Conventional Finite-difference Time-domain Method 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.

Extension of the contour‐path effective‐permittivity finite‐difference time‐domain method to three‐dimensional problems for the analysis of arbitrarily shaped dielectric media

AbstractThe conventional finite‐difference time‐domain (FDTD) method has been formulated in the Cartesian coordinate system. In this case, the staircase approximation should be used even for the analysis of arbitrarily shaped dielectric media. As a result, small meshes are required to accurately model these media. In this letter, we extend the contour‐path effective‐permittivity (CP‐EP) technique to three‐dimensional (3D) problems in which a reasonably accurate solution can be obtained with larger meshes for arbitrarily shaped dielectric media. The formulation is performed with the position of the dielectric medium being considered in each cell, leading to its effective permittivity. We compare the result from the present method with the Mie solution and that from the conventional staircase FDTD method to confirm the effectiveness of the 3D CP‐EP technique. The relative error of the scattering cross‐section is reduced to about half that of the staircase FDTD method.

Relaxation of the Courant Condition in the Explicit Finite-Difference Time-Domain Method With Higher-Degree Differential Terms

A new explicit and nondissipative finite-difference time-domain (FDTD) method in two and three dimensions is proposed for the relaxation of the Courant condition. The third-degree spatial difference terms with second- and fourth-order accuracies are added with coefficients to the time-development equations of FDTD(2,4). Optimal coefficients are obtained by a brute-force search of the dispersion relations, which reduces phase velocity errors but satisfies the numerical stabilities as well. The new method is stable with large Courant numbers, whereas the conventional FDTD methods are unstable. The new method also has smaller numerical errors in the phase velocity than conventional FDTD methods with small Courant numbers.

Improved FDTD Method for Coupling Analysis of a Dielectric-Coated Wire Above Rough Soil Surface Under HPEM Pulse

An improved finite difference time domain (FDTD) method is proposed to calculate the transient coupling of a dielectric-coated wire above the rough soil surface under the high power electromagnetic (HPEM) pulse. The improved method is based on the domain decomposition technique, in which the dielectric-coated wire and the rough surface are allocated into the target subdomain and the rough surface subdomain, respectively. The reflected waveform from the rough surface is computed by applying the FDTD method combined with the time-domain Huygen's technique. The incident field on the target subdomain is calculated through the superposition of the excitation fields generated with the directly incident wave and the reflected wave from the rough surface. The near-field distribution and the energy-flux density (EFD) inside the dielectric-coated wire are simulated by running the FDTD in the target subdomain. The accuracy and high efficiency of the improved method are validated and demonstrated by comparing with the conventional FDTD method. Finally, the influences of some parameters related to the rough soil surface and dielectric-coated wire on the EFD are analyzed through the typical examples.

From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

Efficient HIE-FDTD method for designing a dual-band anisotropic terahertz absorption structure

The finite-difference time-domain (FDTD) method is considered to be one of the most accurate and common methods for the simulation of optical devices. However, the conventional FDTD method is subject to the Courant-Friedrich-Levy condition, resulting in extremely low efficiency for calculating two-dimensional materials (2DMs). Recent researches on the hybrid implicit-explicit FDTD (HIE-FDTD) method show that the method can efficiently simulate homogeneous and isotropic 2DMs such as graphene sheet; however, it is inapplicable to the anisotropic medium. In this paper, we propose an in-plane anisotropic HIE-FDTD method to simulate optical devices containing graphene and black phosphorus (BP) sheets. Numerical analysis shows that the proposed method is accurate and efficient. With this method, we present a novel multi-layer graphene-BP-based dual-band anisotropic terahertz absorption structure (GBP-DATAS) and analyze its optical characteristics. Combining the advantages of graphene and BP localized surface plasmons, the GBP-DATAS demonstrates strong anisotropic plasmonic resonance and high absorption rate in the terahertz band.

