A Locally Conformal Algorithm for Handling Curved Metallic Surfaces and Its Application

This paper describes a modified locally conformal algorithm for finite-difference time-domain (FDTD) method. Fields in the entire computational domain are computed by a regular FDTD algorithm except those near curved metallic surfaces, where special techniques proposed in this paper are applied. The computation efficiency of a regular FDTD method is maintained while a high space-resolution is obtained by this new algorithm. To validate the reliability of the algorithm, coaxial continuous transverse stub arrays at millimeter wave Ka-band and microwave X-band are tested, and the simulated results show good agreement with the experimental results from an HP-8510B Network Analyzer and the simulation results from software package HFSS.     

Incorporating two-port networks with S-parameters into FDTD

A modeling approach for incorporating a two-port network with S-parameters in the finite-difference time-domain (FDTD) method is reported. The proposed method utilizes the time-domain Y-parameters to describe the network characteristics, and incorporates the Y-parameters into the FDTD algorithm. The generalized pencil-of-function technique is applied to improve the memory efficiency of this algorithm by generating a complex exponential series for the Y-parameters and using recursive convolution in the FDTD updating equations. A modeling example is given, which shows that this approach is effective and accurate. This modeling technique can be extended for incorporating any number of N-port networks in the FDTD modeling     

A hybrid Yee algorithm/scalar-wave equation approach

In this paper, two alternate formulations of the Yee algorithm, namely, the finite-difference time-domain (FDTD) vector-wave algorithm and the FDTD scalar-wave algorithm are examined and compared to determine their relative merits and computational efficiency. By using the central-difference divergence relation the conventional Yee algorithm is rewritten as a hybrid Yee/FDTD scalar-wave algorithm. It is found that this can reduce the computation time for many 3-D open geometries, in particular planar structures, by approximately two times as well as reduce the computer-memory requirements by approximately one-third. Moreover, it is demonstrated both mathematically and verified by numerical simulation of a coplanar strip transmission line that this hybrid algorithm is entirely equivalent to the Yee algorithm. In addition, an alternate but mathematically equivalent reformulation of the Enquist-Majda absorbing boundary condition based on the normal field component (relative to the absorbing boundary wall) is given to increase the efficiency of the hybrid algorithm in the modeling of open region problems. Numerical results generated by the hybrid Yee/scalar-wave algorithm for the Vivaldi antenna are given and compared with published experimental work     

A new technique for the stable incorporation of static fieldsolutions in the FDTD method for the analysis of thin wires and narrowstrips

The behavior of the fields around many common objects (e.g., wires, slots, and strips) converges to known static solutions. Incorporation of this a priori knowledge of the fields into the finite-difference time-domain (FDTD) algorithm provides one method for obtaining a more efficient characterization of these structures. Various methods of achieving this have been attempted; however, most have resulted in unstable algorithms. Recent investigations into the stability of FDTD have yielded criteria for stability, and this contribution for the first time links these criteria to a general finite-element formulation of the method. It is shown that the finite-element formulation provides a means by which FDTD may be generalized to include whatever a priori knowledge of the field is available, without compromising stability. Example results are presented for extremely narrow microstrip lines and wires     

The theory of a singularity-enhanced FDTD method for diagonal metal edges

The complete theory of a singularity-enhanced finite-difference time-domain (FDTD) method for a sharp diagonal metal edge is presented. This method is very accurate and efficient for modeling printed microwave components with diagonal metal edges including some microstrip patch antennas, various other printed antennas, and printed transmission lines. Considering the singular nature of electromagnetic fields at a sharp metal edge, new FDTD equations are derived for all electric and magnetic nodes near the edge, using a contour-path subcell approach. The new FDTD equations for the affected nodes differ from the standard (Yee's) FDTD equations only by a few additional coefficients, for which complete mathematical expressions are given. Application of this method to several antenna and transmission-line problems demonstrated significantly improved accuracy over previous methods, without any noticeable computing overhead. A coarse grid can be used in conjunction with this method and hence the required computer memory and time can be reduced drastically. We have used the maximum allowed time step in all our applications and the method was always stable.     

FDTD modeling of lumped ferrites

Implementing ferrites in finite-difference time-domain (FDTD) modeling requires special care because of the complex nature of the ferrite impedance. Considerable computational resources and time are required to directly implement a ferrite in the FDTD method. Fitting the ferrite impedance to an exponential series with the generalized-pencil-of-function (GPOF) method and using recursive convolution is an approach that minimizes the additional computational burden. An FDTD algorithm for a lumped ferrite using GPOF and recursive convolution is presented herein. Two different ferrite impedances in a test enclosure were studied experimentally to demonstrate the FDTD modeling approach. The agreement is generally good     

电磁场FDTD算法的容错分析与实现

 针对时域有限差分(FDTD)算法的计算机实现困难,提出时间与空间容错概念,并详细分析了FDTD算法的容错特性,以及影响容错FDTD执行性能与计算精度的几个关键因素.在容错实现中,本文提出容错写盘时忽略理想匹配层(PML)吸收边界,并利用内存映射技术实现电/磁场值数组,然后将其应用到FDTD算法的时间与空间容错中.数值模拟实例和相关的性能比较结果验证了方法的有效性.     

