Complex materials are of increasing interest in Finite-Difference Time-Domain modeling. For example, when the particle density becomes large, collisional fluid models of plasmas are an attractive alternative to particle in cell methods. Further, frequency dispersive meta-materials are of increasing interest. Thus, Finite-Difference Time-Domain (FDTD) models are derived for magnetized plasmas and for the Lorentz and Drude material models. Previous models of these types of materials make assumptions that may unnecessarily restrict the simulation time step. By considering the solution of the differential equations on the interval of a time step, these assumptions are avoided. Studies show that the resulting magnetized plasma model is numerically stable when the FDTD Courant condition and the Nyquist sampling theorem for the plasma and cyclotron frequencies are obeyed. Waves propagating in the modeled plasma exhibit the correct dispersion relations. Studies also show the Lorentz and Drude material models to be stable up to the FDTD Courant limit and to exhibit the correct dispersion relations.
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