A fast and stable solver for acoustic scattering problems based on the nonuniform grid approach

A fast and stable boundary element method (BEM) algorithm for solving external problems of acoustic scattering by impenetrable bodies is developed. The method employs the Burton-Miller integral equation, which provides stable convergence of iterative solvers, and a generalized multilevel nonuniform grid (MLNG) algorithm for fast evaluation of field integrals. The MLNG approach is used here for the removal of computational bottlenecks involved with repeated matrix-vector multiplications as well as for the low-order basis function regularization of the hyper-singular integral kernel. The method is used for calculating the fields scattered by large acoustic scatterers, including nonconvex bodies with piece-wise smooth surfaces. As a result, the algorithm is capable of accurately incorporating high-frequency effects such as creeping waves and multiple-edges diffractions. In all cases, stable convergence of the method is observed. High accuracy of the method is demonstrated by comparison with the traditional BEM solution. The computational complexity of the method in terms of both the computation time and storage is estimated in practical computations and shown to be close to the asymptotic O(N log N) dependence.