3-D FDTD Method for Fast Calculation of Geomagnetic Storm Electromagnetic Fields

In this article, a 3-D finite-difference time-domain (FDTD) method is proposed for rigorous modeling and fast calculation of ultralow frequency geomagnetic storm electromagnetic fields (GS-EMFs). The proposed FDTD approach enables modeling of large-scale and complex 3-D earth structure (e.g., multilayer ground and earth curvature). Unlike conventional FDTD methods, the proposed FDTD method does not require extensive computational resources when dealing with ultralow frequency problems. In this article, the ground surface GS-EMFs produced by an electrojet (line current and sheet current sources) are compared with those obtained using the classical 1-D approaches for case of uniform and horizontally stratified ground. The effect of horizontally vertically multilayer ground and earth curvature on the GS-EMFs is evaluated by the proposed FDTD method. The presented results fully support the adequacy and efficiency of the proposed FDTD method for modeling of large-scale and complex 3-D earth structures for calculation of GS-EMFs.

A Hybrid CN-FDTD-SPICE Solver for Field-Circuit Analyses in Low-Frequency Wideband Problems

The conventional finite-difference time-domain (FDTD) method is efficient for microwave frequencies, but requires a large number of time steps for low frequencies. In this work, a hybrid Crank–Nicolson (CN) FDTD-SPICE method is applied to field-circuit analyses in low- frequency wideband problems. The unconditionally stable CN-FDTD method is used to give a rapid full wave solution by overcoming the Courant–Friedrichs–Lewy (CFL) condition that constrains the conventional FDTD method at low frequencies. The hybrid CN-FDTD-SPICE method can be used for simulating the interactions between modern electronic circuit systems and a 3-D structure supporting field radiation and interferences. It can greatly improve the computational efficiency over the conventional FDTD method at low frequencies because its time increment can be significantly larger. Three numerical examples are presented to verify the accuracy and efficiency of this hybrid method. Its CPU time is much shorter than that of the conventional FDTD-SPICE method. This CN-FDTD-SPICE method becomes increasingly advantageous when the radiation fields are required as the system integration continues to accelerate.

Time Domain Hybrid Method for the Coupling Analysis of Oblique Transmission Line Network Excited by Ambient Wave

Efficient numerical methods which analyse the coupling within an oblique transmission line network (OTLN) excited by electromagnetic wave are still rare in the literature. A novel time domain hybrid method is proposed in this article, in which finite-difference time-domain (FDTD) method, transmission line (TL) equations, Norton's theorem, and interpolation techniques are organically combined. In this method, the terminal loads and connection nodes of OTLN are first shifted to the center lines of FDTD grids, where the loads and nodes are located. Then the OTLN is divided into several independent oblique transmission lines according to the connecting nodes. Finally, the FDTD method combined with TL equations and interpolation techniques is applied to compute the transient responses on each oblique transmission line, and the Norton's theorem is utilized to build the equivalent circuit models of connecting nodes to realize the transmissions of interference signals on these oblique transmission lines. Numerical simulations of OTLN on the perfect conductor (PEC) ground and in a shielded cavity excited by ambient wave are employed to exhibit the accuracy and efficiency of the proposed method. Because the structure of OTLN does not need to be meshed, the proposed method outperforms the conventional FDTD method in both memory usage and computation time.

A novel hybrid algorithm based on FDTD and WCS‐FDTD methods

In this article, a hybrid algorithm based on traditional finite-difference time-domain (FDTD) and weakly conditionally stable finite-difference time-domain (WCS-FDTD) algorithm is proposed. In this algorithm, the calculation domain is divided into fine-grid region and coarse-grid region. The traditional FDTD method is used to calculate the field value in the coarse-grid region, while the WCS-FDTD method is used in the fine-grid region. The spatial interpolation scheme is applied to the interface of the coarse grid region and fine grid region to insure the stability and precision of the presented hybrid algorithm. As a result, a relatively large time step size, which is only determined by the spatial cell sizes in the coarse grid region, is applied to the entire calculation domain. This scheme yields a significant reduction both of computation time and memory requirement in comparison with the conventional FDTD method and WCS-FDTD method, which are validated by using numerical results.

A MLP Based FDTD Method

In this paper, we proposed a novel multilayer perceptron (MLP) based Finite-Difference Time-Domain (FDTD) method to reduce the time complexity of the conventional FDTD method, MLP neural networks can be used to replace the field quantities update equations and we found that in certain scenario, we can greatly reduce the time complexity of FDTD method.

