Costs and cost scaling in time-domain integral-equation analysis of electromagnetic scattering

Computation of scattering from multi-wavelength bodies is expensive, and costs scale with up to the sixth power of incident frequency. Conventional integral-equation time-domain methods have costs scaling with the fifth power. Here are described modifications to the TETD approach that offer the prospect of a reduction in cost scaling, to possibly the third power of frequency, and an associated large reduction in cost. The approach exploits the pulsed nature of the illumination, which results in surface fields that are small most of the time over most of the body, on bodies that are electrically large. Neglect of these produces some modest increase in error, but allows large reductions in cost and storage requirements. In the examples shown, cost reductions by amounts approaching two orders of magnitude are obtained, with the factor by which casts are reduced itself increasing with roughly the square of the body size; storage requirements are rendered essentially negligible.