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dc.contributor.authorBarton, Michael
dc.contributor.authorCalo, Victor M.
dc.date.accessioned2016-03-15T13:51:12Z
dc.date.available2016-03-15T13:51:12Z
dc.date.issued2016-03-14
dc.identifier.citationOptimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis 2016 Computer Methods in Applied Mechanics and Engineering
dc.identifier.issn00457825
dc.identifier.doi10.1016/j.cma.2016.02.034
dc.identifier.urihttp://hdl.handle.net/10754/601360
dc.description.abstractWe introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Bartoň and Calo, 2016) that transforms optimal quadrature rules from source spaces to target spaces, we derive optimal rules for splines defined on finite domains. Starting with the classical Gaussian quadrature for polynomials, which is an optimal rule for a discontinuous odd-degree space, we derive rules for target spaces of higher continuity. We further show how the homotopy methodology handles cases where the source and target rules require different numbers of optimal quadrature points. We demonstrate it by deriving optimal rules for various odd-degree spline spaces, particularly with non-uniform knot sequences and non-uniform multiplicities. We also discuss convergence of our rules to their asymptotic counterparts, that is, the analogues of the midpoint rule of Hughes et al. (2010), that are exact and optimal for infinite domains. For spaces of low continuities, we numerically show that the derived rules quickly converge to their asymptotic counterparts as the weights and nodes of a few boundary elements differ from the asymptotic values.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0045782516300640
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 14 March 2016. DOI: 10.1016/j.cma.2016.02.034
dc.subjectOptimal quadrature rules
dc.subjectGalerkin method
dc.subjectGaussian quadrature
dc.subjectB-splines
dc.subjectIsogeometric analysis
dc.subjectHomotopy continuation for quadrature
dc.titleOptimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
dc.typeArticle
dc.contributor.departmentCenter for Numerical Porous Media (NumPor)
dc.identifier.journalComputer Methods in Applied Mechanics and Engineering
dc.eprint.versionPost-print
dc.contributor.institutionBasque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
dc.contributor.institutionChair in Computational Geoscience Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Kent Street, Bentley, Perth, Western Australia, 6102, Australia
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personBarton, Michael
kaust.personCalo, Victor M.
refterms.dateFOA2018-03-14T00:00:00Z


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