Transient electromagnetic scattering from dielectric objects using the electric field Integral equation with Laguerre polynomials as temporal basis functions

In this paper, we propose a time-domain electric field integral equation (TD-EFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin´s method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the Laguerre functions. These basis functions are also used as the temporal testing functions. Use of the Laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables. Thus, the time variable along with the Courant condition can be eliminated in a Galerkin formulation using this procedure. We also propose an alternative formulation using a different expansion of the magnetic current. The total computational cost for this new method is similar to that of an implicit marching-on in time (MOT)-EFIE scheme, even though at each step this procedure requires more computations. Numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared.