Wavelet-based solution of integral equations for acoustic scattering
Keywords:Acoustic fields, Computation theory, Integral equations, Matrix algebra, Wavelet transforms, Helmholtz integral equation, Moment matrix, Wavelet expansion, Wavelet localized functions
AbstractIn 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.
How to Cite
Copyright on articles is held by the author(s). The corresponding author has the right to grant on behalf of all authors and does grant on behalf of all authors, a worldwide exclusive licence (or non-exclusive license for government employees) to the Publishers and its licensees in perpetuity, in all forms, formats and media (whether known now or created in the future)
i) to publish, reproduce, distribute, display and store the Contribution;
ii) to translate the Contribution into other languages, create adaptations, reprints, include within collections and create summaries, extracts and/or, abstracts of the Contribution;
iii) to exploit all subsidiary rights in the Contribution,
iv) to provide the inclusion of electronic links from the Contribution to third party material where-ever it may be located;
v) to licence any third party to do any or all of the above.