Fast algorithms for the electromagnetic simulation of planar structures

This paper reviews the state of the art in fast integral equation techniques for solving large scale electromagnetic radiation and compatibility problems. The fast multipole method (FMM) and its frequency and time domain derivatives are discussed. These techniques permit the rapid evaluation of fields due to known sources and hence accelerate the solution of boundary value problems arising in the analysis of a wide variety of electromagnetic phenomena. Specifically, the application of the steepest descent fast multipole method (SDFMM) and the thin stratified medium fast multipole algorithm (TSM-FMA) to the frequency domain analysis of radiation from microstrip structures residing on finite and infinite substrates and ground planes, respectively, is described. In addition, the extension of the FMM concept to plane wave time domain (PWTD) algorithms that permit the analysis of transient phenomena is outlined.