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

Handle URI:
http://hdl.handle.net/10754/558296
Title:
Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system
Authors:
Côrtes, A.M.A.; Coutinho, A.L.G.A.; Dalcin, L.; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
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.
KAUST Department:
Center for Numerical Porous Media (NumPor); Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program
Citation:
Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system 2015 Journal of Computational Science
Journal:
Journal of Computational Science
Issue Date:
20-Feb-2015
DOI:
10.1016/j.jocs.2015.01.005
Type:
Article
ISSN:
18777503
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S1877750315000095
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorCôrtes, A.M.A.en
dc.contributor.authorCoutinho, A.L.G.A.en
dc.contributor.authorDalcin, L.en
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-06-21T09:24:51Zen
dc.date.available2015-06-21T09:24:51Zen
dc.date.issued2015-02-20en
dc.identifier.citationPerformance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system 2015 Journal of Computational Scienceen
dc.identifier.issn18777503en
dc.identifier.doi10.1016/j.jocs.2015.01.005en
dc.identifier.urihttp://hdl.handle.net/10754/558296en
dc.description.abstractThe 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.en
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877750315000095en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Science, 20 February 2015. DOI: 10.1016/j.jocs.2015.01.005en
dc.subjectStokes problemen
dc.subjectBlock-diagonal preconditioneren
dc.subjectKrylov subspace methoden
dc.subjectDivergence-conforming B-spline spacesen
dc.subjectIsogeometric analysisen
dc.titlePerformance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes systemen
dc.typeArticleen
dc.contributor.departmentCenter for Numerical Porous Media (NumPor)en
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalJournal of Computational Scienceen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Civil Engineering, NACAD, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazilen
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Santa Fe, Argentinaen
kaust.authorCortes, Adriano Mauricioen
kaust.authorDalcin, Lisandroen
kaust.authorCalo, Victor M.en
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