Wavelet spectral method and its application to three dimensional acoustic radiation and scattering

In this study, a wavelet approach is presented for efficient solution to three-dimensional acoustic radiation and scattering with arbitrary boundary conditions. By expanding the boundary conditions into two-dimensional biorthogonal interval wavelet bases, the boundary wavelet spectral method is established. Compared with the traditional boundary element method, the same amount of computation is used to compute the wavelet coefficients by using the wavelet weighted Gauss integral method. In the wavelet spectral method, singularity of integrals is removed by Duffy's method, and then it can be calculated by the ordinary Gauss integral method. A highly sparse coefficient matrix system, which can be solved rapidly by sparse solvers, is obtained and the accuracy of the results is still preserved. It is proved by the radiation and scattering examples that, the accuracy of wavelet spectral method is higher than that of boundary element method even though its coefficient matrix is compressed beyond 50%.