An Unconditionally Stable One-Step Arbitrary-Order Leapfrog ADI-FDTD Method and Its Numerical Properties

Yang, Shunchuan; Chen, Zhizhang; Yu, Yiqiang; Wang, Yin

doi:10.1109/tap.2012.2186249

Cited by 87 publications

(46 citation statements)

References 16 publications

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“…As the initial parameter of A is equals to 1, and then the initial parameter value C y0 can be obtained, as shown in (30).…”

Section: Determination Of Controlling Parametersmentioning

confidence: 99%

See 1 more Smart Citation

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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“…As the initial parameter of A is equals to 1, and then the initial parameter value C y0 can be obtained, as shown in (30).…”

Section: Determination Of Controlling Parametersmentioning

confidence: 99%

“…Along the same line, other unconditionally stable methods such as split-step [19][20][21][22][23][24][25][26][27], locally-one-dimensional (LOD) [28] and leapfrog ADI [29,30] FDTD methods were developed. The high-order splitstep FDTD method in [21] has six stages and is represented as 6-stages SS-FDTD herein.…”

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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“…Thererto, numerous (partially) implicit methods have been developed, one of the most successful being the Alternating-DirectionImplicit (ADI) method, which requires the solution of a set of low-rank tridiagonal systems that scale with only one dimension. The traditional ADI method has evolved from a split-step update scheme [1] to a more efficient one-step leapfrog update scheme [2], but the core of the algorithm has always relied on a smart way to split the curl trying not to break the occurring symmetry. Typically, this curl splitting is used to construct an unconditionally stable method, i.e.…”

Section: Introductionmentioning

confidence: 99%

A leapfrog alternating-direction hybrid implicit-explicit FDTD method

Londersele

Zutter

Ginste

2017

2017 IEEE International Symposium on Antennas and Propagation &Amp; USNC/URSI National Radio Science Meeting

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Abstract-A novel curl splitting technique is proposed which makes the leapfrog ADI-FDTD method better equipped for configurations requiring a higher resolution in only one or two dimensions. The proposed method, which is given the name "leapfrog ADHIE-FDTD", hybridizes implicit and explicit update equations such that the time step is solely bounded by the spatial steps in preferred dimensions. This weak conditional stability is rigorously proven and numerically validated.

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“…Recently, one-step leapfrog ADI-FDTD method was developed from the conventional ADI-FDTD method [4] where no mid time-step computations are needed. Therefore, it has better computational efficiency [5,6].…”

Section: Introductionmentioning

confidence: 99%

One-Step Leapfrog Adi-FDTD Method for Lossy Media and Its Stability Analysis

Gao¹,

Zheng²

2013

PIER Letters

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Abstract-A one-step leapfrog alternating-direction-implicit finitedifference time-domain (ADI-FDTD) method for lossy media is presented. Different from the method provided by others, the proposed method is originated from the conventional ADI-FDTD method instead of considering the leapfrog ADI-FDTD method as a perturbation of the conventional explicit FDTD method. Its unconditional stability is analytically proven through a method that combines the von Neumann method with the Jury criterion. In addition, its unconditional stability and computational efficiency are verified through numerical experiments.

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An Unconditionally Stable One-Step Arbitrary-Order Leapfrog ADI-FDTD Method and Its Numerical Properties

Cited by 87 publications

References 16 publications

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

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

A leapfrog alternating-direction hybrid implicit-explicit FDTD method

One-Step Leapfrog Adi-FDTD Method for Lossy Media and Its Stability Analysis

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