A space-time discretization criterion for a stable time-marching solution of the electric field integral equation

Numerical techniques based on a time-domain recursive solution of the electric field integral equation (EFIE) may exhibit instability phenomena induced by the joint space-time discretization. The above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape. We analyze a particular formulation of the method of moments which relies on a triangular-patch geometrical model of the exterior surface of the scattering body and operates according to a “marching-on-in-time” scheme, whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps. A heuristic stability condition is devised which allows us to define a proper time step, as well as a geometrical discretization criterion, ensuring convergence of the numerical procedure and, therefore, eliminating insurgence of late-time oscillations. The stability condition is discussed and validated by means of a few working examples