Isogeometric BDDC deluxe preconditioners for linear elasticity

dc.contributor.authorPavarino, L. F.
dc.contributor.authorScacchi, S.
dc.contributor.authorWidlund, O. B.
dc.contributor.authorZampini, Stefano
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.institutionDipartimento di Matematica, Università Degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy
dc.contributor.institutionDipartimento di Matematica, Università Degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
dc.contributor.institutionCourant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
dc.date.accessioned2018-05-14T13:37:06Z
dc.date.available2018-05-14T13:37:06Z
dc.date.issued2018-03-14
dc.date.published-online2018-03-14
dc.date.published-print2018-06-30
dc.description.abstractBalancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.
dc.description.sponsorshipFor computer time, this research used also the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. The first and second authors’ work was supported by Grants of M.I.U.R. (PRIN 201289A4LX 002) and of Istituto Nazionale di Alta Matematica (INDAM-GNCS). Third author’s work has been supported by the National Science Foundation Grant DMS-1522736.
dc.identifier.citationPavarino LF, Scacchi S, Widlund OB, Zampini S (2018) Isogeometric BDDC deluxe preconditioners for linear elasticity. Mathematical Models and Methods in Applied Sciences: 1–34. Available: http://dx.doi.org/10.1142/S0218202518500367.
dc.identifier.doi10.1142/S0218202518500367
dc.identifier.issn0218-2025
dc.identifier.issn1793-6314
dc.identifier.journalMathematical Models and Methods in Applied Sciences
dc.identifier.urihttp://hdl.handle.net/10754/627852
dc.publisherWorld Scientific Pub Co Pte Lt
dc.relation.urlhttps://www.worldscientific.com/doi/abs/10.1142/S0218202518500367
dc.subjectBDDC deluxe preconditioners
dc.subjectcompressible linear elasticity
dc.subjectDomain decomposition
dc.subjectisogeometric analysis
dc.subjectNURBS
dc.titleIsogeometric BDDC deluxe preconditioners for linear elasticity
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Pavarino, L. F.,equals">Pavarino, L. F.</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Scacchi, S.,equals">Scacchi, S.</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Widlund, O. B.,equals">Widlund, O. B.</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-0435-0433&spc.sf=dc.date.issued&spc.sd=DESC">Zampini, Stefano</a> <a href="https://orcid.org/0000-0002-0435-0433" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Extreme Computing Research Center,equals">Extreme Computing Research Center</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><br><h5>Online Publication Date</h5>2018-03-14<br><br><h5>Print Publication Date</h5>2018-06-30<br><br><h5>Date</h5>2018-03-14</span>
display.details.right<span><h5>Abstract</h5>Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been shown to provide rapidly convergent preconditioned conjugate gradient methods for solving many of the very ill-conditioned systems of algebraic equations which often arise in finite element approximations of a large variety of problems in continuum mechanics. These algorithms have also been developed successfully for problems arising in isogeometric analysis. In particular, the BDDC deluxe version has proven very successful for problems approximated by Non-Uniform Rational B-Splines (NURBS), even those of high order and regularity. One main purpose of this paper is to extend the theory, previously fully developed only for scalar elliptic problems in the plane, to problems of linear elasticity in three dimensions. Numerical experiments supporting the theory are also reported. Some of these experiments highlight the fact that the development of the theory can help to decrease substantially the dimension of the primal space of the BDDC algorithm, which provides the necessary global component of these preconditioners, while maintaining scalability and good convergence rates.<br><br><h5>Citation</h5>Pavarino LF, Scacchi S, Widlund OB, Zampini S (2018) Isogeometric BDDC deluxe preconditioners for linear elasticity. Mathematical Models and Methods in Applied Sciences: 1–34. Available: http://dx.doi.org/10.1142/S0218202518500367.<br><br><h5>Acknowledgements</h5>For computer time, this research used also the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. The first and second authors’ work was supported by Grants of M.I.U.R. (PRIN 201289A4LX 002) and of Istituto Nazionale di Alta Matematica (INDAM-GNCS). Third author’s work has been supported by the National Science Foundation Grant DMS-1522736.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=World Scientific Pub Co Pte Lt,equals">World Scientific Pub Co Pte Lt</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Mathematical Models and Methods in Applied Sciences,equals">Mathematical Models and Methods in Applied Sciences</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1142/S0218202518500367">10.1142/S0218202518500367</a><br><br><h5>Additional Links</h5>https://www.worldscientific.com/doi/abs/10.1142/S0218202518500367</span>
kaust.personZampini, Stefano
orcid.authorPavarino, L. F.
orcid.authorScacchi, S.
orcid.authorWidlund, O. B.
orcid.authorZampini, Stefano::0000-0002-0435-0433
orcid.id0000-0002-0435-0433
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