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dc.contributor.authorBarton, M. 
dc.contributor.authorPuzyrev, V.
dc.contributor.authorDeng, Q.
dc.contributor.authorCalo, V.M.
dc.identifier.issn0377- 0427
dc.description.abstractCalabr{\`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. 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.en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectweighted Gaussian quadratureen_US
dc.subjectisogeometric analysisen_US
dc.subjectmass and stiffness matrix assemblyen_US
dc.titleEfficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splinesen_US
dc.journal.titleJournal of Computational and Applied Mathematicsen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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