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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Deng, Quanling; Calo, Victor (2018)We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural vibration, which we model as a second-order differential eigenvalue problem. The dispersion-minimized mass reduces the ...
Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric AnalysisBarton, M.; Calo, Victor; Deng, Quanling; Puzyrev, Vladimir (2018)© 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric ...
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 ...