An Overview of Time-Domain Integral-Equation Models in Electromagnetics

Abstract

Computational electromagnetics (CEM) embraces a wide variety of formulations and numerical procedures. The basic features which distinguish problems is how the fields are propagated spatially and how they are varied temporally. Spatially, fields can be propagated using Green's functions, modal expansions, rays and the basic Maxwell curl equations. Temporally their time variation may be either harmonic as in the frequency-domain, or impulsive as in the time-domain. Because of the number of permutations that are possible, many different approaches to CEM have been developed that can provide essentially equivalent information. In this paper, we examine the specific approach of using a time-domain integral-equation (TDIE). The basic formulation will be outlined and illustrated by application to a simple problem to illustrate its salient features. Its advantages, limitations, and computational characteristics will be summarized in terms of the problem types to which it is applicable, the kinds of information which it can provide, and computer storage and running time required. Our goal is to characterize models using the TDIE and to put the approach into perspective relative to other tools of computational electromagnetics.