scholarly journals Newmark-FDTD Formulation for Modified Lorentz Dispersive Medium and Its Equivalence to Auxiliary Differential Equation-FDTD with Bilinear Transformation

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Hongjin Choi ◽  
Jeahoon Cho ◽  
Yong Bae Park ◽  
Kyung-Young Jung
Keyword(s):  
Differential Equation ◽  
Numerical Stability ◽  
Dispersive Medium ◽  
Fdtd Method ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Dispersion Models ◽  
Bilinear Transformation ◽  
Quadratic Complex ◽  
Difference Time

The finite-difference time-domain (FDTD) method has been popularly utilized to analyze the electromagnetic (EM) wave propagation in dispersive media. Various dispersion models were introduced to consider the frequency-dependent permittivity, including Debye, Drude, Lorentz, quadratic complex rational function, complex-conjugate pole-residue, and critical point models. The Newmark-FDTD method was recently proposed for the EM analysis of dispersive media and it was shown that the proposed Newmark-FDTD method can give higher stability and better accuracy compared to the conventional auxiliary differential equation- (ADE-) FDTD method. In this work, we extend the Newmark-FDTD method to modified Lorentz medium, which can simply unify aforementioned dispersion models. Moreover, it is found that the ADE-FDTD formulation based on the bilinear transformation is exactly the same as the Newmark-FDTD formulation which can have higher stability and better accuracy compared to the conventional ADE-FDTD. Numerical stability, numerical permittivity, and numerical examples are employed to validate our work.

scholarly journals An Extended Newmark-FDTD Method for Complex Dispersive Media

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yu-Qiang Zhang ◽  
Peng-Ju Yang
Keyword(s):  
Rational Function ◽  
Time Domain ◽  
Fdtd Method ◽  
Polarization Vector ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Time Stepping ◽  
Two Sides ◽  
Difference Time ◽  
Complex Dispersion

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.

scholarly journals Time-Domain Studies of General Dispersive Anisotropic Media by the Complex-Conjugate Pole–Residue Pairs Model

2021 ◽  
Vol 11 (9) ◽  
pp. 3844
Author(s):  
Konstantinos P. Prokopidis ◽  
Dimitrios C. Zografopoulos
Keyword(s):  
Time Domain ◽  
Electromagnetic Wave Propagation ◽  
Frequency Dispersion ◽  
Magnetized Plasma ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Pole Residue ◽  
Permittivity And Permeability ◽  
Arbitrary Frequency ◽  
Difference Time

A novel finite-difference time-domain formulation for the modeling of general anisotropic dispersive media is introduced in this work. The method accounts for fully anisotropic electric or magnetic materials with all elements of the permittivity and permeability tensors being non-zero. In addition, each element shows an arbitrary frequency dispersion described by the complex-conjugate pole–residue pairs model. The efficiency of the technique is demonstrated in benchmark numerical examples involving electromagnetic wave propagation through magnetized plasma, nematic liquid crystals and ferrites.

Application of ADE-FDTD Method in Lossy Lorentz Media

2014 ◽  
Vol 945-949 ◽  
pp. 2486-2489
Author(s):  
Qing Chao Nie ◽  
Bing Kang Chen
Keyword(s):  
Differential Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Theoretical Result ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Time Domain Method ◽  
Domain Method ◽  
Difference Time

A finite-difference time-domain method based on the auxiliary differential equation (ADE) technique is used to obtain the formulation of 2-D TM wave propagation in lossy Lorentz media. In the paper, the reflected coefficients calculated by ADE-FDTD method and the exact theoretical result are better agreement.

Propagation of 2D Electromagnetic Wave in Lossy Lorentz Media Based on Auxiliary Differential Equation of Finite-Difference Time-Domain Method

2014 ◽  
Vol 568-570 ◽  
pp. 1749-1752
Author(s):  
Bing Kang Chen ◽  
Feng Guo
Keyword(s):  
Differential Equation ◽  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Time Domain Method ◽  
Domain Method ◽  
Difference Time

In order to study the reflection of electromagnetic wave in Lorentz media, A finite-difference time-domain method based on the auxiliary differential equation (ADE) technique is used to obtain the formulation of 2-D TM wave propagation in lossy Lorentz media. In 1-D case, the reflected coefficients calculated by ADE-FDTD method and exact theoretical result are excellent agreement. This expresses that the 2-D formulas of electromagnetic wave propagation in lossy Lorentz media are right. Furthermore, Plane wave reflected by Lorentz media layer is calculated and simulated. Results display that reflected effect is evident.

Study on the transmission properties of periodical and quasi-periodical phononic crystal in elastic wave

2015 ◽  
Vol 29 (34) ◽  
pp. 1550229
Author(s):  
Rui Weng ◽  
Yun Zhang ◽  
Ze-Kun Yang ◽  
Yu-Jie Liu ◽  
Bao-Liang Ma ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Numerical Stability ◽  
Phononic Crystal ◽  
Fdtd Method ◽  
Band Gaps ◽  
Structure Model ◽  
Transmission Coefficients ◽  
Transmission Properties ◽  
Difference Time

The propagation of the elastic wave in phononic crystal is different from the normal uniformity medium. The finite-difference time-domain (FDTD) method is irrelevant to structure model and used widely. Moreover, when the numerical stability of FDTD iterations is satisfied, the elastic waves’ transmission property through periodical and quasi-periodical phononic crystal can be achieved. In this paper, the transmission coefficients of elastic wave through two systems are numerically calculated and the results of band gaps are analyzed. The results are helpful to study phononic crystal.

Padé Approximation Method for FDTD Modeling of Wave Propagation in Dispersive Media

2012 ◽  
Vol 268-270 ◽  
pp. 1585-1588
Author(s):  
Wei Chen
Keyword(s):  
Wave Propagation ◽  
Approximation Method ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Padé Approximation ◽  
Fdtd Method ◽  
Dispersive Media ◽  
Pade Approximation ◽  
Air Muscle ◽  
Difference Time

A finite-difference time-domain (FDTD) method for simulating wave propagation in Cole-Cole dispersive media was presented. The main difficulty of the proposed way was the appearance of fractional time derivatives in the FDTD equation. The Padé approximation method was employed to solve this problem. The expansion of the fractional time derivatives could deal with this model. The comparison of analytical and calculated the reflection of a plasma proves the validity of the method. Then apply this method to calculate the reflection of the air-muscle interface.

The CPML for Hybrid Implicit-Explicit FDTD Method Based on Auxiliary Differential Equation

2014 ◽  
Vol 989-994 ◽  
pp. 1869-1872 ◽  
Author(s):  
Yun Fei Mao ◽  
Pu Hua Huang ◽  
Li Guo Ma
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Three Dimensional ◽  
Complex Frequency ◽  
Numerical Examples ◽  
First Order ◽  
Contour Plots ◽  
Difference Time

In this paper, an implementation of the complex-frequency-shifted perfectly matched layer (CPML) is developed for three-dimensional hybrid implicit-explicit (HIE) finite-difference time-domain (FDTD) method based on auxiliary differential equation (ADE). Because of the use of the ADE technique, this method becomes more straightforward and easier to implement. The formulations for the HIE-FDTD CPML are proposed. Numerical examples are given to verify the validity of the presented method. Results show that, both HIE-CPML and FDTD-CPML have almost the same reflection error, while their reflection error is about 30 dB, which is less than HIE Mur’s first-order results. The contour plots indicate that the maximum relative reflection as low as-72 dB is achieved by selecting and .

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