Application of Analytical Expressions for Retarded-Time Potentials in Analyzing the Transient Scattering by Dielectric Objects

Application of analytical formulas for the retarded-time potentials in Müller- and PMCHWT-type time-domain integral equations (TDIEs) is presented. The impulsively excited scalar and vector potentials are evaluated in closed form, and the coupling coefficients can be calculated with high accuracy. Examples of transient analysis of the electromagnetic scattering from dielectric objects are provided and solved with marching-on-in-time (MOT) method. Numerical results show that solutions for Müller-type MOT TDIE are always stable if the coupling coefficients are accurately evaluated, while the PMCHWT type usually suffers from the dc instability.