Dispersion optimized quadratures for isogeometric analysis

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:355

Article

Calo, Victor^1,2,3  Deng, Quanling^1,2  Puzyrev, Vladimir^1,2 

[1] Curtin Univ, Appl Geol, Kent St, Perth, WA 6102, Australia

[2] Curtin Univ, Curtin Inst Computat, Kent St, Perth, WA 6102, Australia

[3] CSIRO, Mineral Resources, Perth, WA 6152, Australia

关键词: Isogeometric analysis;    Quadrature rule;    Dispersion analysis;    Spectrum analysis;   

DOI  :  10.1016/j.cam.2019.01.025

来源: Elsevier

【 摘 要 】

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. 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. The resulting schemes increase the accuracy and robustness of isogeometric analysis for wave propagation as well as the differential eigenvalue problems. We also derive an a posteriori error estimator for the eigenvalue error based on the superconvergence result. We verify with numerical examples the analysis of the performance of the proposed schemes. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free