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Volume 4, Issue 1
On the Influence of the Wavenumber on Compression in a Wavelet Boundary Element Method for the Helmholtz Equation

S. C. Hawkins, K. Chen & P. J. Harris

Int. J. Numer. Anal. Mod., 4 (2007), pp. 48-62.

Published online: 2007-04

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  • Abstract

We examine how the wavenumber influences the compression in a wavelet boundary element method for the Helmholtz equation. We show that for wavelets with high vanishing moments the number of nonzeros in the resulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method as optimal complexity with respect to the number of unknowns. When the mesh spacing is proportional to the wavelength, the complexity of the wavelet boundary element method is approximately proportional to the square of the number of unknowns.

  • Keywords

wavelets, boundary element method, and Helmholtz equation.

  • AMS Subject Headings

65N38, 65R20, 65T60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-48, author = {S. C. Hawkins, K. Chen and P. J. Harris}, title = {On the Influence of the Wavenumber on Compression in a Wavelet Boundary Element Method for the Helmholtz Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {1}, pages = {48--62}, abstract = {

We examine how the wavenumber influences the compression in a wavelet boundary element method for the Helmholtz equation. We show that for wavelets with high vanishing moments the number of nonzeros in the resulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method as optimal complexity with respect to the number of unknowns. When the mesh spacing is proportional to the wavelength, the complexity of the wavelet boundary element method is approximately proportional to the square of the number of unknowns.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/850.html} }
TY - JOUR T1 - On the Influence of the Wavenumber on Compression in a Wavelet Boundary Element Method for the Helmholtz Equation AU - S. C. Hawkins, K. Chen & P. J. Harris JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 48 EP - 62 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/850.html KW - wavelets, boundary element method, and Helmholtz equation. AB -

We examine how the wavenumber influences the compression in a wavelet boundary element method for the Helmholtz equation. We show that for wavelets with high vanishing moments the number of nonzeros in the resulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method as optimal complexity with respect to the number of unknowns. When the mesh spacing is proportional to the wavelength, the complexity of the wavelet boundary element method is approximately proportional to the square of the number of unknowns.

S. C. Hawkins, K. Chen and P. J. Harris. (2007). On the Influence of the Wavenumber on Compression in a Wavelet Boundary Element Method for the Helmholtz Equation. International Journal of Numerical Analysis and Modeling. 4 (1). 48-62. doi:
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