Quadrature blending for isogeometric analysis
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We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. To explain the observed behavior and quantify the approximation errors, we use the generalized Pythagorean eigenvalue error theorem to account for quadrature errors on the resulting weak forms . The proposed blended techniques improve the spectral accuracy of isogeometric analysis on uniform and non-uniform meshes for different polynomial orders and continuity of the basis functions. The convergence rate of the optimally blended schemes is increased by two orders with respect to the case when standard quadratures are applied. Our technique can be applied to arbitrary high-order isogeometric elements.
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Calo, Victor; Deng, Quanling; Puzyrev, Vladimir (2017)© 2017 The Authors. Published by Elsevier B.V. We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. To explain the observed behavior and quantify the approximation errors, ...
Deng, Q.; Barton, M.; Puzyrev, Vladimir; Calo, Victor (2017)We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ...
Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemesPuzyrev, Vladimir; Deng, Quanling; Calo, Victor (2017)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 ...