Solving the Time-Domain Magnetic Field Integral Equation for Dielectric Bodies without the Time Variable through the Use of Entire Domain Laguerre Polynomials

Abstract

In this paper, we propose a time-domain magnetic field integral equation (TD-MFIE) 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 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 as an orthonormal basis function set that is derived from the entire domain Laguerre functions. These basis functions are also used as the temporal testing. Through the use of the Laguerre functions, it is possible to perform the time derivatives in the integral equations analytically. In addition, due to the orthonormality and additivity properties of these basis functions, it is possible to eliminate the time variable completely from the computations, and therefore one does not have to worry about the Courant condition. We also propose an alternative formulation using a different expansion of the electric current. Numerical results involving equivalent currents and far fields computed by the two different implementations of the TD-MFIE are presented and compared.