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In this paper, we analyze the transient electromagnetic response from three-dimensional (3-D) dielectric bodies using a time domain PMCHW (Poggio, Miller, Chang, Harrington, Wu) integral equation. 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 by a set of orthonormal basis functions that are derived from the Laguerre functions. These basis functions are also used as the temporal testing. Use of the Laguerre polynomials as expansion functions characterizing the time variable enables one to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. We also propose an alternative formulation using a differential form of time domain PMCHW equation with a different expansion for the equivalent currents. Numerical results computed by the two proposed methods are presented and compared.

SOLUTION OF TIME DOMAIN PMCHW FORMULATION FOR TRANSIENT ELECTROMAGNETIC SCATTERING FROM ARBITRARILY SHAPED 3-D DIELECTRIC OBJECTS