The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements

Handle URI:
http://hdl.handle.net/10754/555666
Title:
The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements
Authors:
Collier, Nathan; Dalcin, Lisandro ( 0000-0001-8086-0155 ) ; Pardo, David; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using Co B-splines, which span traditional finite element spaces, and Cp-1 B-splines, which represent maximum continuity We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size h and polynomial order of approximation p in addition to the aforementioned continuity of the basis. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most 33p2/8 times more expensive for the more continuous space, although for moderately low p, this number is significantly reduced. Moreover, if static condensation is not employed, this number further reduces to at most a value of 8, even for high p. Preconditioning options can be up to p3 times more expensive to set up, although this difference significantly decreases for some popular preconditioners such as incomplete LU factorization. © 2013 Society for Industrial and Applied Mathematics.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements 2013, 35 (2):A767 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
19-Mar-2013
DOI:
10.1137/120881038
ARXIV:
arXiv:1206.2948
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/120881038; http://arxiv.org/abs/1206.2948
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorCollier, Nathanen
dc.contributor.authorDalcin, Lisandroen
dc.contributor.authorPardo, Daviden
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-05-25T08:29:32Zen
dc.date.available2015-05-25T08:29:32Zen
dc.date.issued2013-03-19en
dc.identifier.citationThe Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements 2013, 35 (2):A767 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/120881038en
dc.identifier.urihttp://hdl.handle.net/10754/555666en
dc.description.abstractIn this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using Co B-splines, which span traditional finite element spaces, and Cp-1 B-splines, which represent maximum continuity We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size h and polynomial order of approximation p in addition to the aforementioned continuity of the basis. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most 33p2/8 times more expensive for the more continuous space, although for moderately low p, this number is significantly reduced. Moreover, if static condensation is not employed, this number further reduces to at most a value of 8, even for high p. Preconditioning options can be up to p3 times more expensive to set up, although this difference significantly decreases for some popular preconditioners such as incomplete LU factorization. © 2013 Society for Industrial and Applied Mathematics.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/120881038en
dc.relation.urlhttp://arxiv.org/abs/1206.2948en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectisogeometric analysisen
dc.subjectiterative solversen
dc.subjectperformanceen
dc.titleThe Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elementsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas, Santa Fe, Argentinaen
dc.contributor.institutionDepartment of Applied Mathematics, Statistics, and Operational Research, The University of the Basque Country UPV/EHU and Ikerbasque, Bilbao, 48160, Spainen
dc.identifier.arxividarXiv:1206.2948en
kaust.authorCollier, Nathaniel Orenen
kaust.authorCalo, Victor M.en
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