An stable and accurate time-marching solution of the time-domain electric integral equation

The well-known marching-on-in-time (MOT) method is usually adopted to solve the time-domain integral equations (TDIE) for transient scattering problems. However, the MOT method suffers from a tendency to instability, which obviously hampers its development and wide application. We employ transformations of the parametric coordinates and Duffy´s coordinates transformation to transform the singular integrals of the time-domain electric field integral equation (TDEFIE) into non-singular integrals, which can be accurately and efficiently evaluated by dividing the transformed domain of integration into sub-domains.