A one-step leapfrog HIE-FDTD method for rotationally symmetric structures

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

This paper develops a perfectly matched layer (PML) for the hybrid implicit explicit finite-difference time-domain (HIE-FDTD) method. It is demonstrated that the inclusion of the PML is a simple extension of the original HIE-FDTD method. It doesn't affect the weakly condition stability and computational accuracy. Simulation results show that when the time step size satisfies with the time stability condition, the reflection error of the HIE-FDTD method is below −90dB, which demonstrates good absorbing performance of the PML method.

The nearly perfectly matched layer (NPML) is incorporated into a novel four-steps weakly conditionally stable hybrid implicit explicit finite difference time domain (HIE-FDTD) method in three-dimensional (3-D) domains in this paper. By dividing the matrix which obtained by the Maxwell's equation into four sub-matrices with the symmetric operation and uniform division and incorporating NPML into it, the time step of the proposed algorithm is divided into four sub-steps, then the formulation of the proposed method is generated. Moreover, numerical results are carried out for different Courant-Friedrichs-Lewy (CFL) numbers at different positions with different NPML layers in 3-D domains, and it has been obtained that the presented formulation is accurate as well as weakly conditionally stable.

A stability-improved hybrid implicit-explicit finite-difference time-domain method (HIE-FDTD) for magnetized graphene is proposed. The graphene is treated as a current source modeled by an auxiliary differential equation which is divided into two separate equations to describe isotropic and anisotropic properties. The one time-step iteration in the conventional algorithm is decomposed into two sub steps where the conventional HIE-FDTD combined with the isotropic equation is implemented first followed by the Crank-Nicolson (CN) scheme combined with the anisotropic equation to retain the stability. Numerical results show that, differently from other recent extensions, the stability condition of the proposed method preserves the same form as that of the conventional HIE-FDTD. We illustrate the application of the proposed algorithm to accurately compute graphene transmission properties e.g., Faraday and Kerr rotations.

In this letter, the current source implementations are presented for the hybrid implicit–explicit finite-difference time-domain (HIE-FDTD), the improved HIE-FDTD, and the leapfrog HIE-FDTD methods. The asymmetry and the field errors of these HIE-FDTD methods are investigated for all possible values of the time index parameters. The proposed implementations give very low asymmetry and field errors for all the three HIE–FDTD methods. The field errors given by these HIE-FDTD methods are lower than those given by the alternating direction implicit finite-difference time-domain (ADI-FDTD) method.

Revisiting the stability of the HIE-FDTD technique for modeling graphene dispersion

This paper presents a new 3-D hybrid implicit explicit (HIE) finite-difference time-domain (FDTD) method with a stability criterion relaxed from the discretization space steps in one direction. The proposed method is particularly useful and efficient for electromagnetic (EM) simulation of structures having fine details in one Cartesian direction such as thin shields and thin slots on a metallic enclosure whose EM analysis are popular and important in electromagnetic compatibility. In this algorithm, unlike common FDTD methods in which both electric and magnetic fields are updated, only the electric field needs to be updated during the time-marching process of the algorithm; hence, it is called as a “single-field” FDTD method. This could be achieved by applying the Crank-Nicolson (CN) scheme only to the electric field, while in earlier HIE-FDTD (and also unconditionally stable FDTD) methods, the CN scheme is applied to both electric and magnetic fields. The proposed algorithm consists of two implicit and three explicit updating equations that can be solved simultaneously (in parallel) by applying multithreading. Thanks to few and simple updating equations of the proposed algorithm, it is computationally more efficient than other HIE-FDTD methods in terms of runtime. The high computational efficiency and accuracy of the proposed method are demonstrated by producing several numerical examples and providing comparison to the results obtained using methods available in the literature.

Two major problems usually arise when the finite-difference time-domain (FDTD) method is used for wideband characterisation of dielectric discontinuities with high permittivity in waveguides. First, reflections are provoked by imperfections in the absorbing boundary conditions. Secondly, many time steps are necessary to overcome the problems associated with the truncation error inherent in the discrete Fourier transform (DFT). The authors present wideband absorbing boundary conditions (ABC) that have been designed to provide optimal behaviour for the analysis of waveguide devices. As an alternative to the classical fast Fourier transform (FFT), Prony's method is used to process the data provided by FDTD in order to obtain the frequency parameters. It was found that this alternative method significantly reduces the CPU time needed to characterise the different devices. The improvements obtained are clearly shown by analysing different dielectric discontinuities in waveguides. The results are compared both with those given by the classical FDTD-FFT method and with those provided by the finite elements method in the frequency domain.

