Adaptive BEM with optimal convergence rates for the Helmholtz equation

被引：13

作者：

Bespalov, Alex ^{[1
]}

Betcke, Timo ^{[2
]}

Haberl, Alexander ^{[3
]}

Praetorius, Dirk ^{[3
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[2] UCL, Ctr Inverse Problems, Gower St, London WC1E 6BT, England

[3] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2019年 / 346卷

基金：

英国工程与自然科学研究理事会; 奥地利科学基金会;

关键词：

Boundary element method; Helmholtz equation; A posteriori error estimate; Adaptive algorithm; Convergence; Optimality; BOUNDARY-ELEMENT METHODS; POSTERIORI ERROR ESTIMATE; INTEGRAL-EQUATIONS; SCATTERING; EFFICIENCY; ALGORITHM; SURFACES; FEM;

D O I：

10.1016/j.cma.2018.12.006

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：260 / 287

页数：28

共 46 条

[21] Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [J].

Feischl, Michael ;

Gantner, Gregor ;

Praetorius, Dirk .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 290 :362-386

[22] Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, part I: weakly-singular integral equation [J].

Feischl, Michael ;

Fuehrer, Thomas ;

Karkulik, Michael ;

Melenk, Jens Markus ;

Praetorius, Dirk .

CALCOLO, 2014, 51 (04) :531-562

[23]

Fuhrer Thomas, 2018, NUMER MATH

[24]

Gantner G, 2017, THESIS TU WIEN

[25] Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines [J].

Gantner, Gregor ;

Haberlik, Daniel ;

Praetorius, Dirk .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2017, 27 (14) :2631-2674

[26] Convergence Rates of Adaptive Methods, Besov Spaces, and Multilevel Approximation [J].

Gantumur, Tsogtgerel .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2017, 17 (04) :917-956

[27] Adaptive boundary element methods with convergence rates [J].

Gantumur, Tsogtgerel .

NUMERISCHE MATHEMATIK, 2013, 124 (03) :471-516

[28] Inverse-type estimates on hp-finite element spaces and applications [J].

Georgoulis, Emmanuil H. .

MATHEMATICS OF COMPUTATION, 2008, 77 (261) :201-219

[29] Finite elements on degenerate meshes: inverse-type inequalities and applications [J].

Graham, IG ;

Hackbusch, W ;

Sauter, SA .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2005, 25 (02) :379-407

[30] Anisotropic mesh refinement: The conditioning of Galerkin boundary element matrices and simple preconditioners [J].

Graham, Ivan G. ;

Mclean, William .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (04) :1487-1513

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