Fast Evaluation of Matrix Elements in Time-Domain Integral Equation Analysis of Planar Structures

Abstract

This paper proposes an efficient method for the evaluation of impedance/admittance matrix elements in time-domain integral equation analysis of uniformly meshed planar structures. In this method, the computation time related to the numerical integration of the required double surface integrals is remarkably reduced by discretizing the integration surfaces in equally spaced quadrature points and using the spatial translation invariant characteristic of the Green's function. It is shown that the computational burden of the proposed method scales as $O({N_q })$ , where $N_q $ is the number of the quadrature points in one integration patch. This feature will remarkably improves the computation time when compared to $O({N_q^2 })$ offered by the conventional quadrature rules. The simulation results of the two cases of a circular aperture located on a parallel plate waveguide and a doubly periodic perfectly conducting structure residing in free space demonstrate the efficiency of the proposed method over its rivals. The accuracy of the proposed method will also be confirmed by comparing the results with those obtained using a commercial finite integration technique and a frequency-domain solver.