Traditional Finite-difference Time-domain Method Research Articles

Application of spatial filtering high order FDTD method in the multi-physics field coupled equations

The traditional finite-difference time-domain method (FDTD(2, 2)) is widely employed to solve the coupled equations of quantum-electromagnetic multi-physics. However, the time step of the traditional explicit FDTD(2, 2) method is limited by the Courant-Friedrichs-Lewy (CFL) condition. Besides, the FDTD(2, 2) method only achieves the second-order accuracy, which can result in significant error accumulation. To overcome this problem, we propose the SF-HO-FDTD(2, q) method with scalable time stability conditions for solving the multi-physics field coupled equations (q denotes q-th order spatial difference scheme). This approach integrates spatial filtering (SF) and higher-order FDTD (HO-FDTD) methods. Moreover, the proposed method requires no further derivation of the iterative equations of the traditional HO-FDTD(2, q) method. It only needs to introduce the SF operation in each numerical iteration process to filter out the spatial high-frequency components arising from the use of time steps that do not satisfy the CFL stability condition. This condition is applied to ensure the stability of the numerical method. Therefore, the proposed method has a high compatibility with the traditional HO-FDTD(2, q) method. Then, the numerical dispersion analysis of the SF-HO-FDTD(2, q) method is theoretically studied. Finally, numerical examples are carried out to confirm the accuracy and efficiency of the strategy suggested in this study.

Deep Long Short-Term Memory Networks-Based Solving Method for the FDTD Method: 2-D Case

In this letter, a novel finite difference time domain (FDTD) solving method is proposed based on the deep long short-term memory (LSTM) networks. The field data in the object domain of traditional FDTD method are applied to train the newly proposed LSTM-based FDTD model, termed as LSTM-FDTD. Distinguished from the traditional FDTD method, the proposed method is not limited by Courant–Friedrichs–Levy (CFL) condition and does not need the conventional absorbing boundary conditions (ABCs). Thus, the proposed method conveniently decreases both the size of computation domain and the algorithm’s complexity. In addition, LSTM-FDTD could reach higher accuracy due to the sequence dependence of LSTM networks. Numerical benchmarks illustrate the efficiency and accuracy of the proposed method.

Newton-ADE FDTD Method for Time-Varying Plasma

A novel finite-difference time-domain (FDTD) method is proposed in this article for electromagnetic (EM) wave propagation in time-varying plasma. It is formulated based on the fundamental Newton’s equation of motion, which governs the relationships among the time-varying electron density, current density and electric field. Utilizing the auxiliary differential equation (ADE) FDTD scheme, the method is aptly referred to as the Newton-ADE FDTD method for time-varying plasma. Traditionally, the previous ADE FDTD methods directly apply the time-varying electron density for the plasma frequency in the update equations of current density and electric field. This is inadequate and incorrect in general time-varying plasma conditions. The formulation of the Newton-ADE FDTD method is provided and compared to that of the traditional ADE FDTD method. It is found that the key difference lies in the new compact term being the time-derivative of logarithm of electron density. Two discretization schemes for this term are provided. The Newton-ADE FDTD method is validated based on the matrix exponential method. Novel stability and convergence analyses are provided for the proposed method in time-varying dispersive media. These analyses show that our proposed method is stable and achieves second-order temporal accuracy. Numerical results are presented for various time-varying plasma conditions. It is demonstrated that when the absolute value for time-derivative of logarithm of electron density is large, e.g., greater than the collision frequency, the Newton-ADE FDTD method can provide correct results, while the traditional ADE FDTD method yields significant differences.

