Finite-difference Time-domain Formulation Research Articles

Unified GSTC-FDTD Algorithm for the Efficient Electromagnetic Analysis of 2D Dispersive Materials

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic wave analysis of complex media. Conventional FDTD analyses of very thin two-dimensional (2D) dispersive materials require overwhelming computing resources because they should use very refined FDTD spatial grids. In this work, we propose a computationally efficient and unified FDTD formulation for 2D dispersive materials based on a combination of the generalized sheet transition condition (GSTC) and the modified Lorentz dispersion model. The proposed FDTD formulation can lead to a significant improvement in computational efficiency compared to the conventional FDTD method, while maintaining high accuracy. Numerical examples validate the improved computational efficiency of the proposed FDTD formulation.

Electromagnetic Modeling Using an FDTD-Equivalent Recurrent Convolution Neural Network: Accurate computing on a deep learning framework

In this study, a recurrent convolutional neural network (RCNN) is designed for full-wave electromagnetic (EM) modeling. This network is equivalent to the finite difference time domain (FDTD) method. The convolutional kernel can describe the finite difference operator, and the recurrent neural network (RNN) provides a framework for the time-marching scheme in FDTD. The network weights are derived from the FDTD formulation, and the training process is not needed. Therefore, this FDTD-RCNN can rigorously solve a given EM modeling problem as an FDTD solver does.

Finite difference time domain method of lightpropagation through inhomogeneous media

Propagation of arbitrarily polarized light through inhomogeneous media is modeled in this paper. The model can include parameters of the media such as relative dielectric constant, relative magnetic constant and electric conductivity. The orientation of the electric field strength of the light source could be defined arbitrarily, and in this paper two polarization modes are considered: transverse electric (TE) mode and transverse magnetic (TM) mode. The electric field vector could change its orientation in dependence on the characteristics of the media. The model developed in this paper is based on the finite difference time domain (FDTD) method and Maxwell’s equations. A two-dimensional formulation of FDTD is applied in this computing. Several cases were considered, and the results obtained in this paper agree with the literature. The model shown in this paper does not require much time for computer processing and can be easily applied for specific cases of media, source, and light.

Efficient Finite-Difference Time-Domain Modeling of Time-Varying Dusty Plasma

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic analysis of dusty plasma sheath in reentering hypersonic vehicles. The time-varying characteristics of dusty plasma should be considered to accurately analyze THz wave propagation in dusty plasma. In this work, we propose an efficient FDTD modeling of time-varying dusty plasma based on the combination of the bilinear transform and the state-space approach. The proposed FDTD formulation for time-varying dusty plasma can lead to a significant improvement in computational efficiency against the conventional shift operator FDTD counterpart while maintaining numerical accuracy. Numerical examples are performed to validate the proposed FDTD modeling of time-varying dusty plasma.

Numerical Accuracy of Finite-Difference Time-Domain Formulations for Magnetized Plasma

The finite-difference time-domain (FDTD) has been widely used to analyze electromagnetic (EM) wave propagation in complex dispersive media. Over the past three decades, a variety of FDTD approaches for the EM wave propagation in magnetized plasma has been presented. In this work, we perform a comprehensive study on the numerical accuracy of four FDTD formulations for magnetized plasma including the JE convolution (JEC) method, the exponential time differencing (ETD) method, the H-J collocated auxiliary differential equation (ADE) method, and the E-J collocated ADE method. Toward this purpose, the numerical permittivity tensor of magnetized plasma in the four FDTD formulations are derived and then we analyze them to determine which approach can provide the best accuracy. It is found that the E-J collocated ADE method can lead to the best accuracy. Numerical examples awere performed to validate our investigations.

Computational Techniques for Design and Analysis of Time-Varying Capacitor Loaded Transmission Lines Using FDTD and Simulink

In this paper, MATLAB based computational approaches for the design and analysis of time-varying capacitors using the finite-difference time-domain (FDTD) technique and the Simulink design environment are presented. The FDTD formulation for multiple lumped capacitors loaded in series on a transmission line is discussed and extended to include time variation of capacitance. The design methodology for the same is also discussed using MATLAB's Simulink using the RF Blockset Library. The developed FDTD formulation and the Simulink method are then used to design a mixer with time-varying capacitors loaded transmission line.

