The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

The fast multipole method (FMM) has been implemented to speed up the matrix‐vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N2) to O(N1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592‐unknown problem can be solved within 24 h on a SUN Sparc 10. © 1995 John Wiley & Sons, Inc.

In this paper, we present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

ABSTRACT|-FISC (Fast Illinois Solver Code) is designed to compute RCS of a target described by a triangular facet le. The problem is formulated by the method of moments (MoM), where the RWG (Rao, Wilton, and Glisson) basis functions are used. The resultant matrix equation is solved iteratively by the conjugate gradient (CG) method. The multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiply in CG. Both complexities for the CPU time per iteration and memory requirements are of O(N logN), where N is the number of unknowns.

The fast multipole method is used to solve the electromagnetic scattering from three‐dimensional conducting bodies of arbitrary shape. The electric field integral equation is discretized by the method of moments. Instead of directly computing the matrix‐vector multiplication, which needs N2 multiplications, this approach reduces the complexity to O(N1.5). © 1994 John Wiley & Sons, Inc.