Three-Dimensional Higher Order PML Based on Alternating Direction Implicit Algorithm

Wu, Peiyu; Jiang, Hao; Xie, Yong; Niu, Li Qiang

doi:10.1109/lawp.2019.2944896

Cited by 25 publications

(19 citation statements)

References 15 publications

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“…y at both sides of the equations and split the resultants, one obtains where A n is the other terms at right sides of (27). The equations can be solved by two steps as…”

Section: Theoretical Approachmentioning

confidence: 99%

“…For the top boundary condition, we obtain Thus, by employing the PBC, the matrices in (29)-(30) can be given as It can be observed that the matrices are no longer tri-diagonal matrices which can not be solve by employing the Thomas algorithm. Thus, an alternative method, the RCM method is employed to decrease the dimension of the matrices and improve the computational efficiency 27 .…”

Section: Theoretical Approachmentioning

confidence: 99%

“…It has been testified that the low-frequency propagation waves can not be absorbed efficiently by employing both SC-PML and CFS-PML. Thus, the higher order PML is proposed not only to alleviate such problem but also further enhanced the absorbing performance 25 – 27 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…y at both sides of the equations and split the resultants, one obtains where A n is the other terms at right sides of (27). The equations can be solved by two steps as…”

Section: Theoretical Approachmentioning

confidence: 99%

Section: Theoretical Approachmentioning

confidence: 99%

See 1 more Smart Citation

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

“…However, most of unconditionally stable higher order PML formulation can merely solve the Maxwell's equations in two-dimensions which cannot be directly employed into practical engineering [27][28][29]. Recently, unconditionally stable higher order PML formulation is proposed in three-dimensions which is based on the alternating direction implicit (ADI) procedure [30]. Comparing LOD procedure with ADI procedure, although they both solve six matrices in each iteration, the LOD procedure can reduce the coefficients and operators leading to enhanced efficiency and resource.…”

Section: Introductionmentioning

confidence: 99%

Computationally Efficient Locally One-Dimensional Algorithm for Open Region Ground Penetrating Radar Problem With Improved Absorption

Han²,

Xie

et al. 2021

IEEE Access

Self Cite

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By incorporating higher order formulation with perfectly matched layer (PML) implementation, unconditionally stable computationally efficient locally one-dimensional (LOD) algorithm with improved absorption is proposed for simulating ground penetrating radar and its open region problems in finite-difference time-domain (FDTD) algorithm. To take advantages of these methods, the proposed implementation shows characteristics of maintaining considerable accuracy, enhancing computational efficiency and improving the entire absorption. These above-mentioned advantages are illustrated through the ground penetrating radar related problem in open regions. It can be concluded from the calculation results that the proposal shows advantages of higher order formulation, PML implementation and LOD procedure which are efficient in remarkable accuracy, considerable efficiency and improved absorption with increment of CFLNs. Meanwhile, the simulation results also indicate that the proposal is an unconditionally stable procedure with the dissatisfaction of Courant-Friedrichs-Levy stability condition. INDEX TERMS Finite-difference time-domain (FDTD), Locally One-Dimensional (LOD), Perfectly matched layer (PML), Ground penetrating radar (GPR).

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“…In this systematic study, the efficient direct-splitting-based CN-FDTD (CNDS-FDTD) method with the CFS-PML scheme is proposed based on the auxiliary differential equation (ADE) method to model 3D all-dielectric photonic nanostructures with monolayer BP metasurfaces in the infrared Terahertz range. The CFS-CNDS-FDTD not only possess higher efficiency than the alternating-direction-implicit FDTD (ADI-FDTD) method [43][44][45][46] due to owning fewer loops at each time step, but is suitable for parallel computation [47][48][49] which can be used to further reduce CPU time [39].…”

Section: Introductionmentioning

confidence: 99%

Direct-Splitting-Based CN-FDTD for Modeling 2D Material Nanostructure Problems

Feng

Zhang

Zeng

et al. 2020

IEEE Open J. Antennas Propag.

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Incorporating a truncation of the complex-frequencyshifted perfectly matched layer (CFS-PML), the direct-splittingbased Crank-Nicolson finite-difference time-domain (CNDS-FDTD) is developed and applied to the infrared two-dimensional layered material (2DLM) black phosphorous (BP) metasurface implementations on the all-dielectric nanostructure. To improve extremely low efficiencies in solving infrared terahertz (THz) problems with the few-atomic-layer thickness of 2DLMs, the CFS-CNDS-FDTD is proposed in demand due to the fact that it possesses capabilities of implicit FDTD method and unsplit-field CFS-PML truncation, respectively, in completely conquering the Courant-Friedrich-Levy condition (CFL) limit and holding good performance. The temporal incremental in the CFS-CNDS-FDTD can reach 1000 times larger than that in the regular FDTD for infrared nanoscale problems centered at the 2.5 THz and then keep accurate. Three-dimensional (3D) numerical cases have been carried out to corroborate the proposed method. The CFS-CNDS-FDTD can not only achieve high accuracies and then saves several dozen times of CPU time as compared to the regular FDTD, but also pave the way for designing all-dielectric nanostructures with other 2DLM metasurfaces. Index Terms-Black phosphorous (BP), Crank-Nicolson finitedifference time-domain (CN-FDTD), complex-frequency-shifted perfectly matched layer (CFS-PML), direct-splitting (DS), metasurface, two-dimensional layered material (2DLM).

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Three-Dimensional Higher Order PML Based on Alternating Direction Implicit Algorithm

Cited by 25 publications

References 15 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

Computationally Efficient Locally One-Dimensional Algorithm for Open Region Ground Penetrating Radar Problem With Improved Absorption

Direct-Splitting-Based CN-FDTD for Modeling 2D Material Nanostructure Problems

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