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dc.contributor.authorBarton, M. 
dc.contributor.authorCalo, V.M.
dc.date.accessioned2016-06-13T13:11:52Z
dc.date.available2016-06-13T13:11:52Z
dc.date.issued2016-01-01
dc.identifier.issn0045-7825
dc.identifier.urihttp://hdl.handle.net/20.500.11824/109
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 (Barton 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.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectB-splines
dc.subjectGalerkin method
dc.subjectGaussian quadrature
dc.subjectHomotopy continuation for quadrature
dc.subjectIsogeometric analysis
dc.subjectOptimal quadrature rules
dc.titleOptimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysisen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.cma.2016.02.034
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0045782516300640
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleComputer Methods in Applied Mechanics and Engineeringen_US


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