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 ERE 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.