Analysis of Convolution Quadrature Applied to the Time-Domain Electric Field Integral Equation

Abstract

We show how to apply convolution quadrature (CQ) to approximate the time domain electric field integral equation (EFIE) for electromagnetic scattering. By a suitable choice of CQ, we prove that the method is unconditionally stable and has the optimal order of convergence. Surprisingly, the resulting semi- discrete EFIE is dispersive and dissipative, and we analyze this phenomena. Finally, we present numerical results supporting and extending our convergence analysis.