Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners

Handle URI:
http://hdl.handle.net/10754/623030
Title:
Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners
Authors:
Beirão Da Veiga, L.; Pavarino, L. F.; Scacchi, S.; Widlund, O. B.; Zampini, Stefano ( 0000-0002-0435-0433 )
Abstract:
Isogeometric analysis has been introduced as an alternative to finite element methods in order to simplify the integration of computer-aided design (CAD) software and the discretization of variational problems of continuum mechanics. In contrast with the finite element case, the basis functions of isogeometric analysis are often not nodal. As a consequence, there are fat interfaces which can easily lead to an increase in the number of interface variables after a decomposition of the parameter space into subdomains. Building on earlier work on the deluxe version of the BDDC (balancing domain decomposition by constraints) family of domain decomposition algorithms, several adaptive algorithms are developed in this paper for scalar elliptic problems in an effort to decrease the dimension of the global, coarse component of these preconditioners. Numerical experiments provide evidence that this work can be successful, yielding scalable and quasi-optimal adaptive BDDC algorithms for isogeometric discretizations.
KAUST Department:
Extreme Computing Research Center
Citation:
Da Veiga LB, Pavarino LF, Scacchi S, Widlund OB, Zampini S (2017) Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners. SIAM Journal on Scientific Computing 39: A281–A302. Available: http://dx.doi.org/10.1137/15M1054675.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
23-Feb-2017
DOI:
10.1137/15M1054675
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
The work of the first three authors was supported by grants from M.I.U.R. (PRIN 201289A4LX 002) and from the Istituto Nazionale di Alta Matematica (INDAM-GNCS). The work of the fourth author was partially supported by National Science Foundation grant DMS-1522736.
Additional Links:
http://epubs.siam.org/doi/10.1137/15M1054675
Appears in Collections:
Articles; Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorBeirão Da Veiga, L.en
dc.contributor.authorPavarino, L. F.en
dc.contributor.authorScacchi, S.en
dc.contributor.authorWidlund, O. B.en
dc.contributor.authorZampini, Stefanoen
dc.date.accessioned2017-03-20T08:46:08Z-
dc.date.available2017-03-20T08:46:08Z-
dc.date.issued2017-02-23en
dc.identifier.citationDa Veiga LB, Pavarino LF, Scacchi S, Widlund OB, Zampini S (2017) Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners. SIAM Journal on Scientific Computing 39: A281–A302. Available: http://dx.doi.org/10.1137/15M1054675.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/15M1054675en
dc.identifier.urihttp://hdl.handle.net/10754/623030-
dc.description.abstractIsogeometric analysis has been introduced as an alternative to finite element methods in order to simplify the integration of computer-aided design (CAD) software and the discretization of variational problems of continuum mechanics. In contrast with the finite element case, the basis functions of isogeometric analysis are often not nodal. As a consequence, there are fat interfaces which can easily lead to an increase in the number of interface variables after a decomposition of the parameter space into subdomains. Building on earlier work on the deluxe version of the BDDC (balancing domain decomposition by constraints) family of domain decomposition algorithms, several adaptive algorithms are developed in this paper for scalar elliptic problems in an effort to decrease the dimension of the global, coarse component of these preconditioners. Numerical experiments provide evidence that this work can be successful, yielding scalable and quasi-optimal adaptive BDDC algorithms for isogeometric discretizations.en
dc.description.sponsorshipThe work of the first three authors was supported by grants from M.I.U.R. (PRIN 201289A4LX 002) and from the Istituto Nazionale di Alta Matematica (INDAM-GNCS). The work of the fourth author was partially supported by National Science Foundation grant DMS-1522736.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1054675en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectAdaptive primal constraintsen
dc.subjectBDDC deluxe preconditionersen
dc.subjectDomain decompositionen
dc.subjectElliptic problemsen
dc.subjectIsogeometric analysisen
dc.titleAdaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditionersen
dc.typeArticleen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via Cozzi, 53, Milano, 20125, , Italyen
dc.contributor.institutionDipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, Milano, 20133, , Italyen
dc.contributor.institutionCourant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, , United Statesen
kaust.authorZampini, Stefanoen
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