Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD
International audience 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...
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ftccsdartic:oai:HAL:hal-01528636v1 2023-05-15T17:08:30+02:00 Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD Imberti, David Erhel, Jocelyne Fluid Flow Analysis, Description and Control from Image Sequences (FLUMINANCE) Inria Rennes – Bretagne Atlantique Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut de Recherche Mathématique de Rennes (IRMAR) AGROCAMPUS OUEST Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1) Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2) Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes) Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA) European Project: 610741,EC:FP7:ICT,FP7-ICT-2013-10,EXA2CT(2013) Longyearbyen, Norway 2017-02-05 https://hal.inria.fr/hal-01528636 https://hal.inria.fr/hal-01528636/document https://hal.inria.fr/hal-01528636/file/fibgmres.pdf en eng HAL CCSD info:eu-repo/grantAgreement/EC/FP7/610741/EU/EXascale Algorithms and Advanced Computational Techniques/EXA2CT hal-01528636 https://hal.inria.fr/hal-01528636 https://hal.inria.fr/hal-01528636/document https://hal.inria.fr/hal-01528636/file/fibgmres.pdf info:eu-repo/semantics/OpenAccess DD24 - International Conference on Domain Decomposition Methods https://hal.inria.fr/hal-01528636 DD24 - International Conference on Domain Decomposition Methods, Feb 2017, Longyearbyen, Norway http://www.ddm.org/dd24/home.html [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] [INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] info:eu-repo/semantics/conferenceObject Conference papers 2017 ftccsdartic 2021-12-19T02:34:24Z International audience 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. Conference Object Longyearbyen Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Longyearbyen Norway |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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ftccsdartic |
language |
English |
topic |
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] [INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] |
spellingShingle |
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] [INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] Imberti, David Erhel, Jocelyne Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD |
topic_facet |
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] [INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] |
description |
International audience 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. |
author2 |
Fluid Flow Analysis, Description and Control from Image Sequences (FLUMINANCE) Inria Rennes – Bretagne Atlantique Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut de Recherche Mathématique de Rennes (IRMAR) AGROCAMPUS OUEST Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1) Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2) Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes) Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA) European Project: 610741,EC:FP7:ICT,FP7-ICT-2013-10,EXA2CT(2013) |
format |
Conference Object |
author |
Imberti, David Erhel, Jocelyne |
author_facet |
Imberti, David Erhel, Jocelyne |
author_sort |
Imberti, David |
title |
Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD |
title_short |
Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD |
title_full |
Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD |
title_fullStr |
Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD |
title_full_unstemmed |
Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD |
title_sort |
solving large sparse linear systems with a variable s-step gmres preconditioned by dd |
publisher |
HAL CCSD |
publishDate |
2017 |
url |
https://hal.inria.fr/hal-01528636 https://hal.inria.fr/hal-01528636/document https://hal.inria.fr/hal-01528636/file/fibgmres.pdf |
op_coverage |
Longyearbyen, Norway |
geographic |
Longyearbyen Norway |
geographic_facet |
Longyearbyen Norway |
genre |
Longyearbyen |
genre_facet |
Longyearbyen |
op_source |
DD24 - International Conference on Domain Decomposition Methods https://hal.inria.fr/hal-01528636 DD24 - International Conference on Domain Decomposition Methods, Feb 2017, Longyearbyen, Norway http://www.ddm.org/dd24/home.html |
op_relation |
info:eu-repo/grantAgreement/EC/FP7/610741/EU/EXascale Algorithms and Advanced Computational Techniques/EXA2CT hal-01528636 https://hal.inria.fr/hal-01528636 https://hal.inria.fr/hal-01528636/document https://hal.inria.fr/hal-01528636/file/fibgmres.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766064264620015616 |