Transformation Optics-Based Finite Difference Time Domain Algorithm for Scattering From Object With Thin Dielectric Coating

A proper dielectric coating can reduce the electromagnetic scattering of the conducting object significantly so that it cannot be detected by the radar. However, when the object contains a thin coating, fine grid size is needed to discretize the thin coating in the conventional finite-difference time-domain (FDTD) algorithm, which increases the amount of memory and computational time significantly. To overcome this dilemma, we present a transformation optics-based FDTD (TO-FDTD) algorithm to accelerate the solution of electromagnetic scattering from objects with thin dielectric coatings. Two kinds of novel TO-FDTD models are proposed in this paper for a coated cylinder and a coated arbitrary polygonal cylinder, respectively. Through coordinate transformation, the size of the object remains unchanged while its thin coating is enlarged to a thicker one, meaning that it can be simulated by the FDTD algorithm with uniform coarse grids instead of fine grids. The transformed material parameters become inhomogeneous and anisotropic in the transformed region, which can be obtained by solving a Jacobian transformation matrix. We then develop a stable FDTD algorithm for solving anisotropic Maxwell’s equations. Bistatic scatterings of coated cylinders and a coated polygonal cylinder are solved by the TO-FDTD algorithm proposed in this paper, respectively. The result of the TO-FDTD algorithm matches well with the exact value and the result of the commercial software Comsol. The computational efficiency and accuracy of the proposed TO-FDTD algorithm are validated by numerical experiments. Numerical results show that the TO-FDTD algorithm has higher computational accuracy than the conventional FDTD algorithm that fails to simulate the absorbing property of the coating, when the same coarse grid size is used in the simulation. Under the same level of accuracy, the proposed TO-FDTD method can improve the computational efficiency by 62-63 times than the conventional FDTD method with fine grids in the simulations in the paper.

A Novel Efficient WLP-Based BOR FDTD Method With Explicit Treating Ideology

In this paper, we proposed a novel efficient weighted Laguerre polynomial (WLP)-based finite-difference time-domain (FDTD) method with explicit treating ideology, which is extremely useful for problems with very fine structures in the body of revolution (BOR) system. By combining the explicit treating ideology and WLP technology, the limitation of time step $\Delta \text{t}$ is effectively eliminated, which results in greatly improved performance. The performing idea of the proposed method can be roughly divided into two parts. First, the conventional WLP-based BOR FDTD method is flexibly transformed into a new one with certain direction explicit calculation by matrix transformation. Second, the initial value calculation and iteration calculation which are based on the different perturbation term are introduced to improve the convergence speed, the efficiency and accuracy of the proposed method. Meanwhile, the proofing results show that the convergence condition of the proposed method is relaxed. The stability analysis shows that the stability condition is determined by the smaller one of the spatial increments $\Delta \rho $ and $\Delta \text{z}$ . Finally, two scattering numerical examples are given to demonstrate the computational accuracy and efficiency of the proposed method.

An FDTD Thin-Wire Model for Lossy Wire Structures With Noncircular Cross Section

This paper presents an effective finite-difference time-domain (FDTD) thin-wire model for lossy wire structures with noncircular cross section in transient analysis. Unique correction factors of field quantities and surface electric field of wire structures are introduced in the model. These parameters are both frequency-dependent and position-variant. They are evaluated in an initialization process and are applied in the updating process using an iterative convolution technique. The proposed method is validated with the transmission line theory analytically and the traditional FDTD method numerically. Three types of wire structures are tested, including rectangular, H-shape, and cross-shape structures. Good agreements are observed. It is found that the computation time is reduced to 1% of that with the conventional FDTD method, and the computer memory to 30% in the tested case. General guidelines on wire zone meshing are provided as well. Finally, this method is applied to analyze lightning surges in a light rail system under a direct lightning stroke.

Fast method for analysing nonlinear composite right/left‐handed transmission lines based on finite‐difference time‐domain method

In this study, a new finite-difference time-domain (FDTD) scheme is presented for analysing nonlinear composite right/left-handed (CRLH) transmission lines, with reduction of the central processing unit time. A step by step analysis is demonstrated to solve the equations for nonlinear CRLH transmission lines based on the FDTD method. The proposed method is applied to a nonlinear CRLH transmission line as an example and the results are confirmed by those of the conventional FDTD method. The comparisons reveal that the presented solution efficiently decreases by about 82% of the computational time consumption.

