hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

被引：9

作者：

Gimperlein, Heiko ^{[1
,2
,3
]}

Ozdemir, Ceyhun ^{[4
]}

Stark, David ^{[1
,2
]}

Stephan, Ernst P. ^{[4
]}

机构：

[1] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[3] Univ Paderborn, Inst Math, Warburger Str 100, D-33098 Paderborn, Germany

[4] Leibniz Univ Hannover, Inst Appl Math, D-30167 Hannover, Germany

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2019年 / 356卷

基金：

英国工程与自然科学研究理事会;

关键词：

Boundary element method; Approximation properties; hp methods; Asymptotic expansion; Wave equation; WEAKLY SINGULAR-OPERATORS; P-VERSION; INTEGRAL-EQUATIONS; APPROXIMATION; CONVERGENCE; LAPLACIAN; CRACK;

D O I：

10.1016/j.cma.2019.07.018

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R-3 exhibit singular behavior from the edges and corners. We present quasi-optimal hp-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an hp-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：145 / 174

页数：30

共 20 条

[1] The hp-version of the boundary element method with quasi-uniform meshes for weakly singular operators on surfaces
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[8] New development of the P and H-P version finite element method with quasi-uniform meshes for elliptic problems
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[10] Sparse convolution quadrature for time domain boundary integral formulations of the wave equation
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