An Unconditionally Stable Conformal LOD-FDTD Method for Curved PEC Objects and its Application to EMC Problems

The traditional finite-difference time-domain (FDTD) method is constrained by the Courant–Friedrich–Levy condition and suffers from the notorious staircase error in electromagnetic simulations. This article proposes a 3-D conformal locally one-dimensional FDTD (CLOD-FDTD) method to address the two issues for modeling perfectly electrical conducting (PEC) objects. By considering the partially filled cells, the proposed CLOD-FDTD method can significantly improve the accuracy compared with the traditional locally one-dimensional FDTD (LOD-FDTD) method and the FDTD method. At the same time, the proposed method preserves unconditional stability, which is analyzed and numerically validated using the von Neumann method. Significant gains in central processing unit time are achieved by using large time steps without sacrificing accuracy. Two numerical examples, including a PEC cylinder and a missile, are used to verify its accuracy and efficiency with different meshes and time steps. It can be found from these examples that the CLOD-FDTD method shows better accuracy and can improve the efficiency compared with those of the traditional FDTD method and the traditional LOD-FDTD method.

Modeling GPR Wave Propagation in Complex Underground Structures Using Conformal ADI-FDTD Algorithm

Ground Penetrating Radar (GPR) is a shallow geophysical method for detecting and locating subsurface targets. The GPR image echo characteristics of complex underground structures can be obtained by carrying out GPR forward modeling research. The traditional finite-difference time-domain (FDTD) method has low efficiency and accuracy. The alternating direction implicit FDTD (ADI-FDTD) algorithm surmounts the stability limitations of the traditional FDTD method, making it possible to select a larger time step for higher computational efficiency. For circular underground structures, a pseudowave produced by the ladder approximation method can be corrected using the surface conformal technique. This paper proposes a high-efficiency and high-accuracy GPR forward modeling method that combines the ADI-FDTD algorithm and surface conformal technology. The performance of the conformal ADI-FDTD algorithm is verified by a simple two-layer model. Based on the proposed algorithm, the GPR image features of three complex underground structure models are obtained. Finally, a field experiment is used to support the accuracy and usefulness of the conformal ADI-FDTD algorithm. The numerical simulation results and experimental results show that the conformal ADI-FDTD algorithm reduces the pseudodiffraction wave caused by the ladder approximation method and can significantly improve the computing efficiency for complex underground structure models.

Universal HIE-FDTD method and progarm implementation for one-dimensional fine structure electromagnetic target simulation

The hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is a weakly conditionally stable finite-difference time-domain (FDTD) method. The time step size of the HIE-FDTD method is only confined by the two coarse spatial cell sizes, so it is widely used in the simulation of electromagnetic targets with fine structures along one direction. In this work, the basic iterative formulations of the HIE-FDTD method are proposed by approximating the formulations of the FDTD method. In these formulations, the iterative coefficients are marked with spatial grid numbers. Therefore, the coefficients can be calculated automatically according to the medium parameters of the spatial cells by indexing the grid numbers. Since the triangular matrix which is used to calculate the electric field is based on the iterative coefficients, the triangular matrix can also be updated automatically. In addition, a method to reduce the number of tridiagonal matrices is proposed in this work, which can effectively reduce the calculation memory and improve the calculation efficiency. In the proposed HIE-FDTD method, equivalent parameters are employed at the interfaces of different media and the convolution perfectly matched layer boundary condition is used to truncate the computational region. Based on the proposed HIE-FDTD method, a series of programs are implemented, which can simulate arbitrary electromagnetic targets with fine structure in one dimension in linear and non-dispersive space. A dielectric plate irradiated by planar wave and a dual-frequency microstrip inverted F antenna are simulated by using these programs. The numerical results are in good agreement with those from the traditional FDTD method and CST software, and the computational efficiency of the proposed HIE-FDTD method is greatly improved in comparison with that of the traditional FDTD method. This study provides a reliable simulation tool for the wide application of the HIE-FDTD method.

