A Finite Difference Delay Modeling Approach to the Discretization of the Time Domain Integral Equations of Electromagnetics

A new method for solving the time-domain integral equations of electromagnetic scattering from conductors is introduced. This method, called finite difference delay modeling, appears to be completely stable and accurate when applied to arbitrary structures. The temporal discretization used is based on finite differences. Specifically, based on a mapping from the Laplace domain to the z-transform domain, first- and second-order unconditionally stable methods are derived. Spatial convergence is achieved using the higher-order divergence-conforming vector bases of Graglia et al. Low frequency instability problems are avoided with the loop-tree decomposition approach. Numerical results will illustrate the accuracy and stability of the technique.