Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD

David Imberti 1 Jocelyne Erhel 1
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : Krylov methods such as GMRES are efficient iterative methods to solve large sparse linear systems, with only a few key kernel operations: the matrix-vector product, solving a preconditioning system, and building the orthonormal Krylov basis. Domain Decomposition methods allow parallel computations for both the matrix-vector products and preconditioning by using a Schwarz approach combined with deflation (similar to a coarse-grid correction). However, building the orthonormal Krylov basis involves scalar products, which in turn have a communication overhead. In order to avoid this communication, it is possible to build the basis by a block of vectors at a time, sometimes at the price of a loss of orthogonality. We define a sequence of such blocks with a variable size. We show through some theoretical results and some numerical experiments that increasing the block size as a Fibonacci sequence improves stability and convergence.
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Communication dans un congrès
DD24 - International Conference on Domain Decomposition Methods, Feb 2017, Longyearbyen, Norway. 2017, 〈http://www.ddm.org/dd24/home.html〉
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https://hal.inria.fr/hal-01528636
Contributeur : Jocelyne Erhel <>
Soumis le : jeudi 23 novembre 2017 - 13:56:57
Dernière modification le : mardi 19 juin 2018 - 11:12:07

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  • HAL Id : hal-01528636, version 1

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David Imberti, Jocelyne Erhel. Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD. DD24 - International Conference on Domain Decomposition Methods, Feb 2017, Longyearbyen, Norway. 2017, 〈http://www.ddm.org/dd24/home.html〉. 〈hal-01528636〉

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