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The purpose of this contribution is to introduce a dual-primal finite-element tearing and interconnecting (DP-FETI) method for the time-domain simulation of large electromagnetic problems. The most distinctive feature of the proposed method is that the continuity of the first-time derivative of the electric field intensity is enforced across the interfaces, unlike the existing formulations in electromagnetics. A theoretical proof is provided to demonstrate that this transmission condition guarantees unconditional stability and energy preservation of the method. Since the condition number of the global interface problem is greatly reduced compared to the standard finite-element time-domain (FETD) method, an iterative solver converges in far fewer iterations. This significantly reduces the simulation time, particularly when implemented on parallel computers. It is numerically shown that the method is scalable with respect to the number of subdomains and the time-step size. The numerical results for simulation of a cavity and bandgap devices are presented to demonstrate capability, accuracy, and efficiency of the proposed time-domain DP-FETI (TD-DP-FETI). [ABSTRACT FROM AUTHOR]

An efficient method based on the recursive fast Fourier transform (FFT) to incorporate both the intra-band and inter-band conductivity terms of graphene into the finite-difference time-domain (FDTD) method is proposed. As it only requires numerical values of the conductivity, it not only does not enforce any restrictions on the conductivity models, but also can directly take into account material properties obtained from measurement. It reduces the total computational cost from O(N²) to O(N log² N) where N is the length of the unknown. The FDTD method is also modified and proven to retain the stability condition of the standard FDTD method. [ABSTRACT FROM AUTHOR]

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]