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A new finite-difference time-domain (FDTD) formulation for modeling graphene is proposed, in which the graphene is modeled as a resistive sheet with a frequency-dependent conductivity. The formulation is first developed in the context of the vector wave finite-element time-domain and then reduced to the FDTD based on the equivalence between these two techniques. The obtained formulation is easy to implement and does not alter the original FDTD update equations. It can be applied to an existing FDTD code by simply adding a correction term to appropriate variables. One of the main contributions of this paper is analyzing the stability of the proposed formulation, which has not been done previously. [ABSTRACT FROM AUTHOR]

Two hybrid formulations combining the finite-element time-domain and the finite-difference time-domain methods are proposed for modeling dispersive materials. The methods are coupled to each other in a non-overlapping fashion using a new finite-element tearing and interconnecting algorithm. In addition, one of them is a fully unconditionally stable hybrid method, in which the time step is not restricted by a stability criterion. The effect of medium dispersion is considered using the Möbius transformation technique. The proposed methods are validated through numerical studies. [ABSTRACT FROM PUBLISHER]

A general framework to combine the finite-difference time-domain (FDTD) and the finite-element time-domain (FETD) formulations, both based on the vector wave equation, is proposed. In contrast to the existing stable hybrid FETD-FDTD, there is no transition layer between two subdomains. In addition, the stability of the proposed approach is analytically proved. This framework allows combining different FDTD and FETD formulations together. Particularly, a fully unconditionally stable hybrid method is proposed, which is proved to be energy conservative too. The key ingredient is a finite-element tearing and interconnecting method for electromagnetic problems with a new interface condition that preserves the stability of the numerical method in each region. Several numerical examples are considered in order to validate the proposed methods. The numerical results match with the reference solutions very well in all cases. [ABSTRACT FROM PUBLISHER]