An Efficient Time-Domain Electromagnetic Algorithm Based on LSTM Neural Network

Although neural networks have been applied in many fields since they were first introduced, the feasibility of applying it to predict the solution of Maxwell's equations remains open. In this letter, we investigate the feasibility of utilizing the long- and short-term memory (LSTM) neural network to solve the time-domain electromagnetic (TDEM) forward problems. With ground truth datasets being generated from the finite-difference time-domain (FDTD) method, a novel LSTM-TDEM model structure is proposed, and trained by a new feasible algorithm specifically designed for time-domain simulation. The strong approximation ability of the LSTM-TDEM method can accurately predict the electromagnetic field distributions for topologies of different geometries, materials, and excitations at different locations. The effectiveness of the proposed LSTM-TDEM method has been validated by several numerical experiments. The average relative error can be as small as 0.63% for 2-D case and 0.35% for 3-D case. It is worth noting that the training data are only 5% (198/4087) and 30% (660/2189) in 2-D and 3-D cases, respectively. Meanwhile, compared with the traditional FDTD method, the proposed method greatly reduces the calculation time, with its speedup ratio more than 1800 and 44 000 times over the FDTD method in 2-D and 3-D cases, respectively.

EMI Analysis of Multiscale Transmission Line Network Using a Hybrid FDTD Method

A hybrid time-domain numerical method based on the full wave finite-difference time-domain (FDTD) method combined with a modified 1-D FDTD method has been proposed to analyze the electromagnetic interference (EMI) of multiscale transmission line networks in a metallic cabin in this article. This method is implemented through two numerical solvers for full wave and transmission line simulations, respectively, by adopting a set of reasonable physical boundary conditions between external fields and transmission line network. By using Ampere's law, the external fields can be transferred to a voltage source that can be further used as the forcing terms in the telegraph equation of the transmission line network. To overcome the challenge introduced by the multiscale size of the transmission line network, we combine 1-D explicit and implicit FDTD methods together to solve the coaxial cables and interconnects in PCB, respectively. Thus, among different subdomains, the hybrid method can be carried with the same time step without the restriction of the stability condition. Numerical examples show the accuracy as well as efficiency of the proposed method compared with the HSPICE and traditional FDTD method. In addition, the method is used successfully in analyzing the EMI effects of a complex transmission line network inside a cabin illuminated by external electromagnetic wave.

A 3-D FDTD Thin-Wire Model of Single-Core Coaxial Cables With Multiple Conductive Layers

In this article, a thin-wire model of single-core coaxial cables with three or more conductive layers is proposed for transient analysis using the finite-difference time-domain (FDTD) method. The multilayer cable is regarded as a series of 2-conductor coaxial transmission lines. The currents in these lines can be, however, unbalanced, and may not return via earth, such as in the case of a direct lightning strike. The FDTD method is employed to evaluate electromagnetic coupling outside the cable. Frequency-dependent surface impedances of conductors are fully considered using the Bessel functions. They are integrated into the time-domain analysis with a vector fitting technique. Updating equations for both lossless and lossy cables are derived. The proposed model is validated transmission line theory analytically and with the traditional FDTD method numerically. Good agreements are observed. Finally, the proposed model is applied to analyze the transients in a cable connection station under a direct lightning strike.

Applications of anisotropic one‐step leapfrog HIE‐FDTD method in microwave circuit and antenna

To verify the effect of artificial anisotropy parameters in one-step leapfrog hybrid implicit-explicit finite-difference time-domain (FDTD) method, we calculated several microwave components with different characteristics. Introduced auxiliary field variable can reduce the program difficulty and improve the computational efficiency without additional computational time and memory cost. Analyses of the numerical results are proved that the calculation time is reduced to about one-sixth compared to the traditional FDTD method for the same example simulated. The memory cost and relative error are remained at a good level. The numerical experiments for microwave circuit and antenna have been well demonstrated the method available.

