Effective Use of Hierarchical Cell Structure for the Fast Multipole Boundary Element Method

The fast multipole boundary element method (FMBEM) is an advanced BEM that leads to drastic reduction of processing time and memory requirements in large-scale steady-state sound field analyses. In the FMBEM, hi-erarchical cell structure is employed to apply multipole expansion in multiple levels, and the setting of the hier-archical cell structure considerably affects the computa-tional efficiency of the FMBEM. This paper deals with effective use of hierarchical cell structure for taking full advantage of the FMBEM. In the former part of the paper, the effect of geometrical arrangement of the cell structure and that of treatment of translation coefficients between cells are investigated through numerical studies. An ef-fective setting of the cell structure is proposed from the results. In the latter half, an efficient method for analyses of symmetrical sound fields is proposed. Both the compu-tational complexity and memory requirements with this method are about 1/2 as small as those with the conven-tional FMBEM. The method is validated through numer-ical study. 1