On the modeling of conducting media with the unconditionally stable ADI-FDTD method

The Courant-Friedrich-Levy stability condition has prevented the conventional finite-difference time-domain (FDTD) method from being effectively applied to conductive materials because of the fine mesh required for the conducting regions. In this paper, the recently developed unconditionally stable alternating-direction-implicit (ADI) FDTD is employed because of its capability in handling a fine mesh with a relatively large time step. The results show that the unconditionally alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method can be used as an effective universal tool in modeling a medium regardless of its conductivity. In addition, the unsplit perfectly matched layer combined with the ADI-FDTD method is implemented in the cylindrical coordinates and is proven to be very effective even with the cylindrical structures that contain open conducting media.     

无条件稳定的交替方向隐式FDTD算法

介绍了一种新的FDTD算法-交替方向隐式时域有限差分法（ADI-FDTD），该方法采用求解微分方程的交替方向隐格式改造了FTD算法，使其能无条件稳定，从而极大地节约计算时间，成为一种计算时域电磁场分布的高效算法，同时，首次尝试利用ADI-FDTD方法结合时域近远场变换技术计算天线方向图，数值实验的结果和传统FDTD方法及理论值进行了对比，数值结果一致性较好，并节约了运算所占用的资源，提高了计算效率。     

二维无条件稳定时域有限差分方法

基于半隐式的Crank-Nicolson差分格式给出了一种无条件稳定时城有限差分方法。和传统FDTD法中采用的显式差分格式不同，对Maxwell方程组采用半隐式差分格式，在时间和空间上仍然是二阶精确的。但时间步长不再受稳定性条件的限制，只需考虑数值色散误差对其取值的制约。利用分裂场完全匹配层吸收边界截断计算空间，为保证PML空间的无条件稳定性，其方程也采用半隐式差分格式。数值结果表明相同条件下US-FDTD方法与传统FDTD方法的计算精度是相同的，而且在增大时间步长时US-FDTD方法是稳定的和收敛的。可以预见US-FDTD方法在模拟具有电小结构问题时具有实际意义。     

The studies of cylindrical microstrip line with the FD-TD method in cylindrical coordinate system

In this paper, a full-wave two dimensional Finite-Difference-Time-Domain method in cylindrical coordinate system is developed, in which the arch is chosen as the difference cell. It is proved that the method is efficient and economical in both CPU time and temporary storage requirement, and potentially useful for the numerical analysis of dispersion of cylindrical guidewave structure. the numerical results, including the dispersive curves of the cylindrical single microstrip line and the coupled microstrip line are presented.     

An unconditionally stable scheme for the finite-difference time-domain method

In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.     

Dispersion analysis of the three-dimensional complex envelope ADI-FDTD method

In this paper, numerical dispersion properties of the three-dimensional complex envelope (CE) alternate-direction implicit finite-difference time-domain (ADI-FDTD) method are studied. The variations of dispersion errors with propagation direction, ratio of carrier to envelope frequencies, and spatial and temporal steps are presented. It is found that the CE ADI-FDTD scheme have much better accuracy and efficiency over the ADI-FDTD, especially with a higher ratio of carrier to envelope frequencies. Therefore, the CE ADI-FDTD is recommended for use in efficient narrow bandwidth electromagnetic modeling.     

Split-field PML implementations for the unconditionally stable LOD-FDTD method

We introduce and compare two split-field implementations of the perfectly matched layer (PML) for the unconditionally stable locally one-dimensional (LOD) finite-difference time-domain (FDTD) method. The LOD-FDTD formalism is expanded in terms of a symmetric source implementation. It is verified that the relative performance of both PML implementations is superior to the split PML performance in the alternating direction implicit (ADI) FDTD method.     

More accurate and efficient unconditionally stable FDTD method

A more accurate and efficient unconditionally stable finite-difference time-domain (US-FDTD) method is proposed. The two key points of the proposed US-FDTD method are: defining the field components at only n and (n + 1) time steps; and arranging the left and right hands of the original updating equations to be as accurate (in respect of time) as possible. It is demonstrated that the US-FDTD method is more efficient (in both computer memory and CUP time) and more accurate than the recently developed ADI-FDTD method     

A stable algorithm for interfacing active and nonlinear devices with the ADI-FDTD method

This letter presents the algorithm to include active and nonlinear lumped devices in three-dimensional alternating-direction-implicit finite-difference time-domain simulations. The late-instability is considered and a late-stable algorithm is proposed. Numerical experiments validate the robustness of this algorithm. It can be applied to the analysis of radio frequency and microwave circuits.     

