An introduction to the fast-MoM in computational electromagnetics

Abstract

Summary form only given. The characterisation and design of microwave packaging, and the need for predicting the radiation directivity and interference pattern of novel interconnect structures, and also the necessity for validating simpler models, all require rigorous numerical methods and fast algorithms which allow parallel computing. To this end integral- rather than differential-formulations seem to be advantageous. The various formulations of integral equations in computational electromagnetics involve volume and surface integrals, which, generally, have to be solved numerically. For nearly three decades Harrington's method of moments (MoMs) has been successfully used to discretize these integrals and to obtain reliable approximations to the field solutions. However, MoM has three drawbacks: (1) The resulting (frequency-dependent impedance) matrices are dense. (2) The interaction coefficients (nondiagonal matrix elements) are Fourier-type integrals, and their numerical calculation is comparatively time consuming. (3) The selfaction coefficients (diagonal matrix elements) are Fourier-type singular integrals, and have to be evaluated carefully in Cauchy's sense (Hadamard's finite part). The author's recent efforts to remove these drawbacks have led to the fast-MoM. In many applications fast-MoM eliminates the difficulties in (2) and (3), and if combined with the wavelet analysis relaxes the drawback in (1). In this review the author first briefly points out useful features of the wavelet theory, and emphasizes the role of iterative techniques for solving large matrix equations. He then focuses on the problems in (2) and (3).