Finite Difference Delay Modeling for Two-Dimensional Transverse Magnetic Time-Domain Integral Equations

A finite difference delay modeling scheme is presented for the solution of the integral equations of two-dimensional transient electromagnetic scattering. The method discretizes the integral equations temporally using first- and second-order finite differences to map the Laplace-domain equations into the Z domain, before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z -domain mapping. Spatial discretization is achieved using second-order Lagrange basis functions with Galerkin's method. Exact curved-patch geometry modeling is used. Numerical results will demonstrate the accuracy and stability of this approach.