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

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 hypersingular, 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 1/2nsym1/2nsym of those using the standard LF-FMBEM, where nsymnsym is the number of planes of symmetry.