Matching criteria and the accuracy of time domain adaptive integral method

The fast Fourier transform (FFT) is successfully used to accelerate the solution of both frequency- and time-domain integral equations. One of the most general and practical FFT-based algorithms is the adaptive integral method (AIM) (see Bleszynski, E. et al., Radio Science, vol.31, no.5, p.1225-51, 1996). The AIM separates the method of moments matrix into near and far-field components, computes the near-field components directly, and approximates the far-field components by using an auxiliary uniform mesh. The repeated multiplications of the far-field components by past and trial current vectors in the time-marching and iterative solution of time- and frequency-domain integral equations are efficiently computed using FFTs. Specifically, AIM (as well as other FFT-based algorithms) reduces the complexity of marching-on-in-time (MOT) based time-domain integral equation solvers (see Bleszynski et al., IEEE APS Int. Symp. Dig., p.176-80, 2001). We consider the MOT-based solution of an electric field integral equation (EFIE) pertinent to the analysis of scattering from a perfect electrically conducting body that resides in unbounded lossless dielectric media. The time-domain AIM for accelerating MOT solvers is reviewed and two methods for approximating the far-field components are compared on their relative merits in terms of accuracy and complexity.