A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene

Li, Ping; Jiang, Li Jun; Bağcı, Hakan

doi:10.1109/tap.2015.2426198

Cited by 40 publications

(28 citation statements)

References 27 publications

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“…In order to consider the presence of graphene, the SIBC in (2) is incorporated by re-formulating the numerical fluxes on the basis of the Rankine-Hugoniot Jump Relations [13], [14], [26]. That is,…”

Section: B Dgtd Formulation Of Maxwell's Equationsmentioning

confidence: 99%

“…Numerical algorithms, which have been developed in recent years to characterize EM interactions on graphene-based devices include the method of moments (MoM) [8], [9], the finite difference time-domain (FDTD) method [10]- [12], the discontinuous Galerkin time-domain (DGTD) method [13], [14], and the partial element equivalent circuit (PEEC) method [15], [16]. Indeed, these algorithms have been extensively used to investigate transmission, reflection, and absorption of EM fields on graphene sheets as well as generation of graphene surface plasmon polaritons (SPPs) within the gigahertz (GHz)-terahertz (THz) frequency band.…”

Section: Introductionmentioning

confidence: 99%

“…time domain methods have to account for temporal dispersive effects. This can be done using the auxiliary differential equation method (ADE) in [13], [17] or the finite integration technique (FIT) in [14].…”

Section: Introductionmentioning

confidence: 99%

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Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects

Jiang

Bağcı

2018

IEEE Trans. Antennas Propagat.

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Abstract-It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wave number (momentum operator) q. In this paper, to account for effects of spatial dispersion on transmission of high speed signals along graphene nanoribbon (GNR) interconnects, a discontinuous Galerkin timedomain (DGTD) algorithm is proposed. The atomically-thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) incorporated into the DGTD scheme. Since the conductivity is a complicated function of q (and one cannot find an analytical Fourier transform pair between q and spatial differential operators), an exact time domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low-q assumption. This approach permits expressing the time domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second-order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation (ADE) method is utilized to eliminates the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer impedance matrix of GNR interconnects, are presented.

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Section: B Dgtd Formulation Of Maxwell's Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects

Jiang

Bağcı

2018

IEEE Trans. Antennas Propagat.

Self Cite

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“…As for more general full-wave numerical simulation, various methods are available, including but not limited to the finite integration technique (FIT) [5], the finite element method (FEM) [6], the method of moments (MOM) [7,8], and the Nyström method [9,10]. For transient electromagnetic analysis, time domain techniques are preferred, e.g., the finite-difference time-domain (FDTD) [11][12][13], discontinuous Galerkin time domain (DGTD) method [14][15][16], and the time-domain integral equation (TDIE) method [17,18].…”

Section: Introductionmentioning

confidence: 99%

“…The TDIE is based on the surface impedance boundary condition. The surface impedance is approximated by a vector fitting (VF) method, which has since its first introduction in 1999 widely applied for its robustness and efficiency [11][12][13][14][15][16][17][18][29][30][31][32][33][34]. Convolution of the temporal surface impedance and current is derived from properties of Laguerre polynomials.…”

Section: Introductionmentioning

confidence: 99%

Marching-on-in-Degree Time-Domain Integral Equation Solver for Transient Electromagnetic Analysis of Graphene

Wang

Liu

Wang³

et al. 2017

Coatings

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Abstract:The marching-on-in-degree (MOD) time-domain integral equation (TDIE) solver for the transient electromagnetic scattering of the graphene is presented in this paper. Graphene's dispersive surface impedance is approximated using rational function expressions of complex conjugate pole-residue pairs with the vector fitting (VF) method. Enforcing the surface impedance boundary condition, TDIE is established and solved in the MOD scheme, where the temporal surface impedance is carefully convoluted with the current. Unconditionally stable transient solution in time domain can be ensured. Wide frequency band information is obtained after the Fourier transform of the time domain solution. Numerical results validate the proposed method.

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Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

Dong

Chen

et al. 2022

Advances in Time‐Domain Computational Electromagnetic Methods

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In the last few decades, the discontinuous Galerkin time-domain (DGTD) method has become widely popular in various fields of engineering due the fact that it benefits from computational advantages that come with finite volume and finite element formulations. Similarly, in the field of computational electromagnetics, the superiority of the DGTD method has been quickly recognized after first few works on its formulation and 1 implementation to solve Maxwell equations. With further developments in more recent years, the DGTD method has become one of the preeminent solutions to tackle a wide variety of challenging large scale electromagnetic problems including those that require multiphysics modeling.This chapter starts with a brief introduction to the DGTD method. This introduction provides the fundamentals of numerical flux, discretization techniques that rely on vector and nodal basis functions, and incorporation of absorbing boundary conditions. This is followed by descriptions of a time-domain boundary integral(TDBI) scheme, which replaces absorbing boundary conditions within the DGTD method, and a multi-step time integration technique, which uses different time step sizes for the DGTD and TDBI parts. Numerical results show that both techniques significantly improve the efficiency, accuracy, and stability of the traditional DGTD method. Then, the chapter continues with the applications of the DGTD method to several real-life practical problems. More specifically, it describes various novel techniques developed to enable the application of the DGTD method to electromagnetic analysis of nanostructures and graphene-based devices, and multiphysics simulation of optoelectronic antennas and source generators. For each application, several numerical examples are provided to demonstrate the accuracy, efficiency, and robustness of the developed techniques.

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A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene

Cited by 40 publications

References 27 publications

Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects

Discontinuous Galerkin Time-Domain Modeling of Graphene Nanoribbon Incorporating the Spatial Dispersion Effects

Marching-on-in-Degree Time-Domain Integral Equation Solver for Transient Electromagnetic Analysis of Graphene

Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

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