Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis

Dispersion-minimizing quadrature rules for C quadratic isogeometric analysis

Dispersion-minimizing quadrature rules for C quadratic isogeometric analysis Quanling Deng, Michael Bartoň, Vladimir Puzyrev, Victor Calo aDepartment of Applied Geology, Curtin University, Kent Street, Bentley, Perth, WA 6102, Australia bBasque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain cMineral Resources, CSIRO, Kensington, Perth, WA 6152, Aust...

Dispersion-optimized quadrature rules for isogeometric analysis: modified inner products, their dispersion properties, and optimally blended schemes

This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeomet...

Efficient Quadrature for High Degree Isogeometric Analysis

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Efficient quadrature for NURBS-based isogeometric analysis

We initiate the study of efficient quadrature rules for NURBS-based isogeometric analysis. A rule of thumb emerges, the “half-point rule”, indicating that optimal rules involve a number of points roughly equal to half the number of degrees-of-freedom, or equivalently half the number of basis functions of the space under consideration. The half-point rule is independent of the polynomial order o...

Quadrature Rules for Fuzzy Integrals