An adaptive expansion technique in the fast multipole method for 3D acoustics problems at low frequencies

An adaptive expansion technique is introduced to the implement fast multipole method (FMM) for acoustics problems at low frequencies in this work. This technique determines the number of expansion terms in multipole to local (M2L) translations according to the distance between the two interaction boxes. As a consequence, the computational efficiency of the fast multipole method is improved significantly. In addition, the numerical examples demonstrate the adaptive algorithm is valid for the hyper-singular boundary face method (HBFM) with FMM and the dual boundary face method (CHBFM) with FMM, although it is obtained by the conventional boundary face method (CBFM) with FMM.