Toeplitz property on order indices of Laguerre expansion methods

The unconditionally stable solution of time-domain integral equations by the classical marching-on-in-order schemes demands O(N_t ³N_s ²) CPU cycles, where N_t and N_s are the number of temporal and spatial unknowns, respectively. Discrete fast Fourier transform (FFT)-based algorithms are proffered to expedite the recursive temporal convolution products of the Toeplitz block aggregates of the retarded interaction matrices through which the overall computational cost and memory requirements reduces to O(alpha(N_s)N_tlog(N_t)) and O(N_talpha(N_s)), respectively. Simulation results for arbitrarily shaped scatterers demonstrate the accuracy and efficiency of the technique.