A new fast time domain integral equation solution algorithm

We propose a novel time-domain impedance matrix compression and solution method applicable to dispersive and/or layered media. The method, which we call the FFT time domain (FFTTD) method, is based on Toeplitz properties of the impedance matrix, in both temporal and spatial indices, allowing application of fast Fourier transforms (FFTs). It departs from the conventional marching-on-in-time (MOT) solution scheme, and utilizes instead an algorithm belonging to the category of superfast direct solutions for block-Toeplitz matrices. The computational cost of the proposed method scales as O(N/sub t/ N/sub s/ log/sup 2/ N/sub t/ log N/sub s/) and O(N/sub t/ N/sub s//sup 4/3/ log/sup 2/ N/sub t/ log N/sub s/) for volume and surface problems respectively, where by N/sub t/ and N/sub s/ we denote the number of temporal and spatial samples.