Time-Domain Analysis of Two-Dimensional Scattering Problems by Use of a Source-Model Technique

Time-domain integral equation based solution techniques have gradually shifted over the last couple of years into the focus of computational electromagnetics research [1]. In this paper, we present a mesh-free time-domain integral equation solution for the problem of electromagnetic scattering by a two-dimensional metallic cylinder illuminated by a TM (transverse magnetic) plane wave pulse. In the proposed solution, we adapt the frequency-domain source model technique (SMT) [2], which has been found to be efficient and versatile computational tool for analysis of time-harmonic wave scattering problems, to allow direct time-domain analysis of transient scattering problems. In this approach, instead of formulating the problem in terms of the current induced on the cylinder surface, it is formulated in terms of a fictitious current residing on a mathematical surface interior to the cylinder surface. A spatio-temporal division for attaining an explicit discretization scheme, which allows the use of a simple marching-on-intime (MOT) algorithm, is presented. The use of an implicit discretization scheme is also discussed, and the advantages of such a scheme are outlined. Finally, the use of a combined-source formulation and its effect on the resulting stability is studied.