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 Hybrid Method Based on Leapfrog ADI-FDTD and FDTD for Solving Multiscale Transmission Line Network

This article proposes a novel hybrid finite-difference time-domain (FDTD) method to calculate the transient responses of the transmission line network based on the leapfrog alternating direction implicit FDTD (leapfrog ADI-FDTD) algorithm and the traditional FDTD method. The proposed hybrid method can be implemented by dividing the transmission line network into two parts that are the interconnects part in a printed circuit board solved by the leapfrog ADI-FDTD and the cable part solved by the traditional FDTD with different mesh sizes and the same time step, respectively. In addition, some boundary conditions should be introduced based on the modified nodal approach and Kirchhoff's law at the terminals of the transmission line network. The numerical results show that the proposed hybrid method is in good agreement with HSPICE. Especially, it is more efficient and applicative for the multiscale transmission line network problems due to the use of the implicit FDTD solver with unconditional stability compared with the traditional FDTD method.

Analysis of GPR Wave Propagation in Complex Underground Structures Using CUDA-Implemented Conformal FDTD Method

Ground penetrating radar (GPR), as a kind of fast, effective, and nondestructive tool, has been widely applied to nondestructive testing of road quality. The finite-difference time-domain method (FDTD) is the common numerical method studying the GPR wave propagation law in layered structure. However, the numerical accuracy and computational efficiency are not high because of the Courant-Friedrichs-Lewy (CFL) stability condition. In order to improve the accuracy and efficiency of FDTD simulation model, a parallel conformal FDTD algorithm based on graphics processor unit (GPU) acceleration technology and surface conformal technique was developed. The numerical simulation results showed that CUDA-implemented conformal FDTD method could greatly reduce computational time and the pseudo-waves generated by the ladder approximation. And the efficiency and accuracy of the proposed method are higher than the traditional FDTD method in simulating GPR wave propagation in two-dimensional (2D) complex underground structures.

New hybrid FDTD algorithm for electromagnetic problem analysis**Project supported by the National Natural Science Foundation of China (Grant No. 61571348) and the Equipment Pre-Research Foundation of China (Grant No. 61405180202).

Since the time step of the traditional finite-difference time-domain (FDTD) method is limited by the small grid size, it is inefficient when dealing with the electromagnetic problems of multi-scale structures. Therefore, the explicit and unconditionally stable FDTD (US-FDTD) approach has been developed to break through the limitation of Courant–Friedrich–Levy (CFL) condition. However, the eigenvalues and eigenvectors of the system matrix must be calculated before the time iteration in the explicit US-FDTD. Moreover, the eigenvalue decomposition is also time consuming, especially for complex electromagnetic problems in practical application. In addition, compared with the traditional FDTD method, the explicit US-FDTD method is more difficult to introduce the absorbing boundary and plane wave. To solve the drawbacks of the traditional FDTD and the explicit US-FDTD, a new hybrid FDTD algorithm is proposed in this paper. This combines the explicit US-FDTD with the traditional FDTD, which not only overcomes the limitation of CFL condition but also reduces the system matrix dimension, and introduces the plane wave and the perfectly matched layer (PML) absorption boundary conveniently. With the hybrid algorithm, the calculation of the eigenvalues is only required in the fine mesh region and adjacent coarse mesh region. Therefore, the calculation efficiency is greatly enhanced. Furthermore, the plane wave and the absorption boundary introduction of the traditional FDTD method can be directly utilized. Numerical results demonstrate the effectiveness, accuracy, stability, and convenience of this hybrid algorithm.

A novel domain decomposition-finite difference time domain method for composite scattering from a target above rough surface

A novel domain decomposition-finite difference time domain (DD-FDTD) method is proposed to improve the computation efficiency of the traditional finite difference time domain (FDTD) method in calculating composite scattering from a target above a rough surface. In this scheme, the target and the rough surface are placed into the target subdomain and the rough surface subdomain, respectively. The incident waves of the target subdomain, including the directly illuminated wave and the nonplanar reflected wave from the rough surface, are introduced by invoking the Huygens’ principle and the equivalence principle. The FDTD method is executed in each subdomain to obtain the scattering fields of the target and the rough surface, and the scattering contribution of the rough surface from the reflected wave of target is taken into account. In comparison with the traditional FDTD method, the proposed method has significant advantages in saving memory usage and in reducing computation time, which is more efficient in solving the composite scattering problems with larger distance between target and rough surface.

