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.
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机译：我们提出了一种适用于色散和/或分层介质的新型时域阻抗矩阵压缩和求解方法。我们将这种方法称为FFT时域（FFTTD）方法，该方法基于阻抗矩阵的Toeplitz属性（在时间和空间索引上），可以应用快速傅里叶变换（FFT）。它与常规的按时行进（MOT）解决方案不同，而是使用一种算法来属于块Toeplitz矩阵的超快速直接解。所提出的方法的计算成本缩放为O（N / sub t / N / sub s / log / sup 2 / N / sub t / log N / sub s /）和O（N / sub t / N / sub s /） // sup 4/3 / log / sup 2 / N / sub t / log N / sub s /）分别表示体积和表面问题，其中N / sub t /和N / sub s /表示时间数和空间样本。
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