjectTerms | Conjugate gradient algorithm Distributed memory multiprocessor Incomplete factorization Partial differential equation Preconditioning |
| Title | An efficient parallel discrete PDE solver |
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