Error reduced ADI-FDTD methods

Ahmed, Iftikhar; Chen, Zhizhang

doi:10.1109/lawp.2005.855630

Cited by 41 publications

(36 citation statements)

References 5 publications

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“…In [6], Zheng clarified that the A-ADI FDTD method is more efficient than the traditional ADI FDTD method to reduce the numerical dispersion error. The 2-D TE-z problem illustrated inside Figure 6 consists of two 2-m-long parallel conducting plates in free space separated by a distance of 0.02 m, used in [8] and [9] for comparison of numerical errors. The numerical experiments were done with a 750-kHz raised cosine, which was held constant after reaching its maximum of 1 V, and cell sizes of 0.02 m along the x and y directions.…”

Section: Analysis Of Numerical Errorsmentioning

confidence: 99%

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Reduction of numerical dispersion by optimizing second‐order cross product derivative term in the ADI‐FDTD method

Kong

Kim

Park

2007

Micro & Optical Tech Letters

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Section: Analysis Of Numerical Errorsmentioning

confidence: 99%

“…Two main approaches have been proposed for the synthesis of metamaterial transmission lines: the dual transmission line model [5][6][7] and the resonant-type approach [8,9]. In the former one, a host line is loaded with series connected capacitances and shunt inductances.…”

Section: Introductionmentioning

confidence: 99%

Reduction of numerical dispersion by optimizing second‐order cross product derivative term in the ADI‐FDTD method

Kong

Kim

Park

2007

Micro & Optical Tech Letters

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“…Nevertheless, it presents large numerical dispersion error with large time steps. To improve the dispersion performance, several methods were proposed, such as error-reduced [6], iterative [7,8], parameter-optimized [9][10][11][12], and artificial-anisotropy methods [13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Two Efficient Unconditionally-Stable Four-Stages Split-Step FDTD Methods With Low Numerical Dispersion

Kong¹,

Chu²,

Li³

2013

PIER B

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Abstract-Two efficient unconditionally-stable four-stages splitstep (SS) finite-difference time-domain (FDTD) methods based on controlling parameters are presented, which provide low numerical dispersion. Firstly, in the first proposed method, the Maxwell's matrix is split into four sub-matrices. Simultaneously, two controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into four sub-steps. The second proposed method is obtained by adjusting the sequence of the submatrices deduced in the first method. Secondly, the theoretical proofs of the unconditional stability and dispersion relations of the proposed methods are given. Furthermore, the processes of obtaining the controlling parameters for the proposed methods are shown. Thirdly, the dispersion characteristics of the proposed methods are also investigated, and numerical dispersion errors of the proposed methods can be decreased significantly. Finally, to substantiate the efficiency of the proposed methods, numerical experiments are presented.

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“…Some methods have been reported for ordinary FDTD based on implicit FDTD to overcome the Courant stability restraint on the time step of fully explicit FDTD. ADI-FDTD [13][14][15][16], and LOD-FDTD [17][18][19][20][21] have been developed for this purpose. In this way, up to 5 times reduction in computation times have been reported [21].…”

Section: Introductionmentioning

confidence: 99%

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

Shahmansouri¹,

Rashidian²

2012

PIER

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Abstract-Split-field finite-difference time-domain (SF-FDTD) method can overcome the limitation of ordinary FDTD in analyzing periodic structures under oblique incidence. On the other hand, huge run times of 3D SF-FDTD, is practically a major burden in its usage for analysis and design of nanostructures, particularly when having dispersive media. Here, details of parallel implementation of 3D SF-FDTD method for dispersive media, combined with totalfield/scattered-field (TF/SF) method for injecting oblique plane wave, are discussed. Graphics processing unit (GPU) has been used for this purpose, and very large speed up factors have been achieved. Also a previously reported formulation of SF-FDTD based on the Drude model for dispersive media, is extended to cover Drude-Lorentz model, which is usually needed for materials such as gold. The resulting reduction in the number of variables in this formulation, not only helps in reducing the computational time, but also makes it possible to be implemented in GPU, where its memory limitation is a major concern. As an example for demonstrating the importance of this method in optimization of nanophotonics structures, improvement in the performance of a refractive index sensor, made of an array of nanodisks, using suitable angle of incidence is reported. To the best of our knowledge this is the first report of GPU implementation of SF-FDTD method, capable of analyzing periodic dispersive media under oblique incidence.

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Error reduced ADI-FDTD methods

Cited by 41 publications

References 5 publications

Reduction of numerical dispersion by optimizing second‐order cross product derivative term in the ADI‐FDTD method

Reduction of numerical dispersion by optimizing second‐order cross product derivative term in the ADI‐FDTD method

Two Efficient Unconditionally-Stable Four-Stages Split-Step FDTD Methods With Low Numerical Dispersion

Gpu Implementation of Split-Field Finite-Difference Time-Domain Method for Drude-Lorentz Dispersive Media

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