Isogeometric spectral approximation for elliptic differential operators

被引：7
作者：
Deng, Quanling [1 ,2 ]
Puzyrev, Vladimir [1 ,2 ]
Calo, Victor [1 ,2 ,3 ]
机构：
[1] Curtin Univ, Curtin Inst Computat, Kent St, Perth, WA 6102, Australia
[2] Curtin Univ, Dept Appl Geol, Kent St, Perth, WA 6102, Australia
[3] CSIRO, Mineral Resources, Perth, WA 6152, Australia
来源：
JOURNAL OF COMPUTATIONAL SCIENCE | 2019年 / 36卷
关键词：
Differential operator; Spectral approximation; Isogeometric analysis; Optimally-blended quadratures; Schrodinger operator; FINITE-ELEMENT; QUADRATURE-RULES; WAVE-PROPAGATION; SPLINE SPACES; EIGENVALUE; DISPERSION; NURBS;
D O I：
10.1016/j.jocs.2018.05.009
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally-blended quadrature rules for the isogeometric spectral approximation of a diffusion-reaction operator with both Dirichlet and Neumann boundary conditions. The blended rules improve the accuracy of the isogeometric approximation. In particular, the optimal blending rules minimize the dispersion error and lead to two extra orders of super-convergence in the eigenvalue error. Various numerical examples (including the Schrodinger operator for quantum mechanics) in one and three spatial dimensions demonstrate the performance of the blended rules. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页数：7
相关论文
共 42 条
[41]   Spectral approximation properties of isogeometric analysis with variable continuity [J].
Puzyrev, Vladimir ;
Deng, Quanling ;
Calo, Victor .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 334 :22-39
[42]   Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes [J].
Puzyrev, Vladimir ;
Deng, Quanling ;
Calo, Victor .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 320 :421-443
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