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Efficient quadrature for NURBS-based isogeometric analysis. (English) Zbl 1227.65029
Summary: 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 of the basis. Efficient rules require taking into account the precise smoothness of basis functions across element boundaries. Several rules of practical interest are obtained, and a numerical procedure for determining efficient rules is presented.
We compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics. The new rules represent improvements over those used previously in isogeometric analysis.

65D32 Numerical quadrature and cubature formulas
65D07 Numerical computation using splines
Full Text: DOI
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