Hybrid Implicit-explicit Finite-difference Time-domain Research Articles

Using Dispersion HIE-FDTD Method to Simulate the Graphene-Based Polarizer

A dispersion hybrid implicit–explicit-finite-difference time-domain (HIE-FDTD) method is used to simulate a graphene-based polarizer in this paper. The surface conductivity of graphene is incorporated into the conventional HIE-FDTD method directly through an auxiliary difference equation (ADE). The time step size in the proposed method has no relation with the fine spatial cells in the graphene layer. The simulation results show that the calculated result of the dispersion HIE-FDTD method agrees very well with that of the conventional ADE-FDTD method, but its computational time is considerably reduced. By using the dispersion HIE-FDTD method, it numerically validates that graphene can be used as a tunable linear-to-circular polarizer through controlling its chemical potential.

Three-dimensional dispersive hybrid implicit–explicit finite-difference time-domain method for simulations of graphene

A dispersive hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method is presented in this paper. Surface conductivity of the graphene is incorporated into the HIE-FDTD method directly through an auxiliary difference equation. The time step size in proposed method has no relation with the fine spatial discretization, so it is very useful for the simulation of the graphene when it needs to be discretized across its thickness. The stability condition of this method is not only determined by the spatial cell sizes Δx and Δz, but also related with the surface conductivity of the graphene. The computational accuracy and efficiency of this method are demonstrated through numerical examples. The results show that with reasonable accuracy, the memory requirement and computation time of the dispersive HIE-FDTD method are both considerably reduced as compared with those of the conventional FDTD method and LOD-FDTD method.

An Efficient 3-D HIE-FDTD Method With Weaker Stability Condition

For analyzing the electromagnetic objects with the fine structures in one direction efficiently, a three-dimensional (3-D) hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method with weaker stability condition is proposed in this paper. First, by adopting the alternating-direction implicit (ADI) scheme, the 3-D Maxwell’s equations are subdivided into two substep procedures, and then by adding some disturbance terms into two substeps, respectively, the proposed method is derived. Compared with the existing HIE-FDTD methods, the Courant–Friedrichs–Lewy (CFL) stability condition of the proposed HIE-FDTD method is weaker, which means the proposed method is more efficient due to the possibility of choosing the larger time step size. In addition, the relationships between the CFL stability conditions and the numerical dispersion errors of the traditional FDTD method, the three HIE-FDTD methods, and the ADI-FDTD method are summarized in order to provide a basis for the choice among them.

HIE-FDTD Method With PML for 2-D Periodic Structures at Oblique Incidence

For analyzing the oblique incident plane wave on periodic structures with the fine structure only in one direction, a hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method with the perfectly matched layer (PML) is derived. First, the field transformation technique is adopted to eliminate the time delay, and the PML formulations are derived by using the auxiliary differential equation (ADE) method. Then, by combining the transformed Maxwell’s equations with the PML formulations and adopting the locally one-dimensional (LOD) scheme, the proposed method with two substep implementations is obtained, which only needs to solve one implicit equation. The Courant–Friedrichs–Lewy (CFL) condition of the proposed method is more relaxed and no longer limited by the fine grid cell size.

The Conformal HIE-FDTD Method for Simulating Tunable Graphene-Based Couplers for THz Applications

An improved hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is proposed for simulating graphene-based patch couplers at terahertz (THz) for different physical and geometrical parameters, where the Drude model of monolayer graphene and the associated auxiliary differential equation (ADE) technique are implemented. In order to accurately model the curved graphene boundaries, the conformal FDTD method is further hybridized with the HIE-FDTD method, which results in a conformal HIE-FDTD method. Numerical results are presented for S-parameters and field distributions of the coupler, which can be adjusted effectively by changing the chemical potential and layer number of graphene patch or substrate permittivity.

A Novel HIE-FDTD Method with Large Time-Step Size [Programmer's Notebook

A novel hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method that is applicable to analyze structures with fine-scale discretization in one or two directions is presented. The more relaxed stability condition and dispersion relation are analytically derived. Simulation results are compared with those obtained by the existing HIE-FDTD method.

