Time-domain analysis of periodic structures at oblique incidence:orthogonal and nonorthogonal FDTD implementations

A novel implementation of periodic boundary conditions incorporated into the finite-difference time-domain (FDTD) technique in both orthogonal and nonorthogonal grids is presented in this paper. The method applied is a field-splitting approach to the discretization of the Floquet-transformed Maxwell equations. As a result, the computational burden is reduced and the stability criterion is relaxed. The results of the two methods are compared to experimental data     

Stability characteristics of absorbing boundary conditions inmicrowave circuit simulations

In this paper, we examine the stability properties of several absorbing boundary conditions in the finite-difference time-domain (FDTD) simulations of microwave circuits. The numerical experiments show that the stability characteristics of absorbing boundary conditions, e.g., Mur's (1981) and perfectly matched layers (PML), can depend upon the discretization of the computational domain     

ANALYSIS OF 2-D EM PROBLEMS ON A COMPOUND RECTANGULAR REGION BY THE METHOD OF LINES

In this paper an extended method of lines for analyzing the electromagnetic boundary valueproblems is presented and applied to the waveguide with a compound rectangular cross-section.A number ofnumerical results are given for the higher mode analysis in a rectangular waveguide with ridges or fins,and in ashielded stripline.In the computation practice,the random errors caused by the discretization of theboundary conditions are decreased by a least-square procedure.     

An accurate scheme for the solution of the time-domain Integral equations of electromagnetics using higher order vector bases and bandlimited extrapolation

Despite the numerous advances made in increasing the computational efficiency of time-domain integral equation (TDIE)-based solvers, the stability and accuracy of TDIE solvers remain problematic. This paper introduces a new numerical method for the accurate solution of TDIEs for scattering from arbitrary perfectly conducting surfaces. The work described in this paper uses the higher order divergence-conforming basis functions of Graglia et al. for spatial discretization and bandlimited interpolation functions for the temporal discretization of the relevant integral equations. Since the basis functions used for the temporal representation are noncausal, an extrapolation scheme is employed to recover the ability to solve the problem by marching on in time. Numerical results demonstrate that the proposed method is stable and that it exhibits superlinear convergence with regard to the spatial discretization and exponential convergence with respect to the temporal discretization.     

新型椭圆函数波导族的保角变换有限差分解法

保角变换一直是求解边值问题的重要方法,但以往在电磁场领域的应用多限于求解静态和准静态问题。利用保角变换及椭圆函数的理论和方法结合数值技术求解导波问题中的二维Ｈｅｌｍｈｏｌｔｚ方程。     

Iterative solution of the eigenvalue problem for a dielectricwaveguide

The authors present a numerical approach to the simulation of dielectric waveguides that is free of spurious modes and is based on the solution of an eigenvalue problem for the two transverse components of the magnetic field. They introduce a new discretization which has several computational advantages. In particular, by careful design of the discretization procedure, the authors obtain systems of equations for the two components which are equivalent in the sense that a rotation over 900 corresponds to a suitable permutation of indices. The eigenvalue problem is solved iteratively by using an adapted version of the Chebyshev-Arnoldi algorithm. This approach takes full advantage of the sparsity of the matrix and circumvents the large memory requirements and the large computational complexity associated with dense methods. This allows the authors to employ meshes that are sufficiently fine to resolve higher modes without large discretization errors     

电磁场计算中一般的逐层递推求解有限元法

相似剖分有限元法在相似剖分的基础上；实现了按层逐步递推计算；使刚度阵阶数大大降低，但对于具有多媒质、多连通场域的问题，相似剖分有限元法处理起来就不十分容易。本文给出一种更为普遍的方法，由于这种方法对于剖分无严格限制，不要求每层剖分相似，也不要求每边节点数目相同，使得在多媒质、多连通场域的问题中，按层逐步递推求解的思想能够实现。另外，可以认为相似剖分有限元法是这种方法的特例。     

A New State-space-based Algorithm to Assess the Stability of the Finite-difference Time-domain Method for 3D Finite Inhomogeneous Problems

