Efficient technique in low-frequency fast multipole boundary element method for plane-symmetric acoustic problems

摘要

The fast multipole boundary element method (FMBEM) has been well known as a highly efficient BEM with the use of the fast multipole method (FMM). In the present paper, an efficient technique for plane-symmetric acoustic problems is proposed in the framework of an FMBEM based on the original multipole expansion theory (FMBEM for low-frequency problems: LF-FMBEM). Presented here are concrete computational procedures, which are based on the symmetries among multipole expansion coefficients for a plane-symmetric sound field produced by monopole or dipole sources. The proposed technique is straightforwardly applicable to a variety of formulations for the BEM, such as hypersin-gular, Burton-Miller, and indirect formulations. Numerical results show an ideal improvement of computational efficiency, with the proposed technique reducing both the computation time and required memory to about 1/2~(n_(sym)) of those using the standard LF-FMBEM, where n_(sym) is the number of planes of symmetry.