An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method

In this study, an alternative algorithm is proposed for modeling narrowband and wideband Lorentzian dispersive materials using the finite-difference time-domain (FDTD) method. Previous algorithms for modeling narrowband and wideband Lorentzian dispersive materials using the FDTD method have been based on a recursive convolution technique. They present two different and independent algorithms for the modeling of the narrowband and wideband Lorentzian dispersive materials, known as the narrowband and wideband Lorentzian recursive convolution algorithms, respectively. The proposed alternative algorithm may be used as a general algorithm for both narrowband and wideband Lorentzian dispersive materials modeling with the FDTD method. The second-order motion equation for the Lorentzian materials is employed as an auxilary differential equation. The proposed auxiliary differential-equation-based algorithm can also be applied to solve the borderline case dispersive electromagnetic problems in the FDTD method. In contrast, the narrowband and wideband Lorentzian recursive convolution algorithms cannot be used for the borderline case. A rectangular cavity, which is partially filled with narrowband and wideband Lorentzian dispersive materials, is presented as a numerical example. The time response of the electric field z component is used to validate and compare the results     

Partially prism-gridded FDTD analysis for layered structures oftransversely curved boundary

In this paper, a partially prism-gridded finite-difference time-domain (FDTD) method is proposed for the analysis of practical microwave and millimeter-wave planar circuits. The method is featured by hybridizing the flexible prism-based finite-element method to handle the region near the curved metallization boundary and the efficient rectangular-gridded FDTD method for most of the regular region. It can be used to deal with shielded or unshielded planar components such as patch antennas, filters, resonators, couplers, dividers, vias, and various transitions between planar transmission lines. Although only representative structures, e.g., grounded via, through hole via, and coplanar waveguide to coplanar stripline transition, are analyzed in this paper, the underlined formulation is applicable to layered structures with arbitrary curved boundary in the transverse direction. The accuracy of this method is verified by comparing the calculated results with those by other methods. Also, by the analysis of computational complexity, the present method is shown to be as efficient as the conventional FDTD method, with negligible overhead in memory and computation time for handling the curved boundary     

Numerical and experimental corroboration of an FDTD thin-slot modelfor slots near corners of shielding enclosures

Simple design maxims to restrict slot dimensions in enclosure designs below a half-wave length are not always adequate for minimizing electromagnetic interference (EMI). Complex interactions between cavity modes, sources, and slots can result in appreciable radiation through nonresonant length slots. The finite-difference time domain (FDTD) method can be employed to pursue these issues with adequate modeling of thin slots. Subcellular FDTD algorithms for modeling thin slots in conductors have previously been developed. One algorithm based on a quasistatic approximation has been shown to agree well with experimental results for thin slots in planes. This FDTD thin-slot algorithm is compared herein with two-dimensional (2-D) moment method results for thin slots near corners and plane wave excitation. FDTD simulations are also compared with measurements for slots near an edge of a cavity with an internal source     

PCB上微带线的电磁耦合时域建模分析方法

基于时域有限差分方法和传输线方程,结合高效网格建模技术,文中提出了一种高效的时域建模算 法,它能有效解决微带线的电磁耦合建模问题,实现空间电磁场与微带线瞬态响应的同步计算。首先,结合经验公 式,计算得到微带线的单位长度分布参数,构建适用于微带线电磁耦合分析的传输线方程。然后,采用时域有限差 分(Finite-Difference Time-Domain, FDTD)方法,结合非均匀网格技术和自动网格生成技术,仿真得到微带线激励场, 并在每个时间步进上引入传输线方程获得等效分布源项。最后,对传输线方程使用FDTD 的中心差分格式进行离 散,实现微带线及其端接电路上瞬态响应的迭代求解。为了验证时域建模算法的正确性和高效性,通过自由空间和 屏蔽腔内PCB 上微带线电磁耦合的数值模拟,从计算精度和耗时两方面与传统FDTD 方法的计算结果进行了对比。     

基于GPU的并行FDTD方法在二维粗糙面散射中的应用

利用显卡(Graphics Processing Unit, GPU)加速时域有限差分(Finite-Difference Time Domain, FDTD)法计算二维粗糙面的双站散射系数, 介绍了FDTD的理论公式以及计算模型.采用各向异性完全匹配层(Uniaxial Perfectly Matched Layer, UPML)截断FDTD计算区域.重点讨论了基于GPU的并行FDTD计算粗糙面双站散射系数的并行设计方案计算流程.在NVIDIA GeForce GTX 570显卡上获得了50.7×的加速比.结果表明:通过对FDTD计算粗糙面散射问题的加速, 极大地提高了计算效率.     

