Scattering analysis via time-domain integral equations: methods to reduce the scaling of cost with frequency

Methods are described by which very large reductions in the cost of time-domain integral-equation scattering computations can be achieved, associated with a reduction in the scaling of operation count with frequency from the fifth to the fourth, or even third, power. There is an accompanying reduction in storage scaling from the fourth to a third, or even second, power of frequency. The additional physical approximation inherent in the methods can be implemented, and the associated degradation in accuracy assessed and the accompanying cost savings estimated, without implementation of the method itself. This is done in this paper. As an example of the results, the head-on backscatter from a four-wavelength NASA almond could be obtained ~1 dB less accurately, at a cost more than an order of magnitude lower. This factor by which costs are reduced would increase with problem size. The issues and difficulties involved in implementation of both the fourth- and third-power approaches are identified and discussed