Traditional boundary element methods with a full matrix equation for acoustic problems, have been met by a challenge in large-scale scientific computation and numerical simulation in engineering. In this paper, the new wavelet approaches have been presented for solving acoustic radiation and scattering, and structural-acoustic coupling. The boundary quantities are expanded in terms of a basis of the orthogonal wavelets on the interval, and a wavelet spectral formulation for solving acoustic problems is derived. Then coupled wavelet spectral and finite element method is formulated for solving sound-structure interaction. The advantages of the new approaches include a highly sparse matrix system which can be solved rapidly by sparse solvers and accurate modeling of curve surface. In the new technique, the iterative technique of frequencies is established for evaluating frequency-response functions through expanding the integral kernel in Taylor series in integral equation. The new technique was employed to investigate the underwater acoustic radiation from a complicate structure which is composed of shells, stiffening ribs and plates. The comparisons of the results from the new technique with analytic solution show that it has high computational efficiency and good accuracy.

At the end of the paper, the prospects of the application of wavelet analysis to numerical computation in acoustic engineering are discussed.