Wavelet-based treatment for nonuniqueness problem of acoustic scattering using integral equations (original) (raw)

Wavelets analysis is a powerful tool to sparsify and consequently speed up the solution o f integral equations. The nonuniqueness problem which arises in solving the integral equation o f acoustic scattering at characteristic frequencies can be solved at the expense o f increasing the problem matrix size. The use of wavelets in expanding the unknown function can efficiently reduce that size since the resulting problem matrix is highly sparse. Examples are discussed for scattering on both acoustically hard and soft spheres. The results are obtained for different Daubechies wavelet orders and sparsification thresholds. A comparison is then presented based on solution accuracy and sparsity ratio.