Volume 36, Issue 1
On Adaptive Wavelet Boundary Element Methods

J. Comp. Math., 36 (2018), pp. 90-109.

Published online: 2018-02

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• Abstract

The present article is concerned with the numerical solution of boundary integral equations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution's best $N$-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geometries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.

• Keywords

41A25, 65N38, 65T60.

helmut.harbrecht@unibas.ch (Helmut Harbrecht)

manuela.utzinger@unibas.ch (Manuela Utzinger)

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@Article{JCM-36-90, author = {Helmut and Harbrecht and helmut.harbrecht@unibas.ch and 5134 and Department of Mathematics and Computer Science, University of Basel, 4001 Basel, Switzerland and Helmut Harbrecht and Manuela and Utzinger and manuela.utzinger@unibas.ch and 6826 and Universit¨at Basel, Departement Mathematik und Informatik, Spiegelgasse 1, 4051 Basel, Schweiz and Manuela Utzinger}, title = {On Adaptive Wavelet Boundary Element Methods}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {1}, pages = {90--109}, abstract = {

The present article is concerned with the numerical solution of boundary integral equations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution's best $N$-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geometries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1610-m2016-0496}, url = {http://global-sci.org/intro/article_detail/jcm/10584.html} }
TY - JOUR T1 - On Adaptive Wavelet Boundary Element Methods AU - Harbrecht , Helmut AU - Utzinger , Manuela JO - Journal of Computational Mathematics VL - 1 SP - 90 EP - 109 PY - 2018 DA - 2018/02 SN - 36 DO - http://doi.org/10.4208/jcm.1610-m2016-0496 UR - https://global-sci.org/intro/article_detail/jcm/10584.html KW - Boundary element method, wavelets, adaptivity. AB -

The present article is concerned with the numerical solution of boundary integral equations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution's best $N$-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geometries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.

Helmut Harbrecht & Manuela Utzinger. (2020). On Adaptive Wavelet Boundary Element Methods. Journal of Computational Mathematics. 36 (1). 90-109. doi:10.4208/jcm.1610-m2016-0496
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