On the use of wavelet transform for the integral-equation solution of acoustic radiation and scattering

In present integral equation methods for acoustic problems, a full matrix equation whose solution has a high computational cost is usually resulted. In this paper, a new wavelet approach is presented for efficient solution of the two-dimensional and axisymmetric acoustic radiation and scattering problems with arbitrary boundary conditions. On the basis of two-dimensional and axisyrmmetric iategral equations, the boundary quantities are expanded in terms of orthogonal or periodic, orthogonal wavelet basis functions and the geometrical representation of the Boundary Element Method is employed to treat the curved computational domain. The approximate analytical formulation deals directly with the singularities for two-dimensional problems and the singular integrals are computed directly by employing highly accurate three-dimensional integration techniques for axisyrnmetric problems. The advantages of the new approach are a highly sparse matrix system which can be solved rapidly by sparse solvers and accurately modeling of curve surface. The results from the new approach are compared with the BEM, the analytical solutions, which demonstrate that the new technique has fast convergence and good accuracy.