Finite-difference time-domain method for calculating photoexcited molecular vibration wave-packet dynamics

We propose a simple numerical calculation method for solving molecular vibrational dynamics. A finite-difference time-domain (FDTD) method is utilized to solve the Schrödinger equation for wave packet dynamics driven by incident light pulses. Vibrational wave function is discretized and divided into real and imaginary parts, and then the Schrödinger equation is solved by temporally and alternately calculating the real and imaginary parts, in a similar manner to the conventional FDTD method. Taking generation of a hot molecule by pump-dump scheme and multi-photon excitation process as examples, we show the validity and usefulness of the proposed method. The dynamics of the vibrational wave packets in the pump-dump scheme and transient virtual excitations of intermediate vibronic state in the three-photon absorption can be easily visualized, and the intensity dependence of excitation population for ultra-high intensity beyond the perturbation theory can be accurately calculated.

The implementation of unconditionally stable higher order PML based on the implicit CNAD-FDTD algorithm

ABSTRACTAn unconditionally stable implementation of the higher order complex frequency-shifted perfectly matched layer (CFS-PML) based on the Crank–Nicolson-approximate-decoupling (CNAD) algorithm and the bilinear transform (BT) method is proposed to terminate the finite-difference time-domain (FDTD) lattice. The proposed scheme not only takes advantage of the CNAD algorithm in terms of reducing computational time but also has the advantage of the conventional FDTD algorithm in terms of absorbing performance. Two numerical examples are provided to validate the proposed implementation in the homogenous free space and lossy FDTD domains. The results show that the proposed scheme can overcome the Courant–Friedrich–Levy condition compared with the conventional FDTD method and further enhance the absorbing performance compared with the first order PML implementation.

Tunable hybrid metal–graphene frequency selective surfaces based on split‐ring resonators by leapfrog ADI‐FDTD method

A tunable hybrid metal–graphene frequency selective surface (FSS) based on split-ring resonators at mid-infrared frequencies is proposed and numerically investigated by an improved leapfrog alternating direction implicit (ADI)-finite-difference time-domain (FDTD) method. The graphene conductivity described by a new closed-form approximate expression is incorporated into the leapfrog ADI-FDTD through the vector-fitting technique and auxiliary differential equation approach. Numerical simulations show that the proposed method has good computational accuracy and higher efficiency compared to conventional FDTD method and analytical solutions. Besides, the transmission and reflection coefficients of the FSS can be effectively adjusted by changing the chemical potential of graphene, the layer number of graphene patch and operating temperature. This work provides a novel method for designing tunable devices for optical plasmonic applications.

An Unconditionally Stable Radial Point Interpolation Meshless Method Based on the Crank–Nicolson Scheme Solution of Wave Equation

A 2-D unconditionally stable radial point interpolation meshless method (RPIM) based on the Crank–Nicolson (CN) scheme is presented. The CN algorithm in the proposed method is applied to only one of the Maxwell equations. It leads to solving the second-order vector wave equation in the time domain. Therefore, only one electromagnetic field is implicitly updated at each iteration. Furthermore, the computational cost of the CN-RPIM scheme is lesser than the conventional RPIM. The Courant–Friedrichs–Lewy condition in the proposed vector wave equation method does not constrain the time step due to its implicit formulation. Moreover, the stability condition of the proposed method is investigated in this paper through its amplification matrix. A 2-D waveguide and a filter are used as examples to validate and to demonstrate the effectiveness and the accuracy of the proposed method. Numerical results are compared with those obtained by the explicit RPIM method and the conventional finite-difference time-domain method.

Enhancing Efficiency of Electromagnetic Simulation in Time Domain with Transformation Optics

With sub-wavelength scaled structures in a large system, the conventional finite-difference time-domain method can consume much computational resources since it includes both the spatial and temporal dimension in the scheme. In order to reduce the computational cost, we combine the novel methodology “transformation optics” in the simulation to map a physical coordinate with designated non-uniform grids to a uniform numerical coordinate. For a demonstration, the transmission spectrum through a sub-wavelength metallic aperture with one-dimensional and two-dimensional coordinate transformation is simulated, and compared with uniform-grid cases. We show that the proposed method is accurate, and the computational cost can be reduced remarkably to at most 5.31%, in comparison with the simulation of the finest uniform grids demonstrated. We are confident that it should be helpful to the simulation study in sub-wavelength optics due to its verified accuracy and efficiency.