Time-domain finite element modeling of dispersive media

A general formulation is developed to model the dispersion effect in the time-domain finite element method (TDFEM). This TDFEM is based on the second-order vector wave equation, in contrast to most FDTD schemes that solve the first-order Maxwell equations. The required convolution integral is evaluated recursively without the need to store the electric fields of all past time steps. This evaluation is made to be of second order in accuracy by adopting a linear interpolation for the fields within each time step. The proposed formulation is shown to be valid for plasma, Debye, and Lorentz media with a single or multiple poles. Three-dimensional numerical examples are given to demonstrate its efficacy.