Wavelet-based solution of integral equations for acoustic scattering

Authors

  • M. Hesham Engineering Math. and Phys. Dept., Faculty of Engineering, Cairo University, Giza 12211, Egypt

Keywords:

Acoustic fields, Computation theory, Integral equations, Matrix algebra, Wavelet transforms, Helmholtz integral equation, Moment matrix, Wavelet expansion, Wavelet localized functions

Abstract

In this work, the multi-resolution wavelet analysis is used to solve Helmholtz integral equation for acoustic scattering. The integral equation is solved using moment method with wavelet basis. The unknown field is expressed as a two fold summation of shifted and dilated forms of a properly chosen mother wavelet. The wavelet expansion covers the scatterer surface for distributing the wavelet localized functions. A simpler formulation of a square wavelet operator is proposed and tested in this investigation to obtain the moment matrix. The proposed operator saves some traditional stages of wavelet transform and accordingly a part of the computations required. The square matrix inversion can be implemented easily on different media. The resulting matrix can be made sparse by applying an appropriate threshold. The solution of such sparse matrix saves a large portion of the computational load. The accuracy of the proposed solution is compared to the exact solution of the problem. Computational savings are illustrated for acoustic scattering on a sphere for different wave numbers and wavelet bases order.

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Published

2006-03-01

How to Cite

1.
Hesham M. Wavelet-based solution of integral equations for acoustic scattering. Canadian Acoustics [Internet]. 2006 Mar. 1 [cited 2022 Jan. 18];34(1):19-27. Available from: https://jcaa.caa-aca.ca/index.php/jcaa/article/view/1785

Issue

Section

Technical Articles