Stability properties of the MOT based time domain augmented electric field integral equation in solving low frequency problems

In this paper, a time-domain augmented electric field integral equation (TD-AEFIE) with improved current continuity equation is proposed to avoid the derivative of the charge density, which is also the unknown together with the current density. The main purpose of this improvement is to overcome the discontinue of the derivative of temporal basis function existed in the original current continuity equation. To improve the late time stability and obtain an accurate MOT solver, the numerical temporal convolutions with analytical retarded potentials are implemented and further developed in TD-AEFIE for solving low-frequency problems. In comparison with traditional methods, the presented method with the 1st-order temporal basis function achieves high precision. Numerical results for the transient scattering problems demonstrate the stability and accuracy of the proposed method in solving low frequency problems.