The Implementation of Convolutional Perfectly Matched Layer (CPML) for One-Step Leapfrog HIE-FDTD Method

The convolutional perfectly matched layer (CPML) is modified and implemented for one-step leapfrog hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method. Its stability is verified in a semi-analytical way and its effectiveness is demonstrated numerically. It is shown that even when time step size is large, the absorbing performance of CPML is still very good.

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

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 .

A Novel 3-D HIE-FDTD Method With One-Step Leapfrog Scheme

This paper presents a novel 3-D leapfrog hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method. By first adopting the Peaceman–Rachford scheme and then the one-step leapfrog scheme, the proposed HIE-FDTD algorithm is implemented in the same manner as the traditional finite-difference time-domain method in which the implicit scheme was applied only in the direction where a fine grid was applied and the explicit scheme was applied in two other directions where a larger grid was used. Further, by introducing auxiliary field variables denoted by $e$ and $h$ , the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical analysis demonstrated that the Courant–Friedrichs–Lewy stability condition of the proposed HIE-FDTD method is determined only by one grid cell size, which is more relaxed than those of the existing HIE-FDTD methods, and the numerical dispersion error is less than that of the alternating-direction implicit method.

A Three-Dimensional HIE-PSTD Scheme for Simulation of Thin Slots

In this paper, a pseudospectral (PS) scheme is introduced into the hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method for solving the shielding effectiveness (SE) of thin slots. The maximum time-step size in this method is only determined by two spatial discretizations and the spatial discretization only needs two cells per wavelength. The 3-D formula of the method is presented and the time stability condition of the method is demonstrated. When this method is applied to simulate thin slots, high computational efficiency is obtained and less computer memory is used, which is demonstrated through numerical examples by comparing with the finite-difference time-domain (FDTD) method, HIE-FDTD method, and alternating-direction implicit (ADI)-FDTD method.

Application of the Z-transform technique to modeling the linear lumped networks in the HIE-FDTD method

In this work, a new lumped-network hybrid implicit–explicit finite-difference time-domain (LN-HIE-FDTD) method has been proposed. This method is derived from combining the 3D HIE-FDTD method with the Z-transform technique for the hybrid system including linear lumped networks. It possesses the advantage of deriving the updating equations immediately for complex circuits. The accuracy of the proposed method is verified from the comparison of calculated results given by the proposed method and the conventional lumped-network FDTD (LN-FDTD) method. The efficiency of the proposed method is verified from the comparison of the CPU time by the two methods. It is demonstrated that the proposed method is numerically efficient while time-saving.

A Novel Hybrid Implicit–Explicit FDTD Algorithm With More Relaxed Stability Condition

To analyze structures with fine-scale dimension in one direction, a novel hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) algorithm is proposed. Numerical formulations of the proposed HIE-FDTD method for a 2-D TE wave are analytically derived, and the stability condition is verified to be quite relaxed by comparing it against the existing HIE-FDTD method.

Implementation of CFS-PML for HIE-FDTD Method

In this letter, the complex frequency-shifted perfectly matched layer (CPML) is applied to hybrid implicit-explicit finite-difference time-domain method (HIE-FDTD). To verify the new formulation, a numerical example is presented. Results show that both HIE-CPML and FDTD-CPML have almost the same reflection error, while their reflection error is smaller than HIE Mur's first-order results. Results for different Courant-Friedrich-Levy numbers (CFLNs) show that even when the CFLN is large, the reflection error is still small. The contour plots show that the maximum reflection error as low as 83 dB is achieved by selecting optimum parameters.

An Efficient Method to Reduce the Numerical Dispersion in the HIE-FDTD Scheme

A parameter optimized approach for reducing the numerical dispersion of the 3-D hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) is presented in this letter. By adding a parameter into the HIE-FDTD formulas, the error of the numerical phase velocity can be controlled, causing the numerical dispersion to decrease significantly. The numerical stability and dispersion relation are presented analytically, and numerical experiments are given to substantiate the proposed method.

