Wavelet-based treatment for nonuniqueness problem of acoustic scattering using integral equations
Keywords:Function evaluation, Functions, Integral equations, Natural frequencies, Problem solving, Wavelet transforms, Daubechies wavelet, Sparsity ratio, Wavelet-based treatment
AbstractWavelets analysis is a powerful tool to sparsify and consequently speed up the solution of integral equations. The nonuniqueness problem which arises in solving the integral equation of acoustic scattering at characteristic frequencies can be solved at the expense of 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.
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