Journal Article10.1016/S0167-8191(01)00092-8
Parallel approximate factorization method for solving discrete elliptic equations
O. Yu. Milyukova
- 01 Sep 2001
- Vol. 27, Iss: 10, pp 1365-1379
21
TL;DR: The method is based on the conjugate gradient algorithm with modified incomplete factorization preconditioning and the use of a domain-decomposition-like ordering of unknowns and the rate of convergence and the efficiency of the proposed method are investigated.
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Abstract: An iterative approximate factorization method is proposed for solving elliptic equations on a rectangular computational domain on distributed memory parallel computers. The method is based on the conjugate gradient algorithm with modified incomplete factorization preconditioning (MICCG(0)) and the use of a domain-decomposition-like ordering of unknowns. The rate of convergence and the efficiency of the proposed method are investigated.
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Citations
Preconditioning techniques for large linear systems: a survey
TL;DR: This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices, including progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions.
1.4K
Parallel iterative methods using factorized preconditioning matrices for solving elliptic equations on triangular grids
TL;DR: Results of the theoretic and experimental studies of the convergence rate of these methods are presented and the solution of model problems on a moderate number processors is used to examine the efficiency of the proposed parallel methods.
6
MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1
TL;DR: Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the sparse matrix collections SuiteSparse are presented.
Approaches MPI+OpenMP implementation of conjugated gradient method with pre-conditioner of block incomplete inverse triangular decomposition of IC1
TL;DR: A new method of using MPI+OpenMP technology for constructing and handling a preconditioner BIIC-IC1 with a number of blocks coinciding with the number of processors is proposed, in which a special ordering of grid nodes inside subareas corresponding to calculations on each processor is used to apply the OpenMP technology.
3
References
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TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.
An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
J. A. Meijerink,H.A. van der Vorst +1 more
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J. M. Ortega
- 30 Apr 1988
TL;DR: The Conjugate Gradient Algorithm and the Iterative Methods for Linear Equations are described, which simplify the derivation of linear algebra to simple linear algebra.
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Numerical Linear Algebra for High-Performance Computers
Jack Dongarra,Iain Duff,Danny C. Sorensen,Henk A. van der Vorst +3 more
- 01 Jan 1998
TL;DR: High-performance numerical linear algebra book covering dense and sparse systems, eigenvalue problems, and vector/parallel processing. Supersedes a 1990 book and includes new material.
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The effect of ordering on preconditioned conjugate gradients
Iain S. Duff,Gérard Meurant +1 more
TL;DR: It is shown empirically that there can be a significant difference in the number of iterations required by the conjugate gradient method and reasons for this marked difference in performance are suggested.
372