Efficient Calculation of 3D Fast Multipole Method (FMM) Phase Integrals using an Analytical Method

Abstract

The fast multipole method (FMM) was originally developed to reduce the computation time and memory required to calculate the scattering problems such as obtaining radar cross section (RCS) of a large object. In the FMM, it is necessary to integrate the phase of each basis region multiplied by its current basis function. However, the phase value is not a linear function, and hence its integration should be performed with care. Integrations of this type have generally been carried out numerically due to lack of an analytical solution. In this paper, we present an analytical method for the phase integral and show that this method can reduce the calculation time compared to the numerical method when a Rao-Wilton-Glisson (RWG) basis function is used as the current basis function set.