Eliminating the DC instability of the time domain electric field integral equation

Transient scattering of electromagnetic fields by perfect conductors is described by the time domain electric field integral equation (TD-EFIE). Discretizing this equation using a space-time Galerkin method results in a system of equations that can be solved by the marching on in time (MOT) algorithm. Unfortunately, the solution is plagued by spurious static currents (DC instability). In this contribution, a spatial Galerkin discretization is first applied to the TD-EFIE. Then, the discrete loop and star components of both basis and testing functions are separated using projection operators (thus avoiding the construction of a loop-star basis). The loop and star components are then rescaled with respect to each other by differentiating or integrating one of these components. This has the effect of removing the possibility for a DC signal to pollute the solution. A temporal Galerkin method then leads to a system that can be solved by the marching-on-in-time algorithm.