Boundary wavelet spectral element method and its applications to exterior acoustic problems

Based on wavelet spectral method and boundary element method, a boundary wavelet spectral element method was proposed in this study. We compute the wavelet coefficients by using the wavelet weighted Gauss integral method, and the same order of operations are needed compared with traditional boundary element method. In the process of computing the coefficients, the singularity of integral is removed by Duffy's method, and then it can be calculated by the ordinary Gauss integral method. A highly sparse matrix system, which can be solved rapidly by sparse solvers, is obtained and the accuracy is still preserved. The method has been tested by acoustic radiation and scattering problems for non-smooth bodies, and good results are obtained. It has been concluded that boundary wavelet spectral element method not only possesses the properties of high accuracy and good compression, but also possesses the properties of flexibility and adaptability as the traditional boundary element method.