BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

Handle URI:
http://hdl.handle.net/10754/626963
Title:
BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields
Authors:
Oh, Duk-Soon; Widlund, Olof B.; Zampini, Stefano ( 0000-0002-0435-0433 ) ; Dohrmann, Clark R.
Abstract:
A BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a deluxe type of weighted average and an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced.; Under the assumption that the subdomains are all built from elements of a coarse triangulation of the given domain, that the meshes of each subdomain are quasi uniform and that the material parameters are constant in each subdomain, a bound is obtained for the condition number of the preconditioned linear system which is independent of the values and the jumps of these parameters across the interface between the subdomains as well as the number of subdomains. Numerical experiments, using the PETSc library, are also presented which support the theory and show the effectiveness of the algorithms even for problems not covered by the theory. Included are also experiments with Brezzi-Douglas-Marini finite element approximations.
KAUST Department:
Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Oh D-S, Widlund OB, Zampini S, Dohrmann CR (2017) BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields. Mathematics of Computation 87: 659–692. Available: http://dx.doi.org/10.1090/mcom/3254.
Publisher:
American Mathematical Society (AMS)
Journal:
Mathematics of Computation
Issue Date:
13-Jun-2017
DOI:
10.1090/mcom/3254
Type:
Article
ISSN:
0025-5718; 1088-6842
Sponsors:
The work of the second author was supported in part by the National Science Foundation Grants DMS-1216564 and DMS-1522736.
Additional Links:
http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03254-3/
Appears in Collections:
Articles; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorOh, Duk-Soonen
dc.contributor.authorWidlund, Olof B.en
dc.contributor.authorZampini, Stefanoen
dc.contributor.authorDohrmann, Clark R.en
dc.date.accessioned2018-02-01T07:24:59Z-
dc.date.available2018-02-01T07:24:59Z-
dc.date.issued2017-06-13en
dc.identifier.citationOh D-S, Widlund OB, Zampini S, Dohrmann CR (2017) BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields. Mathematics of Computation 87: 659–692. Available: http://dx.doi.org/10.1090/mcom/3254.en
dc.identifier.issn0025-5718en
dc.identifier.issn1088-6842en
dc.identifier.doi10.1090/mcom/3254en
dc.identifier.urihttp://hdl.handle.net/10754/626963-
dc.description.abstractA BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a deluxe type of weighted average and an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced.en
dc.description.abstractUnder the assumption that the subdomains are all built from elements of a coarse triangulation of the given domain, that the meshes of each subdomain are quasi uniform and that the material parameters are constant in each subdomain, a bound is obtained for the condition number of the preconditioned linear system which is independent of the values and the jumps of these parameters across the interface between the subdomains as well as the number of subdomains. Numerical experiments, using the PETSc library, are also presented which support the theory and show the effectiveness of the algorithms even for problems not covered by the theory. Included are also experiments with Brezzi-Douglas-Marini finite element approximations.en
dc.description.sponsorshipThe work of the second author was supported in part by the National Science Foundation Grants DMS-1216564 and DMS-1522736.en
dc.publisherAmerican Mathematical Society (AMS)en
dc.relation.urlhttp://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03254-3/en
dc.subjectDomain decompositionen
dc.subjectBDDC preconditioneren
dc.subjectRaviart-Thomas finite elementsen
dc.subjectmultilevel preconditionersen
dc.subjectadaptive selection of coarse spacesen
dc.titleBDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fieldsen
dc.typeArticleen
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalMathematics of Computationen
dc.contributor.institutionDepartment of Mathematics, Rutgers University, Piscataway, NJ, 08854, , United Statesen
dc.contributor.institutionCourant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, , United Statesen
dc.contributor.institutionComputational Solid Mechanics and Structural Dynamics, Sandia National Laboratories, Albuquerque, NM, 87185, , United Statesen
kaust.authorZampini, Stefanoen
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