Time-domain electromagnetic computations using a modified EFIE kernel and field-source equilibrium relations

A form for the electric-field dyadic Green\´s function for free space is derived that allows explicit time evolution of the modified electric-field integral equation (EFIE) applied to surface scattering. The modified EFIE kernel, here called a "source function," has an integrable singularity in the source region, and is shown to be equivalent, in the frequency domain, to the standard dyadic Green\´s function. With definitions of "local" and "non-local" fields at a conductor surface, both electric and magnetic versions of the relations between non-local fields and equilibrium surface sources (currents and charges) are derived. These field-source equilibrium (FSE) relations are exact if all the non-local fields are included: the interaction fields, as well as the usual incident fields from distant sources. When the interaction fields are neglected, the magnetic-field version of the FSE relations becomes the usual physical optics approximation. Source functions and the FSE relations were used in two three-dimensional, time-domain numerical simulations to compute radiation patterns from a conical helical antenna driven at a fixed frequency, and scattering of a CW plane wave by a perfectly conducting sphere. This surface-scattering simulation was explicit but remained stable. Excellent agreement between the computed and known results validated the approach.