FDTD analysis of a metal-strip-loaded dielectric leaky-wave antenna

The finite-difference time-domain (FDTD) method is used to analyze a dielectric leaky-wave antenna comprising metal strips etched on a rectangular dielectric rod. The radiation patterns of the leaky-wave antenna with and without the transition are determined by using FDTD. The effects of the launching discontinuity on the performance of the antenna are discussed. In addition, the application of the perfectly matched layer (PML) technique to the three-dimensional (3-D) dielectric waveguide and its performance, compared to those of the Mur's (1981) first-order and super-absorbing Mur's first-order absorbing boundary conditions (ABCs) are described. In addition, the effects caused by perturbation on the wave propagation characteristics of dielectric waveguide are also discussed. The FDTD results are verified by a W-band experiment and found to be in good agreement     

Conformal method to eliminate the ADI-FDTD staircasing errors

The alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable method and allows the time step to be increased beyond the Courant-Friedrich-Levy (CFL) stability condition. This method is potentially very useful for modeling electrically small but complex features often encountered in applications. As the regular FDTD method, however, the spatial discretization in the ADI-FDTD method is only first-order accurate for discontinuous media; several researchers have shown that the errors can be very high when the regular ADI-FDTD method is applied to such discontinuous media. On the other hand, the conformal FDTD method has recently emerged as an efficient FDTD method with higher order accuracy. In this work, a second-order accurate ADI-FDTD method using the conformal approximation of spatial derivatives is proposed. This new scheme, called the ADI-CFDTD method, retains the second-order accuracy in both temporal and spatial discretizations even for discontinuous media with metallic structures, and is unconditionally stable. 2D and 3D examples demonstrate the efficacy of this method and its application in EMC problems.     

Numerical Analysis for an Improved ADI-FDTD Method

The numerical performance of an improved alternating direction implicit finite-difference time-domain (ADI–FDTD) method is studied in this letter. Theoretical analysis shows that this method is unconditionally stable and has low splitting error. Compared with the regular ADI–FDTD method, this method is a better splitting formulation for the Crank–Nicolson FDTD method.      

色散金属的时域有限差分方法

表面等离子体激元具有使光场局域化和局域电磁场增强等特性,在纳米光子学和微观检测等诸多领域显示出广泛的应用潜力.时域有限差分（FDTD）数值计算方法能仿真激光与亚波长金属微结构相互作用的表面等离子体效应.金属具有色散性质,其相对介电常数模型有Drude模型和Lorentzs模型及它们相结合的Drude-Lorentzs模型,能拟合金属在可见光和近红外部分或全部波段的色散特性.FDTD数值计算要采用增加辅助变量和相应的辅助差分方程的方法使FDTD迭代计算稳定.     

A 3-D precise integration time-domain method without the restraints of the courant-friedrich-levy stability condition for the numerical solution of Maxwell's equations

In this paper, a new three-dimensional time-domain method for solving vector Maxwell's equations, called the precise-integration time-domain (PITD) algorithm, is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on the precise-integration technique. It is shown that this method is quite stable even when the CFL condition is not satisfied. Although the memory requirement of the PITD method is much larger than that of the finite-difference time-domain (FDTD) method, this new algorithm is very appealing since the time step used in the simulation is no longer restricted by stability. As a result, computation speed can be improved. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than the FDTD scheme. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the accuracy of the PITD is independent of the time-step size.     

On the solution of a class of large body problems with full orpartial circular symmetry by using the finite-difference time-domain(FDTD) method

This paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry. The method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem. It does so by dividing the problem into two parts: a larger 3-D region with circular symmetry, and a smaller 2-D region without circular symmetry. An finite-difference time-domain (FDTD) algorithm is used to analyze the circularly symmetric 3-D case, while a method of moments (MoM) code is employed for the nonsymmetric part of the structure. The results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system. The advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2-D as opposed to a full 3-D FDTD simulation. In addition to enhancing computational efficiency, the FDTD algorithm used in this paper also features one improvement over conventional FDTD methods: a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces. The accuracy of the method is validated via a comparison of simulated and measured results     

Finite-difference time-domain modeling of frequency selective surfaces using impedance sheet conditions

Novel finite-difference time-domain (FDTD) models of frequency-selective surfaces (FSS) based on impedance sheet conditions are developed. The analytical basis of the models lies in impedance sheet conditions with general reactive grid impedances applying to a great variety of grid realizations. New models for periodic arrays of metal particles and for the complementary structures of slots in metal screen are formulated for FDTD in the case of normal incidence. The properties of the FSS are included in the grid impedance, which is implemented into FDTD, considerably simplifying the otherwise extremely cumbersome modeling task. The convergence and the accuracy of the models are assessed with numerical simulations by comparing with analytical and measured reference results.     

A Modified High Order FDTD Method Based on Wave Equation

A modified (2M, 4) scheme of the high-order two-dimensional finite-difference time-domain (FDTD) method based on wave equation is proposed. It has the fourth-order accuracy in the time domain using the symplectic integrator propagator, and the 2M-order accuracy in the space domain using the discrete singular convolution method. The distinctive features between the modified scheme and the traditional (2M, 4) FDTD based on Yee algorithm are listed as follows. First, the modified scheme is based on the wave equation. Second, the computational region is discretized by uniform mesh rather than the Yee mesh. Third, the modified scheme costs less memory than the Yee algorithm because fewer field elements are involved in computation. Numerical examples are provided to validate its accuracy and effectiveness