The finite-difference time-domain (FDTD) method is an explicit time discretization scheme for Maxwell's equations. In this context it is well-known that explicit time discretization schemes have a stability induced time step restriction. In this paper, we recast the spatial discretization of Maxwell's equations, initially without time discretization, into a more convenient format, called the FDTD state-space system. This in turn allows us to derive a new algorithm in order to determine the stability limit of FDTD for lossy, inhomogeneous finite problems. It is shown that a crucial parameter is the spectral norm of the matrix resulting from the spatial discretization of the curl operator. In a rectangular simulation domain the time step upper bound can be calculated in closed form and results in a time step limit less stringent than the Courant condition. Finally, the validity of the technique is illustrated by means of some pertinent numerical examples.     

Analysis of the Scattering Characteristic of Several Waveguide Components Using Boundary Element Method

Several kinds of waveguide components such as curved waveguide bends, arbitrary angle waveguide bends and T-junctions have been analyzed with boundary element method in this paper. A new discretization method for the boundary element method to solve the waveguide discontinuities has been given. The numerical results obtained agree well with the experimental results and numerical results in other literature. Especially, the scattering characteristics of Forded E-, H-plane T-junctions in 3mm band have been analyzed using boundary element method and the calculation results are presented.     

Innovative absorbing-boundary conditions for the efficient FDTDanalysis of lightning-interaction problems

Absorbing boundary conditions are developed for the efficient truncation of three-dimensional finite-difference time-domain (3-D FDTD) meshes, used for the analysis of low-frequency transient problems, such as the lightning interaction with an aircraft. The proposed boundary conditions are combined with an innovative time-marching scheme in order to assure numerical stability of the FDTD procedure for millions of time-iterations. The main advantage of the developed approach consists in the great computer saving allowed in the analysis of FDTD problems in which the space discretization step is several thousands of times smaller than the minimum wavelength excited by the transient source. Numerical applications are included in order to demonstrate the accuracy and efficiency of the proposed method     

Time-domain BIE analysis of large three-dimensional electromagneticscattering problems

A time-domain boundary integral equation (BIE) solution of the magnetic field integral equation (MFIE) for large electromagnetic scattering problems is presented. It employs isoparametric curvilinear quadratic elements to model fields, geometry, and time dependence, eliminating staircasing problems. The approach is implicit, which seems to provide both stability and permits arbitrary local mesh refinement to model geometrically difficult regions without the significant cost penalty explicit methods suffer. Error dependence on discretization is investigated; accurate results are obtained with as few as five nodes per wavelength. The performance both on large scatterers and on low-radar cross section (RCS) scatterers is demonstrated, including the six wavelength “NASA almond,” two spheres, a thirteen wavelength missile, and a “high-Q” cavity     

Extension and validation of a perfectly matched layer formulation for the unconditionally stable D-H FDTD method

In this letter, a modification to the recently proposed unconditionally stable D-H ADI FDTD method is presented that considerably reduces the late-time error induced by the corner cells. The PML boundary is derived from the direct discretization of the modified D-H Maxwell's equations rather than the superposition of uniaxial PML boundaries. An optimal choice of the PML conductivity profile coefficients is proposed. Results show that the reflection error of the PML is limited for increased time step size beyond the Courant-Friedrichs-Lewy stability bound, and maximum reflection errors are 15 to 20 dB lower than the original formulation.     

A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations

This paper presents a general approach for the stability analysis of the time-domain finite-element method (TDFEM) for electromagnetic simulations. Derived from the discrete system analysis, the approach determines the stability by analyzing the root-locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix. The approach is applicable to the TDFEM simulation involving dispersive media and to various temporal discretization schemes such as the central difference, forward difference, backward difference, and Newmark methods. It is shown that the stability of the TDFEM is determined by the material property and by the temporal and spatial discretization schemes. The proposed approach is applied to a variety of TDFEM schemes, which include: (1) time-domain finite-element modeling of dispersive media; (2) time-domain finite element-boundary integral method; (3) higher order TDFEM; and (4) orthogonal TDFEM. Numerical results demonstrate the validity of the proposed approach for stability analysis.     

