Numerical calculation of scattering from a conducting sphere by using Greengard-Rokhlin's fast multipole algorithm

Fast multipole algorithms (FMAs) are used in the numerical calculation of EM wave scattering as the acceleration technique. Previously, we applied Greengard-Rokhlin's FMA (GRFMA) (Greengard, L. and Rokhlin, V., J. Comput. Phys., vol.73. p.325-48, 1987) to the numerical calculation of two-dimensional scattering and reduced the order of floating-point operations and the amount of used memory for the matrix-vector product to O(L), where L is the size of the matrix (Nakashima, N. and Tateiba, M., Proc. IEEE AP-S. vol.2. p.606-9, 2002; Proc. IEICE ISAP-i02, p.193-6, 2002). We now apply GRFMA to the numerical calculation of scattering from a conducting sphere as a simple example of three-dimensional scattering, and estimate the orders of both the computation time and used memory.