Search

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]

A new finite-element Gaussian belief propagation (FGaBP) algorithm for multi-physics applications is presented in this paper. The FGaBP method is first modified for solving the heat-transfer problem and then verified against an analytical solution. Combined with a Gauss–Seidel algorithm, FGaBP is used to solve the coupled electrical–thermal problem that emerges in radiofrequency ablation of hepatic tumors while the extent of the ablated zone is computed for a simplified model. The multi-physics FGaBP algorithm preserves the parallel scalability of FGaBP as in previous uni-physics works. [ABSTRACT FROM AUTHOR]

In this paper, a new finite element Gaussian belief propagation (FGaBP) method is presented for time-domain applications. The unconditionally stable Newmark time-stepping scheme is combined with FGaBP for this purpose. As shown empirically, the method converges for increasing time step sizes without losing stability. The combined FGaBP-time stepping is able to retain the parallel scalability from FGaBP as in previous work. In addition, this paper also shows that lossy material properties can be easily supported by the method with minimal changes to its formulation. [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]

The finite-element time-domain (FETD) solution of the vector wave equation (VWE) is directly extended to doubly dispersive media using the bilinear transform approach. The proposed formulation is quite general and flexible in the sense of material dispersion model in contrast to limitations of existing convolutional-based approaches. In addition, it can be implemented in a very straightforward and efficient manner. A stability analysis is performed that demonstrates the unconditional stability of the original formulation is preserved in the dispersive case. However, in order to avoid the well-known late-time instabilities that arise in this formulation, an alternative formulation is considered and extended to the dispersive case with the same approach. Several numerical examples are simulated to verify the validity and accuracy of the proposed formulations. The late-time stability of the alternative formulation is tested through a numerical example with 20 million time steps. The solution is completely free from late-time growth. [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]

Several finite-element time-domain (FETD) formulations to model inhomogeneous and electrically/magnetically/doubly dispersive materials based on the second-order vector wave equation discretized by the Newmark-\beta scheme are developed. In contrast to the existing formulations, which employ recursive convolution (RC) approaches, we use a Möbius transformation method to derive our new formulations. Hence, the obtained equations are not only simpler in form and easier to derive and implement, but also do not suffer from the intrinsic limitations of the RC methods in modeling arbitrary high-order media. To obtain the formulations, we first demonstrate that the update equation for the electric field strength \e\ in the mixed Crank-Nicolson (CN) FETD formulation, which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first-order differential equations using Crank-Nicolson scheme in time, is equivalent to the unconditionally stable (US) second-order vector wave equation for the same variable (\e\) discretized by the Newmark-\beta method with \beta =1/4. In addition, we show that the update equation for the magnetic flux density \b\ in CN-FETD is the same as the second-order vector wave equation for \b\ on the dual grid discretized again by a similar Newmark-\beta method. [ABSTRACT FROM PUBLISHER]

In this letter, we describe an easy approach to implement the first-order Bayliss-Turkel-like absorbing boundary condition (ABC) in two mixed finite-element time-domain (FETD) formulations, namely the Crank–Nicolson FETD (CN-FETD) and the leap-frog FETD (LF-FETD). The idea is to introduce a current source distribution on the outer boundary of the domain such that it cancels outgoing waves. The current distribution is obtained based on the ABC relation. In addition, we show that the CN-FETD and the LF-FETD are equivalent to the FETD based on the vector wave equation discretized by the Newmark-\beta method in time with \beta=1/4 and 0, respectively. Having utilized these equivalences, we demonstrate that our approach to implement the ABC in the mixed formulations lead to the same result as the vector wave FETD truncated with the same ABC. A numerical example is provided to validate our formulations. [ABSTRACT FROM PUBLISHER]