A Leapfrog Formulation of the 3D ADI-FDTD Algorithm

Cooke, S.J.; Botton, M.; Antonsen, Thomas M.; Levush, B.

doi:10.1109/cemtd.2007.4373546

Cited by 74 publications

(71 citation statements)

References 3 publications

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“…The equations for other components e y | As pointed out in [10] an additional benefit is the absence of the mixed difference terms in (65) and (66) on the contrary to (61) through (64), where the terms…”

Section: The Approximate Implicit Formulation: Adi-fdtd Methodsmentioning

confidence: 99%

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On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

Sumichrast¹

2013

Journal of Electrical Engineering

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Some strategies used in the computer simulation of wave phenomena by means of finite differences in time-domain (FDTD) method are reviewed and discussed here. It is shown that the wave equation in its discretised form possesses different properties in comparison with the true differential formulation. In this part the issues of stability and numerical dispersion for two-and three-dimensional case of wave propagation in homogeneous space are thoroughly investigated.

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Section: The Approximate Implicit Formulation: Adi-fdtd Methodsmentioning

confidence: 99%

“…The calculation can be further re-organised in a "leapfrog" way [10]. When the direction of the time axis in (61) is reversed around the point n, ie n + 1 2 ⇒ n − 1 2 , c∆ t ⇒ −c∆ t , and subtracting the result from (61) one arrives at the "leapfrog" algorithm [10] …”

Section: The Approximate Implicit Formulation: Adi-fdtd Methodsmentioning

confidence: 99%

On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

Sumichrast¹

2013

Journal of Electrical Engineering

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“…For the leapfrog ADI-FDTD method for lossless media, these coefficients are unity and permit the exact cancellation of the mixed derivative terms. However, the previous derivation of the leapfrog ADI-FDTD method [1] is no longer directly applicable for the leapfrog ADI-FDTD method for lossy media, as these coefficient are non-unity, and they do not eliminate the mixed derivative terms. Further discussion with detailed explanations of the above is provided in the Appendix.…”

Section: Formulation For Lossy Mediamentioning

confidence: 99%

“…Recently an unconditionally stable leapfrog alternating-directionimplicit finite-difference time-domain (ADI-FDTD) method that is free from the Courant-Friedrich-Lewy (CFL) stability criterion has been developed [1]. The leapfrog ADI-FDTD method is derived from the ADI-FDTD method [2][3][4], and has similar numerical stability and dispersion properties as the ADI-FDTD method [5].…”

Section: Introductionmentioning

confidence: 99%

Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media

Gan¹,

Tan²

2012

PIER M

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Abstract-This paper presents an unconditionally stable leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for lossy media. Conductivity terms of lossy media are incorporated into the leapfrog ADI-FDTD method in an analogous manner as the conventional explicit FDTD method since the leapfrog ADI-FDTD method is a perturbation of the conventional explicit FDTD method. Implementation of the leapfrog ADI-FDTD method for lossy media with special consideration for boundary condition is provided. Numerical results and examples are presented to validate the formulation.

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“…As a result, the required memory and CPU time are more than those of the conventional FDTD method. 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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A Leapfrog Formulation of the 3D ADI-FDTD Algorithm

Cited by 74 publications

References 3 publications

On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media

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

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