Numerical Stability of Modified Lorentz FDTD Unified From Various Dispersion Models.

The finite-difference time-domain (FDTD) method has been widely used to analyze electromagnetic wave propagation in complex dispersive media. Until now, there are many reported dispersion models including Debye, Drude, Lorentz, complex-conjugate pole-residue (CCPR), quadratic complex rational function (QCRF), and modified Lorentz (mLor). The mLor FDTD is promising since the mLor dispersion model can simply unify other dispersion models. To fully utilize the unified mLor FDTD method, it is of great importance to investigate its numerical stability in the aspects of the original dispersion model parameters. In this work, the numerical stability of the mLor FDTD formulation unified from the aforementioned dispersion models is comprehensively studied. It is found out that the numerical stability conditions of the original model-based FDTD method are equivalent to its unified mLor FDTD counterparts. However, when unifying the mLor FDTD formulation for the QCRF model, a proper Courant number should be used. Otherwise, its unified mLor FDTD simulation may suffer from numerical instability, different from other dispersion models. Numerical examples are performed to validate our investigations.

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

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.

Accurate and Efficient Finite-Difference Time- Domain Formulation of Dusty Plasma

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic analysis of complex dispersive media. The shift-operator (SO)-FDTD or auxiliary differential equation (ADE)-FDTD formulation has been mainly employed for dusty plasma. Each FDTD formulation has its pros and cons. SO-FDTD is accurate but not computationally efficient. ADE-FDTD needs fewer computational resources, but its accuracy is poor. Here, we propose an accurate and efficient FDTD formulation for dusty plasma, based on the bilinear transform (BT). We perform a comprehensive study on the numerical permittivity and the computational efficiency for three FDTD formulations. Numerical examples are employed to illustrate that the proposed BT-FDTD outperforms the previously reported FDTD formulations for dusty plasma. In addition, based on the proposed BT-FDTD simulations, the effect of dust particles on EM wave propagation is investigated in the GHz band and the THz band.

Implementation of Passive and Active Circuit Elements in Cylindrical Finite-Difference Time-Domain Formulation

The implementation of passive and active linear circuit elements in cylindrical finite-difference time-domain technique (CFDTD) is developed. The updating equations for active element such as a voltage sources and passive elements such as resistors, capacitors and inductors are represented for elements located along one of the cylindrical coordinate’s independent parameters. The analytical solutions for simple circuit configurations are computed and used as a reference to verify and confirm the accuracy of the developed CFDTD formulation and numerical results.

Perfectly Matched Layer Formulation of the INBC-FDTD Algorithm for Electromagnetic Analysis of Thin Film Materials

The impedance network boundary condition (INBC)-based finite-difference time-domain (FDTD) method has been widely used for electromagnetic analysis of highly conductive thin film materials. In the INBC-FDTD formulation, the electromagnetic field variations inside the thin film material are taken into account mathematically and thus extremely small FDTD grids are not necessary for the FDTD modeling of the material. Therefore, computational efficiency of the INBC-FDTD formulation is significantly better than other FDTD formulations. Albeit with this great advantage, the INBC-FDTD formulation cannot be fully employed for thin film materials because the corresponding perfectly matched layer (PML) formulation has not been reported in literature. In this work, we propose a PML formulation suitable for the INBC-FDTD algorithm. Numerical examples illustrate that the proposed PML-INBC-FDTD formulation can yield good absorption performance and also it can improve computational efficiency while maintaining numerical accuracy.

Simplified FDTD Formulations for Magnetostatic Biased Graphene Simulations

Simplified finite difference time domain (FDTD) formulations are presented for magnetostatic biased graphene simulations. In this respect, graphene's anisotropic conductivity is incorporated into the FDTD algorithm by using the second-order Runge-Kutta (RK) scheme with the minimal additional computational resources. Moreover, the complex frequency shifted perfectly matched layer is combined with the presented RK-FDTD formulations to model open-space graphene structures. Numerical tests are included to validate the given formulations.