Improved hybrid implicit–explicit finite-difference time-domain method with higher accuracy and user-defined stability condition

An improved hybrid implicit–explicit finite-difference time-domain (IHIE-FDTD) method is presented in this paper. Compared with the conventional hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method, this new method has higher accuracy. The time-step size in the IHIE-FDTD is determined by a user-defined parameter and is arbitrarily alterable. The numerical performance of the proposed method over the conventional HIE-FDTD method and alternating-direction implicit finite-difference time-domain method is demonstrated through numerical examples.

Three-dimensional hybrid implicit–explicit finite-difference time-domain method in the cylindrical coordinate system

A novel hybrid implicit–explicit (HIE) finite-difference time-domain (FDTD) method, which is extremely useful for problems with very fine structures along the ϕ-direction in cylindrical coordinate system, is presented. This method has higher computation efficiency than conventional cylindrical FDTD methods, because the time step in this method is only determined by the space discretisations in the radial and vertical directions. The numerical stability of the proposed HIE–FDTD method is presented analytically. Compared with the cylindrical alternating-direction implicit (ADI)–FDTD method, this HIE–FDTD method has higher accuracy, especially for larger time step size. At each time step, the HIE–FDTD method requires the solution of two tridiagonal matrices and four explicit updates. While maintaining the same size of time step, the central processing unit (CPU) time for this weakly conditionally stable FDTD method can be reduced to about 3/5 of that for the ADI–FDTD scheme. The numerical performance of the proposed HIE–FDTD over the conventional cylindrical FDTD method and cylindrical ADI–FDTD method is demonstrated through numerical examples.

Stability and Numerical Dispersion Analysis of a 3D Hybrid Implicit-Explicit FDTD Method

A three-dimensional hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is recently proposed for the solution of three-dimensional Maxwell's equations. In this communication, its stability and numerical dispersion relation are derived and analyzed in detail. In order to evaluate its performance, the comparison between it and other two FDTD methods is made, i.e., the Yee-FDTD method and the alternation-direction implicit (ADI)-FDTD method. The final results show that the stability condition of the HIE-FDTD method is relatively relaxed in comparison with that of the Yee-FDTD method. However, the performance of the numerical dispersion of the HIE-FDTD method will unfortunately deteriorate in some special directions, which could be worse than those of the Yee-FDTD method and the ADI-FDTD method.

Implementation of connection boundary for HIE‐FDTD method

AbstractThe implementation of connection boundary for the hybrid implicit‐explicit finite‐difference time‐domain (HIE‐FDTD) method is discussed in this article. It shows that the incident field of the HIE‐FDTD method must be split into two time steps. Compared with the implementation method commonly used in the conventional FDTD scheme, this method is weakly conditionally stable and has higher accuracy. The theory proposed in this article is validated through numerical examples. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1347–1352, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23390

Numerical Simulation Using HIE-FDTD Method to Estimate Various Antennas With Fine Scale Structures

The hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is employed to solve the problems of various antennas with fine scale structures. In this method, a larger time-step size than allowed by the CFL stability condition limitation can be set because the algorithm of this method is weakly conditionally stable. Consequently, an increase in computational efforts caused by fine cells due to thin slots or small substrate of antennas can be prevented. The results from the HIE-FDTD method agree well with results from the conventional finite-difference time-domain (FDTD) method, and the required CPU time for the HIE-FDTD method is much shorter than that for the FDTD method. Compared with the alternating-direction implicit FDTD (ADI-FDTD) method, the HIE-FDTD method has better accuracy and higher efficiency, which is demonstrated by numerical examples.

Convolutional perfectly matched layer for weakly conditionally stable hybrid implicit and explicit‐FDTD method

AbstractIn this article, we developed and implemented the convolutional perfectly matched layer (CPML) for the hybrid implicit explicit finite‐difference time‐domain (HIE‐FDTD) method. The method is validated against the conventional FDTD‐PML method and is found promising. The development of CPML is able to extend the HIE‐FDTD to open surface problems, which works at higher CFL numbers in comparing to the conventional FDTD method. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 3106–3109, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22962