Convolution-Free Modelling of Dispersive Media in the Time-Domain Finite-Element Solution of the Vector Wave Equation

摘要

A new approach to derive finite-element time-domain (FETD) formulations for modelling a general linear dispersive media is developed. The formulation starts from the mixed FETD discretized by Whitney forms in space and the Crank-Nicolson (CN) method in time. The effect of the media dispersion is taken into account separately using a bilinear transformation approach. Having combined these equations, a formulation is reached that reduces to the second-order vector wave equation discretized by the Newmark-β method with β = 1/4 in non-dispersive media. So, our formulation can be considered as an extension of the unconditionally stable (US) vector wave equation to dispersive media using a bilinear transformation method. Therefore, it does not suffer from intrinsic limitations of the existing convolution-based formulations. Furthermore, it can be concluded that the CN-FETD is a mixed version of the vector wave equation discretized by Whitney forms in space and the US Newmark-β method in time. Finally, the formulation is applied to obtain reflection and transmission coefficients of a doubly dispersive dielectric slab and highly accurate results are reached.