Study on Tunable Magnetized Plasma Frequency Selective Surface Using JEC-FDTD Method

The tunability of traditional frequency selective surfaces (FSSs) is inconvenient using metal material patch as periodic element, utilizing genetic algorithms to model FSS layers obtaining desired filtering electromagnetic waves effect. However, plasma tube is used as an element of the frequency selection surfaces substituting traditional metal patch in this article. A 3-D finite-difference time-domain (FDTD) formulation for dispersive media called the JE convolution (JEC) method is derived using the convolution relationship between the current density $J$ and the electric field $E$ to simulate the interaction of incident wave and magnetized plasma FSS. Numerical experimental results show that the electron number density of magnetized plasma has a significant effect on the resonance frequency, which can be modulated to the desired filtering by varying the density in the magnetized plasma elements. Whereas the magnetized plasma FSSs behave exactly like a perfect electric conductor (PEC) increasing the electron number density to a certain degree. Thus, modulation based on the ionized electron number density of the magnetized plasma can be designed into a tunable plasma FSS. Both the collision model and the noncollision model of the magnetized plasma are proposed to research electromagnetic transmission characteristics of FSS. It shows that the collision frequency only affects the reflectivity while has no effect on the resonance frequency in the following numerical experiments. In addition, magnetization intensity of the plasma FSS is also taken into consideration. The users obtaining the desired resonance frequency and transmission characteristics of plasma FSS by simply tuning the plasma’s electron number density, collision frequency, and magnetization intensity. So the magnetized plasma FSS can not only improve the electromagnetic shielding effect but also facilitate the modulation and rapid response to achieve the desired filtering effect. What is more, the magnetized plasma FSS can be turned off to achieve transparency, which greatly expands the universality of magnetized plasma FSS.

Finite-difference time-domain modeling of multi-stage soil ionization with residual resistivities—Part II: Numerical validation

The second part of this manuscript presents numerical validation results for the finite-difference time-domain (FDTD) multi-stage soil ionization formulation with residual resistivities proposed and described in the first part of this work (Part I: Theoretical Background and the Proposed FDTD Formulation). For broadly validating the developed numerical method, it is applied to model three field experiments from literature. Two of the experiments involve distinct single rod grounding systems buried vertically in different soils. Additionally, in order to validate the proposed model for a geometrically more complex grounding system, the transient response of a square grounding grid is calculated and compared to experimental results Substantial improvements on conformity of the transient curves produced by using the FDTD method with respect to experimental results are obtained using the proposed formulation. The influence of the injection electrode for properly reproducing experimental results is numerically determined. Finally, precision and stability of proposed method are also discussed and illustrated with numerical experiments.

Finite-difference time-domain modeling of multi-stage soil ionization with residual resistivities—Part I: Theoretical background and the proposed FDTD formulation

In this first part of the paper, a Finite-Difference Time-Domain (FDTD) model for multi-stage soil ionization with residual resistivities is proposed to obtain realistic transient responses of grounding systems subjected to high intensity currents. Four phases of soil ionization process are modeled: non-ionization (linear soil representation), presparking (first stage of ionization), sparking (second stage of ionization) and deionization. Mechanisms identified experimentally in literature for water ionization explain presparking and sparking phases of soil ionization. Weak ionization in clusters of gas bubbles produced due to high current flows explains the presparking phase. The sparking phase is governed by ionization of aqueous solutions in soil. A mathematical function is defined to represent the rise of electrical conductivity over time for each point in the soil FDTD lattice during sparking phase. Additionally, effects associated with limited production of free charges over time and their increasing reduction of mobility are considered by means of residual resistivities in presparking and sparking phases. Due to the complex nature of the phenomenon, which involves various physical processes, comprehensive theoretical background is also provided in part I. The second part of the paper presents numerical validation cases for the proposed FDTD soil ionization model.

FDTD Modeling for the Accurate Electromagnetic Wave Analysis of Graphene

We develop a finite-difference time-domain (FDTD) method suitable for the electromagnetic (EM) analysis of graphene. In this work, we employ the modified Lorentz model for dispersion modeling, the two-dimensional (2-D) sheet model for geometrical modeling, and the complex-frequency-shifted (CFS)-perfectly matched layer (PML) for the absorbing boundary condition. In specific, the accurate complex-conjugate pole-residue (CCPR) dispersion model is first adapted for the electrical modeling of graphene by using the robust vector fitting. Next, the CCPR parameters are converted to the modified Lorentz parameters and then the modified Lorentz-based dispersive FDTD formulation is used to enhance the computational efficiency. In FDTD cell modeling, the 2-D sheet cells are allocated for graphene rather than the conventional FDTD cell-based modeling. Finally, CFS-PML are employed for terminating the computational domain to avoid the late-time instability. The presented FDTD approach is validated in numerical examples for graphene-based parallel plate waveguides.