On the convergence of common FDTD feed models for antennas

The finite-difference time-domain (FDTD) method is routinely used to calculate the input admittance/impedance of simple antennas. The value of the input admittance/impedance depends on the level of discretization used in the method, and should converge to a final value as the discretization becomes finer. In this paper, the level of discretization necessary for convergence is studied using two common feed models: the hard-source feed and the transmission-line feed. First, the simplest and most naive methods for introducing the voltage and the current in these models are considered, and the results for the admittance are shown not to converge. Next, improved methods for introducing the voltage and current in these models are constructed. The results for the admittance are then shown to converge, and guidelines are offered for the level of discretization needed for convergence. In addition, two general problems associated with the computation of the admittance are discussed: the agreement between admittances computed with different simple feed models, and the agreement between these admittances and measurements.     

Discretization method for current continuity equation containingmagnetic field

Discretization methods for the current continuity equation in the presence of a magnetic field are studied. To produce a nonoscillatory solution, a novel discretization method is presented. It can eliminate the crosswind effect and has improved stability     

对流扩散方程的离散技术及数值实验

本文研究了对流扩散方程的离散技术,并进行了大量数值实验。研究表明,scharfetter—Gummel的广义形式可以良好地消除内部的非物理振荡,且对边界层生成振荡的传播有抑制作用,但不能有效地消除边界层振荡。     

A Precise Time-Step Integration Method for Transient Analysis of Lossy Nonuniform Transmission Lines

This paper presents a novel time-domain integration method for transient analysis of nonuniform multiconductor transmission lines (MTLs). It can solve the time response of various kinds of transmission lines with arbitrary coupling status. The spatial discretization in this method is the same as the finite-difference time-domain (FDTD) algorithm. However, in order to eliminate the Courant-Friedrich-Levy condition constraint, a precise time-step integration method is utilized in time-domain calculation. It gives an analytical solution in the time domain for the spatial discretized Telegrapher's equations with linear boundary conditions. Large time steps can be adopted in the integration process to achieve accurate results efficiently. In the analysis of transmission lines with frequency-dependent parameters, a passive equivalent model is introduced, which leads to the similar semidiscrete model as that for the frequency-independent case. In addition, a rigorous proof of the passivity of the model is provided. Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.     

An Arbitrary-Order LOD-FDTD Method and its Stability and Numerical Dispersion

An arbitrary-order unconditionally stable three-dimensional (3-D) locally-one- dimensional finite-difference time-method (FDTD) (LOD-FDTD) method is proposed. Theoretical proof and numerical verification of the unconditional stability are shown and numerical dispersion is derived analytically. Effects of discretization parameters on the numerical dispersion errors are studied comprehensively. It is found that the second-order LOD-FDTD has the same level of numerical dispersion error as that of the unconditionally stable alternating direction implicit finite-difference time-domain (ADI-FDTD) method and other LOD-FDTD methods but with higher computational efficiency. To reduce the dispersion errors, either a higher-order LOD-FDTD method or a denser grid can be applied, but the choice has to be carefully made in order to achieve best trade-off between the accuracy and computational efficiency. The work presented in this paper lays the foundations and guidelines for practical uses of the LOD method including the potential mixed-order LOD-FDTD methods.      

A multilevel formulation of the finite-element method forelectromagnetic scattering

Multigrid techniques for three-dimensional (3-D) electromagnetic scattering problems are presented. The numerical representation of the physical problem is accomplished via a finite-element discretization, with nodal basis functions. A total magnetic field formulation with a vector absorbing boundary condition (ABC) is used. The principal features of the multilevel technique are outlined. The basic multigrid algorithms are described and estimations of their computational requirements are derived. The multilevel code is tested with several scattering problems for which analytical solutions exist. The obtained results clearly indicate the stability, accuracy, and efficiency of the multigrid method     

Error improvement of temporal discretization in TDFEM for electromagnetic analysis

Integral method is employed in this paper to alleviate the error accumulation of differential equation discretization about time variant t in Time Domain Finite Element Method （TDFEM） for electromagnetic simulation. The error growth and the stability condition of the presented method and classical central difference scheme are analyzed. The electromagnetic responses of 2D lossless cavities are investigated with TDFEM; high accuracy is validated with numerical results presented.