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.

Study on SAR Distribution of Human Body on the Vehicle Platform Using a Modified FDTD Method

This paper is devoted to characterizing the specific absorption rate (SAR) distribution of a human body model in a vehicle-based shelter in the presence of high-power intentional electromagnetic pulse (IEMP) radiation using a modified finite-difference time-domain (FDTD) method. The proposed method combines the FDTD(2, 4) method along with dielectric conformal techniques, where the updating equations of FDTD(2, 4) method are modified by introducing an effective dielectric constant and a new conductivity derived by area average of different dielectric regions including coating layer in nine spatial discrete cells. Numerical results show that our method even with coarse meshes has good agreements and efficiency comparing with the traditional FDTD method and CST simulation tool. Furthermore, the proposed method is applied to predict the SAR distribution of human body in a vehicle-based metallic shelter, where the peak SAR and average SAR are captured and compared in the presence of an IEMP with different polarizations and incident angles.

Hybrid FDTD Method for Studying Electromagnetic Coupling Effects of Transmission Line Networks

This letter proposes a novel hybrid finite-difference time domain (FDTD) method, which combines the full-wave FDTD (2, 4) method with a thin-wire model, a transmission-line equation, the Kirchhoff's law, and a two-port equivalent-circuit FDTD model, where antenna–cable coupling model and modified nodal analysis method are also implemented through a set of proper boundary conditions. In our method, both coaxial cable and thin-wire antenna are treated together without geometric meshing for full-wave simulation, and all the coupling processes among fields, transmission line equations, and circuit loads are carried out at the same time step. Such hybrid method is verified by comparing with both PSPICE and traditional FDTD method, and good agreements are obtained. Further, the proposed method is successfully applied to predict the transient electromagnetic responses of some complex transmission line networks in a vehicle-based metallic shelter.

The Extended Thin Wire Model of Lossy Round Wire Structures for FDTD Simulations

This paper presents an extended thin-wire model for simulating lightning surge or wave propagation on lossy round wire structures. The wire structures are represented with time-domain cascade circuits, and are integrated into a traditional finite-difference time-domain (FDTD) thin-wire model for the simulation. The model for solid round conductors, cylindrical tubes, and coaxial conductors is provided, and the skin effect is fully considered. In the coaxial structure, the currents in both inner and outer conductors are not necessarily balanced. The proposed model has been validated analytically and numerically, and good agreements have been observed. It has been applied to analyze lightning current sharing in a lossy radio-frequency coaxial cable. Compared with the traditional FDTD method, this extended thin-wire model requires less memory space and computation time in the simulation.

A research on the electromagnetic properties of Plasma Photonic Crystal based on the Symplectic Finite-Difference Time-Domain method

The Symplectic Finite-Difference Time-Domain (SFDTD) method was applied to simulate the one-dimensional unmagnetized Plasma Photonic Crystal (PPC) with a sandwich structure. Compared with the traditional Finite-difference Time-Domain (FDTD) method, the results from the SFDTD method are reliable and accurate. Also the SFDTD method has better numerical dispersion characteristics than the traditional FDTD method and the Multi-Resolution Time-Domain (MRTD) method too. Electromagnetic propagation process by differential Gaussian pulse is given in the PPC band gap with the SFDTD method used. The influence of the plasma frequency and the thickness ratio of plasma and medium to PPC on the band gap structure is analyzed. The plasma frequency most affects the PPC in low-frequency range. Also the propagation of an electromagnetic wave can be controlled by the thickness ratio of plasma and medium. The results above prove that the SFDTD method can give the right and better results on the research of PPC.