dc.contributor.author Barton, M. dc.contributor.author Puzyrev, V. dc.contributor.author Deng, Q. dc.contributor.author Calo, V.M. dc.date.accessioned 2019-11-14T13:57:24Z dc.date.available 2019-11-14T13:57:24Z dc.date.issued 2019-12-14 dc.identifier.issn 0377- 0427 dc.identifier.uri http://hdl.handle.net/20.500.11824/1042 dc.description.abstract Calabr{\`o} et al. [10] changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of magnitude faster. Considering a B-spline basis function as a non-negative measure, each mass matrix row is integrated by its own quadrature rule with respect to that measure. Each rule is easy to compute as it leads to a linear system of equations, however, the quadrature rules are of the Newton-Cotes type, that is, they require a number of quadrature points that is equal to the dimension of the spline space. In this work, we propose weighted quadrature rules of Gaussian type which require the minimum number of quadrature points while guaranteeing exactness of integration with respect to the weight function. The weighted Gaussian rules arise as solutions of non-linear systems of equations. We derive rules for the mass and stiffness matrices for uniform $C^1$ quadratic and $C^2$ cubic isogeometric discretizations. en_US In each parameter direction, our rules require locally only $p+1$ quadrature points, $p$ being the polynomial degree. While the nodes cannot be reused for various weight functions as in [10], the computational cost of the mass and stiffness matrix assembly is comparable. dc.description.sponsorship RYC-2017-22649 en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject weighted Gaussian quadrature en_US dc.subject B-splines en_US dc.subject isogeometric analysis en_US dc.subject mass and stiffness matrix assembly en_US dc.title Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines en_US dc.type info:eu-repo/semantics/article en_US dc.relation.projectID ES/1PE/SEV-2017-0718 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Journal of Computational and Applied Mathematics en_US
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