Time-domain combined field integral equation using laguerre polynomials as temporal basis functions

In this paper, we propose a novel formulation to solve the time-domain combined field integral equation (TD-CFIE) for analysing the transient electromagnetic response from three-dimensional (3D) closed conducting bodies. Instead of the conventional marching-on in time (MOT) technique, the solution methods in this paper are based on the Galerkin's method that involves separate spatial and temporal testing procedure. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3D closed structures. The time-domain unknown coefficient is approximated as an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. With the representation of the derivative of the transient coefficient in an analytic form, the time derivative terms in the integral equations can be handled analytically. We also propose an alternative formulation to solve the TD-CFIE. Two methods are presented that results in very accurate and stable transient responses from conducting objects. Numerical results are presented and compared with the inverse discrete Fourier transform (IDFT) of frequency-domain combined field integral equation (FD-CFIE) solutions.