Semi-analytical recursive convolution finite-element time-domain method for electromagnetic analysis of dispersive media

Based on the idea of semi-analytical convolution in digital signal processing (DSP), a new technique of finite-element time-domain (FETD) for dealing with dispersive media is presented. By comparison with semi-analytical convolution in DSP, a unified recursive formulation of semi-analytical convolution for three kinds of dispersive media models i.e. Drude model, Debye model and Lorentz model is described. This formulation includes electric field E and complex polarization vector psi. On the other hand, the weak form solution of the FETD equation on account of the idea of DSP and the iteration equation including E and psi are obtained. Then the achievement of semi-analytical recursive convolution finite-element time-domain (SARC-FETD) method is developed by combining the above two equations. Finally, the feasibility of this algorithm is validated with three-dimension numerical examples.