Dispersion optimized quadratures for isogeometric analysis
For researchers in isogeometric analysis, this work provides a method to enhance accuracy in wave propagation and eigenvalue problems, though it is an incremental improvement over existing quadrature techniques.
This paper develops quadrature blending schemes that minimize dispersion error in isogeometric analysis up to polynomial order seven, achieving two extra orders of convergence (superconvergence) on eigenvalue errors while maintaining optimal eigenfunction convergence. The schemes improve accuracy and robustness for wave propagation and eigenvalue problems.
We develop and analyze quadrature blending schemes that minimize the dispersion error of isogeometric analysis up to polynomial order seven with maximum continuity in the span ($C^{p-1}$). The schemes yield two extra orders of convergence (superconvergence) on the eigenvalue errors, while the eigenfunction errors are of optimal convergence order. Both dispersion and spectrum analysis are unified in the form of a Taylor expansion for eigenvalue errors. As a consequence, the schemes increase the accuracy and robustness of isogeometric analysis for wave propagation as well as the differential eigenvalue problems. We analyze the methods' robustness and efficacy and utilize numerical examples to verify our analysis of the performance of the proposed schemes.