The unconditionally stable pseudospectral time-domain (PSTD) method

This letter presents a new time-domain method for Maxwell's equations, in which the unconditionally stable techniques, the alternating direction implicit (ADI) and the split-step (SS) schemes, are developed for the pseudospectral time-domain (PSTD) algorithm to maintain stability while achieving higher accuracy and efficiency over the FDTD method. The multidomain strategy is employed to allow for a flexible treatment of internal inhomogeneities. Numerical results demonstrate the unconditional stability and the second-order accuracy for both ADI- and SS-PSTD algorithms.     

Error between unconditionally stable FDTD methods and conventional FDTD method

Both the ADI-FDTD method and the CN-FDTD method can be viewed as approximate factorisation of the conventional FDTD scheme, so the error between these methods and the conventional FDTD method is obtained. It is shown that the error is associated with the time step size, the permittivity and the permeability of the medium, and the spatial variation rate of field. The space discretisation has no relation with the error, which is demonstrated by numerical examples     

An unconditionally stable 3-D ADI-MRTD method free of the CFLstability condition

In this paper, an alternating direction implicit (ADI) technique is applied to the recently developed multiresolution time-domain (MRTD) method, resulting in an unconditionally stable ADI-MRTD scheme free of the Courant-Friedich-Lecy (CFL) stability condition. The unconditional stability is theoretically proved, and preliminary numerical results are presented to validate the scheme. Because the scheme is now free of the stability condition, its time step is determined only by modeling accuracy. The price for having the unconditional stability is, however, that the required computation memory becomes almost twice of that for the original MRTD     

An unconditionally stable subcell model for arbitrarily oriented thin wires in the FETD method

A computational subcell model for thin wires is developed for electromagnetic simulations. The Maxwell equations are discretized by a finite element approximation on a tetrahedral grid. The wires are described by a second-order equation for the current. The geometry of the wires can be chosen independent of the volume grid. A symmetric coupling between field and wires yields a stable semi-discrete field-wire system and an unconditionally stable fully discrete field-wire system. The system of equations is in each time step solved by a preconditioned conjugate gradient method. The accuracy of the subcell model is demonstrated for dipole and loop antennas with comparisons with the method of moments and experimental data.     

Uniaxial perfectly matched layer media for an unconditionally stable 3-D ADI-FD-TD method

An unsplit-field perfectly matched layer (PML) medium based on Gedney's uniaxial PML (UPML) scheme is proposed for an unconditionally stable three-dimensional alternating direction implicit finite-difference time-domain (ADI-FD-TD) method. The effectiveness of the proposed ADI-UPML absorber is demonstrated through a numerical example. In addition, to have a better understanding on the ADI-FD-TD method, the actual performance (i.e., while both the reflection and dispersion errors are considered) of the ADI-UPML as a function of the time step is also illustrated.     

Analyses of bounces on power distribution networks using an unconditionally stable finite-difference time-domain method

An unconditionally stable finite-difference time-domain (US-FDTD) method is utilized for analyzing the bounces on structures of power distribution networks (PDNs), which is a critical issue in the electromagnetic compatibility analysis of mobile devices. The US-FDTD method does not utilize the explicit leapfrog time scheme of conventional FDTD method and can solve problems with fine structures well, such as via, thin material and so on. By using this full-wave method, electromagnetic fields between power/ground plane pairs are analyzed and discontinuities of through-hole vias are taken into account in the modeling of PDNs.     

Unconditionally stable ADI-FDTD formulations of the APML for frequency-dependent media

Unconditional stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating frequency-dependent media. The formulations are based on the auxiliary differential equation and the alternating direction implicit finite-difference time-domain (ADI-FDTD) methods. Numerical examples carried out in one and two dimensions show that the proposed formulations remain unconditionally stable with inclusion of material dispersion into ADI-FDTD implementation of APML.     

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.     

基于柱坐标系抛物方程的太赫兹目标RCS计算

针对太赫兹(THz)波段目标雷达散射截面(RCS)的计算问题,提出柱坐标系抛物方程模型的计算方法。基于柱坐标系中的电场通解式,利用三角函数的正交性分解各模式的激励系数,将抛物方程方法拓展到柱坐标系,得到柱坐标系中抛物方程的分步傅里叶求解形式。在此基础上,将目标等效为一系列的面元或线元,然后通过边界条件和场的迭代递推方法求解抛物方程,进而获得这一系列面元在传播方向某一截面上的散射场。数值算例表明,该方法能用于电大尺寸目标的RCS计算,相比于传统的抛物方程方法,克服了散射角度的限制,计算误差更小。     

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.     

Extension of the ADI-FDTD method to Debye media

This paper describes an extension of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method to analyze problems involving Debye media.