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 here 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-intime'' 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.