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dc.contributor.authorCollier, Nathan
dc.contributor.authorDalcin, Lisandro
dc.contributor.authorPardo, David
dc.contributor.authorCalo, Victor M.
dc.date.accessioned2015-05-25T08:29:32Z
dc.date.available2015-05-25T08:29:32Z
dc.date.issued2013-03-19
dc.identifier.citationThe Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements 2013, 35 (2):A767 SIAM Journal on Scientific Computing
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/120881038
dc.identifier.urihttp://hdl.handle.net/10754/555666
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.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/120881038
dc.relation.urlhttp://arxiv.org/abs/1206.2948
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.subjectisogeometric analysis
dc.subjectiterative solvers
dc.subjectperformance
dc.titleThe Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Division
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas, Santa Fe, Argentina
dc.contributor.institutionDepartment of Applied Mathematics, Statistics, and Operational Research, The University of the Basque Country UPV/EHU and Ikerbasque, Bilbao, 48160, Spain
dc.identifier.arxividarXiv:1206.2948
kaust.personCollier, Nathan
kaust.personCalo, Victor M.
refterms.dateFOA2018-06-13T14:07:46Z
dc.date.published-online2013-03-19
dc.date.published-print2013-01
dc.date.posted2012-06-13


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