### 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 re-sulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method has 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.

Original language | English |
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Pages (from-to) | 48-62 |

Number of pages | 15 |

Journal | International Journal of Numerical Analysis and Modeling |

Volume | 4 |

Issue number | 1 |

Publication status | Published - 2007 |

### Keywords

- Wavelets
- Boundary element method
- Helmholtz equation

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## Cite this

Hawkins, S. C., Chen, K., & Harris, P. (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. http://www.math.ualberta.ca/ijnam/Volume-4-2007/No-1-07/2007-01-04.pdf