Two-dimensional finite-difference time-domain formulation for sound propagation in a temperature-dependent elastomer-fluid medium.

This study focuses on the two-dimensional (2-D) finite-difference time-domain (FDTD) formulations to investigate the acoustic wave propagation in elastomers contained in a fluid region under different thermal conditions. The developed FDTD formulation is based on a direct solution of the time-domain wave equation and the Havriliak-Negami (H-N) dynamic mechanical response of the elastomers. The H-N representation, including double fractional derivative operators, can be accurately transferred from the frequency-domain to the time-domain by using Riemann-Liouville theory and the Grunwald-Letnikov operator for fractional derivative approximations. Since the Williams-Landel-Ferry shift function is related to the relaxation time for different thermal conditions, the proposed scheme represents a simple and accurate prediction of acoustic wave propagation for varying thermal conditions. The pulse-wave propagation in a viscous fluid field is simulated by investigating the Navier-Stokes equations. The acoustic properties of different elastomers in a variety of temperatures are obtained by means of the proposed FDTD formulation and validated by a good agreement with the experimental data over a wide frequency range. Additionally, the 2-D examples relevant to wave propagation in different elastomers contained in a fluid field are implemented. The proposed FDTD formulation can be used to predict 2-D acoustic wave propagation in different thermal conditions accurately.

FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Frequency-Dependent Lossy Multi-Conductor Transmission Lines

A finite-difference time-domain (FDTD) formulation for a uniform frequency-dependent lossy multi-conductor transmission line (MTL) is presented. It is based on a distributed parameter MTL model using partial resistances and partial inductances. In order to consider both skin and proximity effects, the partial internal impedances are computed with a boundary element method (BEM) formulation, enforcing a high-order surface impedance boundary condition (SIBC). The proposed FDTD formulation is numerically validated with two test cases.

Comprehensive Study on Numerical Aspects of Modified Lorentz Model-Based Dispersive FDTD Formulations

Finite-difference time domain (FDTD) has been widely used to analyze electromagnetic wave interaction with dispersive media. It is of great necessity to incorporate a dispersion model into FDTD formulation for electromagnetic wave analysis of dispersive media. Recently, it was reported that the modified Lorentz model can cover Debye, Drude, Lorentz, critical point, and quadratic complex rational function models. In this work, it is illustrated that the modified Lorentz model can also cover the complex-conjugate pole-residue model which is one of the most popular dispersion models. Modified Lorentz-based dispersive FDTD has not been thoroughly studied, especially for numerical aspects. In this work, we investigate auxiliary differential equation (ADE)-FDTD formulations for the modified Lorentz model based on electric flux density (D), current (J), or polarization (P). We perform a comprehensive study on memory requirement, the number of arithmetic operations, numerical stability, and numerical permittivity for the above three ADE-FDTD formulations. In addition, the bilinear transformation (BT) is incorporated into modified Lorentz-based FDTD formulations and it will be shown that the utilization of the BT can lead to better performance in terms of numerical stability and numerical accuracy. Numerical examples are used to demonstrate our work.

Smart Graphene-Based Frequency Selective Surface Designed to Act as Single or Dual Band Device with Reconfigurable Operation Bands

In this paper, a finite-difference time-domain (FDTD) formulation, based on the exponential matrix and on thin material sheet methods is developed for modeling subcellular thin graphene sheets. This formulation is validated by reproducing graphene frequency selective surfaces (FSS) known from literature. Then, we propose in this work a smart graphene FSS device. Smartness is obtained by means of a unity cell formed by a graphene ring with a graphene sheet placed in its aperture. By properly regulating the chemical potentials of the graphene elements, two frequency-tunable modus operandi are obtained: single- or dual-band rejection modes. When the device operates in its dual-band rejection mode, either of the rejection bands can be shifted individually in the frequency spectrum. Additionally, both rejection bands can also be reconfigured simultaneously.