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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/78615
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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 Técnicas2025-09-29T09:46:38Zoai: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:34982025-09-29 09:46:39.094CONICET 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 |
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1844613456467066880 |
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13.070432 |