Analysis of Transient Scattering for Rectangular Incident Waves using the Discrete Laguerre Transforms

摘要

By expressing the transient electromagnetic behaviors in terms of continuous orthonormal Laguerre polynomials, we can obtain an unconditionally stable solution of the time domain electric field integral equation (TD-EFIE) for three-dimensional (3-D) arbitrary shaped conducting bodies. Besides using Gaussian type pulses, rectangular and triangular pulses are also used as incident waves in this method. However, because of the discontinuity in a rectangular pulse, Gibbs phenomenon will occur around the point of discontinuity when a continuous basis functions are used to approximate the incident wave in a least square sense. Noting that we deal with discrete data during our computation in a computer, we introduce the discrete Laugerre functions to solve TD-EFIE. They are exactly othonormal in a discrete sense. In this paper, we use the discrete Laguerre basis functions to approximate its continuous counterparts and then use them to express the rectangular incident wave and the response. Simulation results show that there's no Gibbs phenomenon. Furthermore, the computation of the Laguerre transform of the incident wave is more efficient.