Evaluation of Convolution Integrals at Late-times Revisited

Abstract

The late-time evaluation of electromagnetic (EM) field quantities yielded by convolution integrals that combine Green's functions available at discrete time samples and strictly causal excitations is critically revisited. A typical situation is used for tracing the causes of the divergent late-time behavior that is often experienced. A framework combining a suitable integral partitioning with a polynomial approximation is shown to effectively guarantee the integrals' convergence. The formulation is validated via numerical experiments evidencing its accuracy and computational efficacy. The method is amenable to be used in a wide range of problems requiring the late-time evaluation of convolution integrals of the indicated type.