Recent Applications of Multipole Expansions in Computational Electromagnetics

Abstract

Multipole expansions can be regarded as a classical analytical method in Electromagnetics [Jac98] [Str41], however they are of considerable interest for numerical procedures as well. Generally, multipole methods allow an efficient calculation of electromagnetic fields, for instance to evaluate the interference between radiating systems. Since each of the multipole terms can be regarded as a mode, the expansion allows a simple physical interpretation. This contribution starts with an introduction into the spherical-multipole analysis of electromagnetic fields. Two applications of multipole expansions will be discussed: First a brief summary of the Fast-Multipole Method will be given, then a procedure is described which shows how the benefits from multipole representations can be exploited to efficiently represent and post-process numerically or asymptotically obtained results.