Electromagnetic scattering from homogeneous dielectric bodies using the finite difference delay modeling method

In recent years, time domain integral equation (TDIE) based methods for solving electromagnetic problems have become popular due to improvements in their stability and accuracy. Particular attention has been paid to conductive scatterers. One scheme uses noncausal temporal bases and bandlimited extrapolation technique applying on the conductors, and then makes an extension to the dielectric bodies. While this approach is very accurate, it only works for small step sizes and can be made unstable in rare cases. Other methods can be made stable in all cases but cannot model curved geometry. A newer method, called finite difference delay modeling (FDDM), appears to be absolutely stable and accurate. The temporal discretization is made based on a finite difference inspired mapping from the Laplace domain to the z-transform domain. In this paper, we continue to extend this new scheme to model the scattering from homogeneous dielectric bodies based on the coupled Poggio-Miller-Chang-Harrington-Wu (Tsai) (PMCHW) equations. First- and second-order unconditionally stable methods are applied. The FDDM method has predictable stability and absolute convergence properties when applied to arbitrary structures. Low frequency instability problems can be avoided by well-known stabilization techniques.