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dc.contributor.author
Collier, Nathan
dc.contributor.author
Dalcin, Lisandro Daniel
dc.contributor.author
Calo, Victor
dc.contributor.author
Pardo, David
dc.date.available
2016-12-01T21:08:07Z
dc.date.issued
2013-03
dc.identifier.citation
Collier, Nathan; Dalcin, Lisandro Daniel; Calo, Victor; Pardo, David; The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements; Siam Publications; Siam Journal On Scientific Computing; 35; 2; 3-2013; 767-784
dc.identifier.issn
1064-8275
dc.identifier.uri
http://hdl.handle.net/11336/8633
dc.description.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 C0 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 hand 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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Siam Publications
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Isogeometric Analysis
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Iterative Solvers
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Performance
dc.subject.classification
Mecánica Aplicada
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Ingeniería Mecánica
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INGENIERÍAS Y TECNOLOGÍAS
dc.title
The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-11-24T14:13:19Z
dc.journal.volume
35
dc.journal.number
2
dc.journal.pagination
767-784
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Philadelphia
dc.description.fil
Fil: Collier, Nathan. King Abdullah University of Science and Technology; Arabia Saudita
dc.description.fil
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina
dc.description.fil
Fil: Calo, Victor. The University of the Basque Country UPV/EHU and Ikerbasque; España
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Fil: Pardo, David. King Abdullah University of Science and Technology; Arabia Saudita
dc.journal.title
Siam Journal On Scientific Computing
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1137/120881038
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/120881038?journalCode=sjoce3