Stable and accurate solution of time-domain electric field integral equation

The time-domain electric, magnetic and combined field integral equations (TDEFIE, TDMFIE and TDCFIE) have been applied widely to the analysis of transient scattering from conducting bodies. The marching-on-in-time (MOT) schemes, relying on suitable spatial integral rules and an implicit time-stepping method, have been found to be always stable for solving the TDCFIE and TDMFIE. Unfortunately, the same is not true for the TDEFIE. The non-singular integral is evaluated using the standard Gaussian quadrature rules, and the transformations of the parametric coordinates and plane polar coordinates are employed to transform the singular integrals of TDEFIE into non-singular integrals, which can be accurately and efficiently evaluated by dividing the original domain of integration into sub-domains. Simulation results demonstrate that this approach produces rather stable and more accurate results without resort to any averaging processes. It is more important that this method suits any temporal basis functions and can be extended to high-order spatial basis functions.