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Volume 36, Issue 1
On Adaptive Wavelet Boundary Element Methods

Helmut Harbrecht & Manuela Utzinger

DOI: 10.4208/jcm.1610-m2016-0496

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

Boundary element method, wavelets, adaptivity.

  • AMS Subject Headings

41A25, 65N38, 65T60.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

helmut.harbrecht@unibas.ch (Helmut Harbrecht)

manuela.utzinger@unibas.ch (Manuela Utzinger)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-90, author = {Harbrecht , Helmut and Utzinger , Manuela}, 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.

Harbrecht , Helmut and Utzinger , Manuela. (2018). 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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