A fast multipole boundary element method for 3D multi-domain acoustic scattering problems based on the Burton–Miller formulation

Abstract

A fast multipole boundary element method (FMBEM) for 3D multi-domain acoustic scattering problems based on the Burton–Miller formulation is presented in this paper. A multi-tree structure is designed for the multi-domain FMBEM. It results in mismatch of leaves and well separate cells definition in different domains and complicates the implementation of the algorithm, especially for preconditioning. A preconditioner based on boundary blocks is devised for the multi-domain FMBEM and its efficiency in reducing the number of iterations in solving large-scale multi-domain scattering problems is demonstrated. In addition to the analytical moment, another method, based on the anti-symmetry of the moment kernel, is developed to reduce the moment computation further by a factor of two. Frequency sweep analysis of a penetrable sphere shows that the multi-domain FMBEM based on the Burton–Miller formulation can overcome the non-unique solution problem at the fictitious eigenfrequencies. Several other numerical examples are presented to demonstrate the accuracy and efficiency of the developed multi-domain FMBEM for acoustic problems. In spite of the high cost of memory and CPU time for the multi-tree structure in the multi-domain FMBEM, a large BEM model studied with a PC has 0.3 million elements corresponding to 0.6 million unknowns, which clearly shows the potential of the developed FMBEM in solving large-scale multi-domain acoustics problems.