Novel techniques for numerically efficient solution of multiscale problems in computational electromagnetics

Abstract Multiscale problems in numerical electromagnetics are becoming increasingly common with the advent and widespread usage of compact mobile phones, body area networks, small and nano antennas, sensors, high‐speed interconnects, integrated circuits, and complex electronic packaging structures, to name just a few commercial applications. Numerical electromagnetic modeling and simulation of structures with multiscale features are highly challenging due to the fact that electrically small as well as large features are simultaneously present in the model that demands for discretization of the computational domain such that the number of degrees of freedom is very large, thus levying a heavy burden on the computational resources. The multiscale nature of a given problem also exacerbates the challenge of generating very fine meshes that do not introduce instabilities or ill‐conditioned behaviors. In this paper, we present novel techniques for an efficient solution of multiscale problems in the time‐domain. The proposed techniques handle arbitrarily shaped objects with fine features by using the dipole moment–based method of moments (MoM) type formulation in the MoM domain and electrically large objects in the finite‐difference time‐domain (FDTD) domain. Scattered fields in the MoM domain are obtained in closed forms and directly in the time‐domain at the desired observation points on a planar interface, which are combined with the conventional FDTD update equations. The time‐domain scattered fields computed by using the MoM formulations presented herein are stable in their implementation.