An accurate solution to time domain integral equations for homogeneous dielectric bodies using loop-tree decomposition and bandlimited extrapolation

This work presents a stable and accurate method to solve the electromagnetic scattering from homogeneous dielectric scatterers using time domain integral equations (TDIE). In particular, it applies a loop-tree decomposition to the spatial testing functions and separately handles the solenoidal testing functions. For this purpose, the presented TDIE solver uses Rao-Wilton-Glisson (RWG) basis functions and bandlimited interpolatory functions (BLIF) to discretize the integral equations spatially and temporally, respectively, and implements a bandlimited extrapolation technique to overcome the noncausality introduced by the BLIF. Numerical results presented in this paper demonstrate the accuracy and stability of the method and illustrate the exponential convergence with respect to a temporal discretization parameter.