2-D Unconditionally Stable CFS-PML Based on CNDG for Truncating Unmagnetized Plasma Media

Li, Jianxiong; Shi, Xueyang; Jiang, Haolin

doi:10.1109/lmwc.2017.2678429

Cited by 5 publications

(12 citation statements)

References 8 publications

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“…The updated equation of auxiliary field obtained by PLRC method can be calculated as By substituting (21) and (22) into (23), the updated equation of magnetic component in the y-direction can be given as…”

Section: Theoretical Approachmentioning

confidence: 99%

Extraordinary optical transmission through periodic Drude-like graphene sheets using FDTD algorithms and its unconditionally stable approximate Crank–Nicolson implementation

Sun

Chi

et al. 2020

Sci Rep

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Based upon the approximate Crank–Nicolson (CN) finite-difference time-domain method implementation, the unconditionally stable algorithm is proposed to investigate the wave propagation and transmission through extremely thin graphene layers. More precisely, by incorporating the CN Douglas–Gunn algorithm, the piecewise linear recursive convolution method and the auxiliary differential equation method, the analytical model is proposed for Drude-like graphene model. To obtain the solution of the governing equations, the perfectly matched layer and the periodic boundary condition are applied to the graphene structure with two dimensional nano-materials. Numerical examples are carried out for further investigation. During the simulation, the influences of the parameters such as the grating slit and its thickness on the wave transmission are investigated and discussed. The result shows that not only the graphene grating has high transmission performance but also the proposed methods have considerable performance and accuracy.

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Section: Theoretical Approachmentioning

confidence: 99%

Extraordinary optical transmission through periodic Drude-like graphene sheets using FDTD algorithms and its unconditionally stable approximate Crank–Nicolson implementation

Sun

Chi

et al. 2020

Sci Rep

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show abstract

“…where ( ) r ε ω is the complex relative permittivity of the isotropic dispersive media. In the following, the implementations of the CNDG-CFS-PML based on the ADE method [34][35][36] 5and 8- (14) in [32].…”

Section: Formulationmentioning

confidence: 99%

“…where t ∆ is the time step. After discretizing the time domain expressions of x H , y H , z D and the auxiliary variables y g , x g , x f , y f by CN scheme and then substituting 7into the expression of z D , one obtains the same discrete equations as (17)- (23) in [32]. The differences are the coefficients…”

Section: Formulationmentioning

confidence: 99%

“…Due to the frequency dependent material properties, some special technologies have been developed to derive the time-domain updated equations, such as the ADE method [24], Z-transform method [25], recursive convolution (RC) method [26], piecewise linear recursive convolution (PLRC) method [27], trapezoidal recursive convolution (TRC) method [28], and so on. Synthetically considering the three aspects above, some PML algorithms based on unconditionally stable FDTD were presented to truncate dispersive media [29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we extend the content of [32] and discuss in detail the CNDG-CFS-PML algorithm, using different shapes of computational domains for the purpose of demonstrating the effectiveness of the algorithm. Furthermore, for the simplicity of formula derivation, the algorithm also combines different PML processing techniques and different analysis methods of the electric field reasonably according to the relative permittivity of dispersive media to illustrate its versatility.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Implementation of the Crank‐Nicolson Douglas‐Gunn finite‐difference time domain with complex frequency‐shifted perfectly matched layer for modeling unbounded isotropic dispersive media in two dimensions

Shi

Jiang

2019

Micro & Optical Tech Letters

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To model open-domain problems with Drude, Lorentz, and Debye media, the complex frequency-shifted perfectly matched layer (CFS-PML) is adopted to truncate the Crank-Nicolson Douglas-Gunn finite-difference time-domain (CNDG-FDTD) region. The auxiliary differential equation (ADE) and the bilinear Z-transform (BZT) methods are incorporated separately into the implementations of CNDG-CFS-PML formulations, while the ADE, piecewise linear recursive convolution (PLRC), and trapezoidal recursive convolution (TRC) methods are utilized to model dispersive media. The proposed formulations can not only circumvent the stability condition, but have the advantages of the CFS-PML in attenuating the evanescent waves and reducing the late-time reflection. Three numerical examples have been carried out to validate these formulations. The simulation results show that the proposed CNDG-CFS-PML algorithm is efficient in absorbing performance and saving more computational time compared with the conventional FDTD method, which leads to extensive applicability and acts as a very good prospect.

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Bandpass signal formulation with hybrid implicit‐explicit procedure in open regions for unmagnetized plasma

Wang²,

Xie

et al. 2021

Int J RF Microw Comput Aided Eng

Self Cite

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The finite-difference time-domain (FDTD) algorithm shows disadvantages in bandpass signal simulation with fine structures along a single direction. The reason is that FDTD algorithm exists the Courant-Friedrichs-Levy (CFL) condition and bases on the lowpass-sampling theorem. Based on the numerical implementation, hybrid implicit-explicit procedure and complex envelope method are introduced. As a full-wave simulation method, higher order concept is incorporated into perfectly matched layer (PML) formulation for improving absorption at boundaries of the lattice. For unmagnetized plasma simulation, piecewise linear recursive convolution method is modified according to the bandpass signal. Through numerical example, the proposed algorithm shows considerable performance during the entire simulation which can be concluded from several aspects: (1) It takes advantages of higher order concept which shows enhanced absorption. ( 2) The proposed algorithm can overcome the CFL condition and maintain stability with the increment of time steps. (3) It shows considerable efficiency and accuracy in simulating structures with fine details along a single direction. (4) It can alleviate time increment problem among implicit algorithms with lower CFL numbers.

show abstract

2-D Unconditionally Stable CFS-PML Based on CNDG for Truncating Unmagnetized Plasma Media

Cited by 5 publications

References 8 publications

Extraordinary optical transmission through periodic Drude-like graphene sheets using FDTD algorithms and its unconditionally stable approximate Crank–Nicolson implementation

Extraordinary optical transmission through periodic Drude-like graphene sheets using FDTD algorithms and its unconditionally stable approximate Crank–Nicolson implementation

Implementation of the Crank‐Nicolson Douglas‐Gunn finite‐difference time domain with complex frequency‐shifted perfectly matched layer for modeling unbounded isotropic dispersive media in two dimensions

Bandpass signal formulation with hybrid implicit‐explicit procedure in open regions for unmagnetized plasma

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