This paper considers speed-up of a calculation of an absorbing boundary condition (ABC) of the finite-difference time-domain (FDTD) method based on a time-domain surface integral equation. The most popular ABC of the FDTD method, the perfectly matched layer (PML), is still required to be modified for its accuracy in cases of near field and large incident angle to ABC. The ABC based on the time-domain surface integral equation is free from such confinements of the ABC location and incident angle. On the other hand, it is known that extremely heavy computation cost is required for the time-domain surface integral. In this work, it is attempted to reduce the computation cost of the surface integral equation to use spherical harmonics expression for harmonic Green's function in the surface integral equation.

To improve the hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method in solving three-dimensional electromagnetic problem with fine scale structure, an effective method combining HIE-FDTD with convolutional perfectly matched layer (CPML) absorbing boundary is developed. The formulae and numerical examples are presented, and the fine scale structure is innovatively turned from y-direction into z-direction of the propagation. Compared to the conventional FDTD-CPML, the proposed method holds less CPU time and lower relative reflection error. When the Courant-Friedrich-Levy number reaching 6, the error remains below -75.3 dB and the CPU time is only about 36.64%.

The absorbing boundary conditions (ABCs) are essential to terminate the computational space when the finite-difference time-domain (FDTD) method is applied to analyze electromagnetic (EM) problems. With the ABCs, the fields on the truncated boundaries are evaluated by the interior fields. In this paper, the relationship between the fields on the terminated boundaries and the interior fields is expressed as the transfer functions in the Z-domain. The proper transfer functions are determined from the radiation condition or the transmission condition. Simplifying these transfer functions into rational functions, we obtain different schemes of the ABCs. In this paper, both the transfer functions and coefficients of the final ABCs are derived and expressed as recurrence formulas for the convenience of programming. This method has the property of simplicity and flexibility. The ABCs obtained by this method show good absorbing performance and numerical stability in the practical applications.

The importance of dielectric losses in planar microstrip structures is evaluated with the finite-difference time-domain (FDTD) method. This analysis was previously not possible in many FDTD simulators due to a lack of absorbing boundary conditions (ABCs), which appropriately terminate air/dielectric interfaces for which the dielectric is lossy. The newly proposed lossy two-time derivative Lorentzian material (L2TDLM) model ABC allows for these terminations and is presented and implemented here for three-dimensional FDTD simulations. The effect of dielectric losses on several well-known planar microstrip structures is evaluated. It is shown that the inclusion of these losses in FDTD simulations, which is facilitated by the L2TDLM ABC, is, in fact, important to predict the performance of resonant structure on lossy dielectric substrates.

A modal absorbing boundary condition (ABC) based on the discrete Green's function (DGF) is introduced and applied for termination of waveguides simulated by means of the finite-difference time-domain (FDTD) method. The differences between the developed approach and implementations already demonstrated in the literature are presented. By applying DGF, a consistent theoretical approach to modal ABC in the FDTD method is obtained. Developed ABC is applicable to propagating and evanescent modes yielding the reflection error below -250 dB. Because the perfect matching may be computationally expensive, results of investigations of the tradeoff between computational efficiency and accuracy of the developed method are presented.

The numerical dispersion is one of the main factors to affect the accuracy of the finite-difference time-domain (FDTD) method. It can be easy to be taken for granted that a smaller time step leads to smaller simulation errors. This paper reveals that smaller time steps do not always make more accurate results in FDTD simulations. We analytically investigated how time steps affect the numerical dispersion of two FDTD methods: the leapfrog FDTD(2,2) method and the FDTD(2,4) method. The investigations in this paper show that in the FDTD(2,2) method, a larger time step limited by the Courant-Friedrichs-Lewy (CFL) condition is more helpful to reduce the numerical dispersion error. However, in the FDTD(2,4) method, as the time step grows, the numerical dispersion error decreases at the beginning and then increases. Several numerical examples are carried out to verify our analysis.

Both in the transmission line matrix (TLM) and the finite difference time domain (FDTD) methods, absorbing boundary conditions (ABCs) are used to truncate the computational domain for the simulation of open boundary problems. A comparison of the performance of ABCs applied to TLM and FDTD is presented. The results indicate a significant improvement in the performance of an ABC when applied to TLM compared to the performance of the same ABC when applied to FDTD. An explanation for this improvement in the performance is given.