An efficient and highly accurate solver for multi-body acoustic scattering problems involving rotationally symmetric scatterers

摘要

A numerical method for solving the equations modeling acoustic scattering ispresented. The method is capable of handling several dozen scatterers, each ofwhich is several wave-lengths long, on a personal work station. Even forgeometries involving cavities, solutions accurate to seven digits or betterwere obtained. The method relies on a Boundary Integral Equation formulation ofthe scattering problem, discretized using a high-order accurate Nystr\"ommethod. A hybrid iterative/direct solver is used in which a local scatteringmatrix for each body is computed, and then GMRES, accelerated by the FastMultipole Method, is used to handle reflections between the scatterers. Themain limitation of the method described is that it currently applies only toscattering bodies that are rotationally symmetric.