Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system

Autores
Côrtes, A.M.A.; Coutinho, A.L.G.A.; Dalcin, Lisandro Daniel; Calo, V.M.
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.
Fil: Côrtes, A.M.A.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Coutinho, A.L.G.A.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
Fil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia Saudita
Materia
Block-Diagonal Preconditioner
Divergence-Conforming B-Spline Spaces
Isogeometric Analysis
Krylov Subspace Method
Stokes Problem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/78615
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/78615
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes systemCôrtes, A.M.A.Coutinho, A.L.G.A.Dalcin, Lisandro DanielCalo, V.M.Block-Diagonal PreconditionerDivergence-Conforming B-Spline SpacesIsogeometric AnalysisKrylov Subspace MethodStokes ProblemThe recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.Fil: Côrtes, A.M.A.. Universidade Federal do Rio de Janeiro; BrasilFil: Coutinho, A.L.G.A.. Universidade Federal do Rio de Janeiro; BrasilFil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia SauditaElsevier B.V.2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/78615Côrtes, A.M.A.; Coutinho, A.L.G.A.; Dalcin, Lisandro Daniel; Calo, V.M.; Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system; Elsevier B.V.; Journal of Computational Science; 11; 11-2015; 123-1361877-7503CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jocs.2015.01.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:15:30Zoai:ri.conicet.gov.ar:11336/78615instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:15:30.467CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
title Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
spellingShingle Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
Côrtes, A.M.A.
Block-Diagonal Preconditioner
Divergence-Conforming B-Spline Spaces
Isogeometric Analysis
Krylov Subspace Method
Stokes Problem
title_short Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
title_full Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
title_fullStr Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
title_full_unstemmed Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
title_sort Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
dc.creator.none.fl_str_mv Côrtes, A.M.A.
Coutinho, A.L.G.A.
Dalcin, Lisandro Daniel
Calo, V.M.
author Côrtes, A.M.A.
author_facet Côrtes, A.M.A.
Coutinho, A.L.G.A.
Dalcin, Lisandro Daniel
Calo, V.M.
author_role author
author2 Coutinho, A.L.G.A.
Dalcin, Lisandro Daniel
Calo, V.M.
author2_role author
author
author
dc.subject.none.fl_str_mv Block-Diagonal Preconditioner
Divergence-Conforming B-Spline Spaces
Isogeometric Analysis
Krylov Subspace Method
Stokes Problem
topic Block-Diagonal Preconditioner
Divergence-Conforming B-Spline Spaces
Isogeometric Analysis
Krylov Subspace Method
Stokes Problem
dc.description.none.fl_txt_mv The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.
Fil: Côrtes, A.M.A.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Coutinho, A.L.G.A.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
Fil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia Saudita
description The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/78615
Côrtes, A.M.A.; Coutinho, A.L.G.A.; Dalcin, Lisandro Daniel; Calo, V.M.; Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system; Elsevier B.V.; Journal of Computational Science; 11; 11-2015; 123-136
1877-7503
CONICET Digital
CONICET
url http://hdl.handle.net/11336/78615
identifier_str_mv Côrtes, A.M.A.; Coutinho, A.L.G.A.; Dalcin, Lisandro Daniel; Calo, V.M.; Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system; Elsevier B.V.; Journal of Computational Science; 11; 11-2015; 123-136
1877-7503
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jocs.2015.01.005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846781590039953408
score 12.982451

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