Fast analysis of transient scattering in lossy media

2002, IEEE Antennas and Wireless Propagation Letters

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AI-generated Abstract

This letter presents a fast Fourier transform (FFT)-based algorithm designed to reduce the computational complexity associated with traditional marching-on-in-time (MOT) methods for analyzing transient electromagnetic (EM) scattering in unbounded lossy media. The proposed approach significantly lowers the operational count from O(N^2) to O(N log N), allowing efficient analysis of perfectly conducting structures. The algorithm takes advantage of the convolutional nature of time-stepping and employs a combination of temporal and spatial FFTs to efficiently process simulations, which is validated through numerical examples.

Figures (5)

Let S denote the surface of a perfect electrically conducting body residing in a lossy homogeneous background with con- stant conductivity a, permeability j, and permittivity ¢. An in- cident transient electric field E™(r, t) induces a surface cur- rent density J(r, ¢) on S; this current, in turn, radiates a scat- tered field. Assuming that E™¢(r, t) does not interact with $ for ¢ < 0 and forcing the total electric field tangential to S to vanish leads to the following time-domain EFIE:

Fig. 1. The system of equations (4) in matrix form. The matrices form a lower diagonal Toeplitz structure due to the time invariance and causality of the Green’s function and uniform time stepping. As the algorithm progresses, larger blocks can be multiplied via the FFT.

Fig. 2. Transient current density at the center of a 6 m X 6 m perfectly conducting plate. solver, transient scattering from a 6 m x 6 m conducting square plate lying on the r—y plane is analyzed. The incident field is a 4 polarized plane wave pulse traveling in the —Z direction with Gaussian temporal signature at z = 0. The incident pulse is modulated at 200 MHz, and 99.997% of the power of the Gaussian is in the frequency band 150-250 MHz. The conductivity of the medium is ¢ = 3 x 1073 S/m, and the skin depth at 200 MHz is 1.8 m. The plate current is represented using N, = 7080 spatial rooftop basis functions (on a 60 x 60 mesh), and T(t) is chosen to be a cubic polynomial interpolation function [16]. The simulation is carried out for 500 time steps with At = 0.2083 ns. The magnitude of the y-directed current density at the center of the plate is shown in Fig. 2, which demonstrates that the scheme exhibits late-time stability. In Fig. 3, the components of the scattered field 6 m away from the center of the plate in the x—y plane are displayed. The results from the proposed solver are compared with those obtained by a frequency domain code based on the conjugate gradient (CG)-FFT algorithm [14] at 200 MHz. Both results are practically identical.

Fig.4. Total time spent on computing the convolutions in (4) by an FFT-MOT based simulator with and without using temporal FFTs. Fig. 3. The magnitude of the (a) r- and (b) @-components of the scattered electric field 6 m away from the center of the plate at the x—y plane.