Fast multipole method solution of three dimensional integral equation

Abstract

The fast multipole method (FMM) speeds up the matrix-vector multiply in the conjugate gradient method when it is used to solve the matrix equation iteratively. In this paper, FMM is applied to solve the electromagnetic scattering from 3D arbitrary shape conducting bodies. The electric field integral equation (EFIE), magnetic field integral equation (MFIF), and combined field integral equation (CFIE) are considered. FMM formula for CFIE has been derived, which reduces the complexity of a matrix-vector multiply from O(N2) to O(N1.5), where N is the number of unknowns. With a nonnested method, using the ray-propagation fast multipole algorithm, the cost of an FMM matrix vector multiply is reduced to O(N4/3). A multilevel fast multipole algorithm (MLFMA) is implemented, whose complexity is further reduced to O(NlogN). The FMM also requires less memory, and hence, can solve a larger problem on a small computer.