Mesh truncation conditions for finite element/finite difference simulations of electromagnetic wave phenomena in unbounded regions.

Abstract

A new local method for finite difference/finite element mesh truncation in the frequency domain is investigated. The method is based on the Measured Equation of Invariance (MEI) concept recently proposed by Mei, et al. (1) for the numerical solution of electro-magnetic wave scattering by perfectly conducting targets in unbounded regions. An MEI is a numerically derived discrete, linear equation which relates the field at a given boundary node to the field values at neighboring nodes. For each boundary node, a different MEI is constructed. Given such a condition for each node, a computationally efficient and accurate FD/FE grid truncation can be achieved. Since the derivation of the MEI is not based on any far-field assumptions, unlike most other local methods, the mesh truncation condition can be applied just a few cells away from the scatterer's boundary. The method is extended to treat the case of penetrable scatterers. Three different approaches are considered. The first is based upon a direct application of Huygen's principle. The second relies on equivalent source concepts. The final method proposed employs a distribution of multipoles, referred to as multiple multipoles, to generate the MEI's. The MEI-based mesh truncation conditions are implemented for the first time in a finite element formulation and numerical results are presented for time-harmonic scattering by a variety of two-dimensional targets. The feasibility of constructing an accurate truncation condition for the mesh interior to a homogeneous penetrable scatterer is also examined. In addition to the study conducted for finite difference/finite element mesh truncation in the frequency domain, a time domain truncation scheme based on the principles of linearity and superposition is considered. The method is demonstrated for a guided wave structure.