Complex multipole beam approach to acoustic scattering problems

A novel approach to reducing the matrix size associated with the boundary element/moment method solution of the problem of acoustic scattering from arbitrarily shaped closed bodies is presented in this paper. The key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space. On the scatterer boundary, the fields generated by these multipole sources resemble the Gabor basis functions. By utilizing the properties of the Gabor series, guidelines for selecting the orders as well as locations of the multipole sources are developed. The present approach not only reduces the number of unknowns, but also generates a generalized impedance matrix with a banded structure. The accuracy of the proposed method is verified by using internal accuracy checks and by comparing the numerical results with the analytic solutions for spherical scatterers.