Investigation of the Stability of ADE-FDTD Methods for Modified Lorentz Media

Prokopidis, Konstantinos P.; Zografopoulos, Dimitrios C.

doi:10.1109/lmwc.2014.2303170

Cited by 27 publications

(29 citation statements)

References 8 publications

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“…, which is the same as the D-E stability polynomial found in [4]. Hence, the presented J-E ADE FDTD imple-mentation can have the same stability constrains as those of the D-E ADE-FDTD implementation.…”

Section: Formulationsmentioning

confidence: 57%

“…In this context, two auxiliary differential equation (ADE) schemes have been used in the m-Lo FDTD implementation: one is based on the D-E ADE [2], while the other is based on the J-E ADE [3] ADE scheme. Very recently, the stability of these ADE schemes was studied by the combination of the von Neumann and the Routh-Hurwitz criterion [4]. It has been concluded in [4] that "the J-E implementation is proven more restrictive compared to D-E" and "the D-E implementation is more robust in terms of stability".…”

Section: Introductionmentioning

confidence: 99%

“…Very recently, the stability of these ADE schemes was studied by the combination of the von Neumann and the Routh-Hurwitz criterion [4]. It has been concluded in [4] that "the J-E implementation is proven more restrictive compared to D-E" and "the D-E implementation is more robust in terms of stability". In order to avoid drawing inaccurate conclusions regarding the J-E ADE-FDTD scheme in general, it is shown in this comment that when the bilinear frequency approximation technique is used in the FDTD discretization of the J-E ADE, the same stability polynomial as that of the D-E ADE scheme will be obtained, and therefore, the same stability conditions will be applied.…”

Section: Introductionmentioning

confidence: 99%

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On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

Ramadan

2015

IEEE Microw. Wireless Compon. Lett.

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Recently, the stability of the D-E and the J-E auxiliary differential equation (ADE) schemes, which are used in implementing the modified Lorentz dispersive model in the finite difference time domain (FDTD) algorithm, has been studied by Prokopidis and Zografopoulos and it has been concluded that "the J-E implementation is proven more restrictive compared to D-E" and "the D-E implementation is more robust in terms of stability," In order to avoid drawing inaccurate conclusions regarding the J-E ADE-FDTD scheme in general, it is shown in this comment that if the bilinear frequency approximation technique is used in the FDTD discretization of the J-E ADE scheme, one can obtain the same stability polynomial as that of the D-E ADE scheme, and therefore, the same stability conditions will be applied. Hence, the stability limitations of the ADE scheme are based on the FDTD discretization methodology rather than the ADE-method itself. Finally, a numerical example carried out in a one-dimensional domain shows that the presented J-E ADE implementation is numerically stable as well as accurate as the D-E ADE counterpart.Index Terms-Auxiliary differential equation (ADE), bilinear frequency approximation, finite difference time domain (FDTD), modified Lorentz model, Routh-Hurwitz, stability analysis, von Neumann.

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Section: Formulationsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

Ramadan

2015

IEEE Microw. Wireless Compon. Lett.

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“…The accuracy of the extended Newmark-FDTD algorithm is discussed below. Moreover, for simplicity and without loss of generality, let Q = 1 and ε ∞ = 0; the permittivity of dispersive media becomes a rational fraction form similar to (5).…”

Section: Analysis Of Accuracy and Stabilitymentioning

confidence: 99%

“…In the analysis of dispersive materials using the FDTD approach, it is required that the variation of dielectric parameters with frequency is modeled efficiently and accurately. In recent years, some novel dispersive models have been introduced, for example, the complex-conjugate pole-residue (CCPR) model [3], critical point (CP) model [4], modified Lorentz (m-Lo) model [5], and quadratic complex rational function (QCRF) model [6]. Some hybrid dispersion models, such as the DrudeLorentz model [7,8] and Drude-CP model [4,9], were also usually adopted.…”

Section: Introductionmentioning

confidence: 99%

An Extended Newmark-FDTD Method for Complex Dispersive Media

Zhang

2018

International Journal of Antennas and Propagation

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Based on polarizability in the form of a complex quadratic rational function, a novel finite-difference time-domain (FDTD) approach combined with the Newmark algorithm is presented for dealing with a complex dispersive medium. In this paper, the time-stepping equation of the polarization vector is derived by applying simultaneously the Newmark algorithm to the two sides of a second-order time-domain differential equation obtained from the relation between the polarization vector and electric field intensity in the frequency domain by the inverse Fourier transform. Then, its accuracy and stability are discussed from the two aspects of theoretical analysis and numerical computation. It is observed that this method possesses the advantages of high accuracy, high stability, and a wide application scope and can thus be applied to the treatment of many complex dispersion models, including the complex conjugate pole residue model, critical point model, modified Lorentz model, and complex quadratic rational function.

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An HIE‐FDTD algorithm for dispersive media with modified Lorentz model

Chen

2022

Micro & Optical Tech Letters

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In this letter, a hybrid implicit–explicit finite difference time domain (HIE‐FDTD) method is developed to simulate general dispersive media with modified Lorentz model. The dispersive media is described through modified Lorentz model and is incorporated into the HIE‐FDTD method by two different auxiliary differential equations (ADEs). One ADE establishes the relationship between the electric displacement and electric field intensity and the other one establishes the connection between the electric current density and electric field intensity. Numerical examples are conducted and it can be seen from the numerical results that the proposed algorithm can simulate dispersive media correctly and also improve computational efficiency compared with the FDTD method and one unconditionally stable FDTD method.

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Investigation of the Stability of ADE-FDTD Methods for Modified Lorentz Media

Cited by 27 publications

References 8 publications

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

An Extended Newmark-FDTD Method for Complex Dispersive Media

An HIE‐FDTD algorithm for dispersive media with modified Lorentz model

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