FFT Accelerated Marching-on-in-Order Methods

A fast, yet unconditionally stable, solution of time-domain electric field integral equations (EFIE) pertinent to the scattering analysis of uniformly meshed conducting structures is introduced. A discrete fast Fourier transform (FFT)-based algorithm is proffered to expedite the recursive spatial convolution products of the Toeplitz-block-Toeplitz retarded interaction matrices in a new marching-without-time-variable scheme. The total computational cost and storage requirements of the proposed method scales as O(N_t ² N_slog(N_s)) and O(N_tN_s), respectively, as opposed to O(N_t ² N_s ²) and O(N_tN² _s) for classical marching-on-in-order methods, where N_t and N_s are the number of temporal and spatial unknowns, respectively. Simulation results for long strip, platelike, and cylindrical scatterers demonstrate the accuracy and efficiency of the technique.