A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

Handle URI:
http://hdl.handle.net/10754/621073
Title:
A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
Authors:
Cortes, Adriano Mauricio ( 0000-0002-0141-9706 ) ; Dalcin, Lisandro ( 0000-0001-8086-0155 ) ; Sarmiento, Adel ( 0000-0003-0668-2084 ) ; Collier, N.; 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−supinf−sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show how the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Applied Mathematics and Computational Science Program
Citation:
Côrtes AMA, Dalcin L, Sarmiento A, Collier N, Calo VM (2016) A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2016.10.014.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Oct-2016
DOI:
10.1016/j.cma.2016.10.014
Type:
Article
ISSN:
0045-7825
Sponsors:
This publication was made possible in part by a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation), by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie grant agreement No 644602 and the Center for Numerical Porous Media at King Abdullah University of Science and Technology (KAUST). The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0045782516313093
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorCortes, Adriano Mauricioen
dc.contributor.authorDalcin, Lisandroen
dc.contributor.authorSarmiento, Adelen
dc.contributor.authorCollier, N.en
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2016-10-20T11:52:09Z-
dc.date.available2016-10-20T11:52:09Z-
dc.date.issued2016-10en
dc.identifier.citationCôrtes AMA, Dalcin L, Sarmiento A, Collier N, Calo VM (2016) A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2016.10.014.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2016.10.014en
dc.identifier.urihttp://hdl.handle.net/10754/621073-
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−supinf−sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show how the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.en
dc.description.sponsorshipThis publication was made possible in part by a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation), by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie grant agreement No 644602 and the Center for Numerical Porous Media at King Abdullah University of Science and Technology (KAUST). The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0045782516313093en
dc.rights© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 licenseen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectIsogeometric analysisen
dc.subjectB-spline compatible vector field discretizationen
dc.subjectKrylov subspace methodsen
dc.subjectBlock preconditionersen
dc.subjectStokes flowen
dc.titleA scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problemen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics and Statistics Federal State University of Rio de Janeiro Rio de Janeiro, Brazilen
dc.contributor.institutionCentro de Investigacion de Metodos Computacionales (CIMEC), Consejo Nacional de Investigaciones Cientıficas y Tecnicas (CONICET),Santa Fe, Argentinaen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, USAen
kaust.authorCortes, Adriano Mauricioen
kaust.authorDalcin, Lisandroen
kaust.authorSarmiento, Adelen
kaust.authorCalo, Victor M.en
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