When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k?

被引：0

作者：

Graham, I. G. ^{[1
]}

Loehndorf, M. ^{[2
]}

Melenk, J. M. ^{[3
]}

Spence, E. A. ^{[1
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Kapsch TrafficCom, A-1120 Vienna, Austria

[3] Tech Univ Wien, Inst Anal & Sci Comp, A-1040 Vienna, Austria

来源：

BIT NUMERICAL MATHEMATICS | 2015年 / 55卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Helmholtz equation; High frequency; Boundary integral equation; Boundary element method; Pollution effect; FREQUENCY ACOUSTIC SCATTERING; INTEGRAL-OPERATORS; WAVE-NUMBER; CONVEX POLYGONS; ELEMENT METHOD; INDEFINITE; APPROXIMATION;

D O I：

10.1007/s10543-014-0501-5

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We consider solving the sound-soft scattering problem for the Helmholtz equation with the -version of the boundary element method using the standard second-kind combined-field integral equations. We obtain sufficient conditions for the relative best approximation error to be bounded independently of . For certain geometries, these rigorously justify the commonly-held belief that a fixed number of degrees of freedom per wavelength is sufficient to keep the relative best approximation error bounded independently of . We then obtain sufficient conditions for the Galerkin method to be quasi-optimal, with the constant of quasi-optimality independent of . Numerical experiments indicate that, while these conditions for quasi-optimality are sufficient, they are not necessary for many geometries.

引用

页码：171 / 214

页数：44

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