An Efficient Galerkin Scheme to Solve the Time Domain Integral Equation for Wire-Grid Models Involving Multiple Incident Pulses

In this work, a straight forward method of moments (MOM) procedure to solve the time domain integral equation (TDIE) is presented and applied to a wire-grid model of an arbitrarily-shaped conducting body. The conducting body is illuminated by a Gaussian plane wave. Contrary to all the available time domain algorithms, the present procedure does not involve marching in time thus eliminating error accumulation, a major source for late-time instability problem. The procedure presented in this work is conceptually simple, numerically efficient, and handles multiple excitations in a trivial manner, all the while remaining stable. The numerical procedure utilizes pulse functions for space variable and time-shifted Gaussian functions for time variable, respectively. Further, the numerical procedure adopts the Galerkin method of solution implying the usage of the same time and space functions for both expansion and testing. The numerical results obtained in the time domain are validated by comparing with the data obtained from the frequency domain solution at several frequencies and performing an inverse discrete Fourier transform.