基于高阶时域有限差分算法的电磁波传播计算

利用FDTD(2,4)高阶时域有限差分(Finite-Difference Time-Domain,FDTD)算法并结合滑动窗口的思想,对电磁波传播特性进行了仿真计算.采用的高阶FDTD算法在空间上达到四阶精度,与二阶精度的传统FDTD算法相比,在相同每波长采样数的条件下,数值色散误差能得到进一步的减少.在源脉冲传播较长距离时,数值色散的减少使得时域下脉冲扩展现象得到改善,滑动子窗口仍然能包含着激励源脉冲的全部信息,从而可更加准确地计算长距离电波传播特性.另外,在相同的数值色散误差容限下,每波长采样数比传统二阶FDTD方法有所减少,从而节省存储空间,加快计算速度.     

辛算法的稳定性及数值色散性分析

引入一种新的数值计算方法 —辛算法求解Maxwell方程,即在时间上用不同阶数的辛差分格式离散,空间分别采用二阶及四阶精度的差分格式离散,建立了求解二维Maxwell方程的各阶辛算法,探讨了各阶辛算法的稳定性及数值色散性.通过理论上的分析及数值计算表明,在空间采用相同的二阶精度的中心差分离散格式时,一阶、二阶辛算法(T1S2、T2S2) 的稳定性及数值色散性与时域有限差分(FDTD)法一致,高阶辛算法的稳定性与FDTD法相当;四阶辛算法结合四阶精度的空间差分格式(T4S4) 较FDTD法具有更为优越的数值色散性.对二维TMz波的数值计算结果表明,高阶辛算法较FDTD法有着更大的计算优势.     

FDTD法分析等离子体对通信信号的影响

介绍了时域有限差分(FDTD)算法的基本原理,对FDTD算法进行了理论研究和公式推导,建立等离子体的模型,并运用FDTD算法对等离子体和电磁波间的作用机理进行了数值计算。运用MATLAB软件对结果进行了仿真,分析了等离子频率、等离子数量和碰撞频率等重要参数对电磁波反射特性的影响,并由此可得计算结果与目前的解析法和WKB方法结果接近,具有很高的准确性。     

等离子体的交替方向隐式时域有限差分方法

首次把交替方向隐式时域有限差分法(ADI-FDTD)推广到色散介质——无碰撞非磁化等离子体中,计算了非磁化等离子体与电磁波的相互怍用,使用ADI技术给出了无碰撞等离子体介质中的ADI-FDTD迭代公式．并解析地证明了等离子ADI-FDTD算法也是无条件稳定的,数值计算表明,等离子体ADI-FDTD算法与传统的FDTD的计算结果吻合,计算效率更高。     

三维情况下平面介质交界面处二阶精度FDTD方程

提出了一种新的二阶精度时域有限差分法(FDTD)算法,针对研究区域介质填充不均匀,包含平面介质交界面的情况.新算法在交界面处利用非均匀网格建模,通过积分形式Maxwell方程的离散和交界面处连续场分量的泰勒级数展开,给出了平面介质交界面处三维情况下的二阶精度FDTD方程.该方法在保证介质交界面处电磁场量二阶精度的同时,合理划分不同介质区域粗细网格,在不增加计算容量和计算时间的基础上,有效地提高算法整体的计算精度.最后对介质谐振腔结构和微带电路进行模拟,验证了本文算法的精度高于标准的FDTD方法.     

分析非均匀填充圆柱介质谐振器的二阶精度FDTD公式

从积分形式的Maxwell方程出发，利用连续函数的Taylor级数展开，严格地给出了包含介质交界面的二阶精度时域有限差分(FDTD)公式，解决了以往FDTD法处理非均匀介质填充区域问题时只有一阶精度的问题。分析表明，为了获得二阶精度，除了需要引入适当等效介电常数外，还必须采用适当非均匀网格。该方法被用于轴对称圆柱介质谐振器的分析。计算结果与理论值吻合良好，计算精度比传统的FDTD方法提高了一个数量级以上。     

新型无条件稳定SSCN-FDTD算法

提出了一种新型的基于split-step方案和Crank-Nicolson方案的时域有限差分法(finite-difference timedomain method FDTD),并且证明了此种算法的无条件稳定性.所提出的算法采用新的矩阵分解形式,沿着x、y、z三个方向进行分解,将三维问题转化为一维问题,与alternating direction implicit(ADI)-FDTD算法、split-step(SS)-FDTD(1,2)算法和SS-FDTD(2,2)算法相比,减少了计算复杂度,提高了计算效率;同时所提出的算法具有二阶时间精度和二阶空间精度.新型算法的推导程序比基于指数因子分解的无条件FDTD算法更简单.将新型算法用于计算谐振腔结构,在计算相对误差一致的情况下,计算时间比ADI-FDTD算法节省约31%,比SS-FDTD(1,2)算法节省约13.5%.     

基于辛算法的二维电磁场散射问题的研究

辛算法是保持Hamilton系统辛结构的一种新的数值方法,由于 Maxwell方程是一无穷维Hamilton系统,因此可将辛算法用于电磁场模拟中.本文提出一种基于辛分块Runge-Kutta(PRK)方法的显式辛算法,并将它成功应用于二维电磁散射问题的计算中.通过对金属方柱散射场的数值模拟,比较了FDTD法和低阶辛算法(一阶和二阶),结果表明低阶辛算法不仅与FDTD法精度相当,而且可以减少存储空间和计算时间,尤其是一阶辛算法节省了大约的CPU时间,提高了计算速度,体现了该算法的优越性.     

基于改进WKB的非均匀等离子体中脉冲波形研究

WKB是研究非均匀等离子体中电磁波传播现象时经常采用的一种经典计算方法,但是该方法忽略了电磁波传播过程中前向波和后向波的耦合效应。为了提高计算结果的准确度,可利用差分传输矩阵技术,将WKB解由原来的一阶近似提升至二阶近似,使得计算结果中包含了由于耦合效应引起的衰减部分。通过此改进WKB方法,以对称分布参数等离子体层模型为例,对电磁波信号经等离子体层传播后波形的变化进行了计算和分析。并通过快速傅里叶变换,给出了时域高斯脉冲信号波形的具体算例,计算结果表明通过该种方法能够有效的分析信号波形变化。     

磁化等离子体覆盖二维导体目标FDTD分析

采用z变换方法把FDTD推广应用于二维各向异性色散介质－磁化等离子体中,该算法同时解决了电磁波在各向异性和频率色散介质中传播的问题,给出了各向异性磁化等离子体中FDTD迭代公式.计算了各向异性磁化等离子体涂敷Von Karman型导体柱前后其单站RCS的变化情况,分析了等离子体参数对其RCS的影响.结果表明恰当地选择等离子体参数能有效地减少目标的RCS.     

A higher order FDTD method for EM propagation in a collisionlesscold plasma

A fourth-order in time and space, finite-difference time-domain (FDTD) scheme is presented for radio-wave propagation in a lossless cold plasma. As with previously reported fourth-order schemes, the methodology is founded on the principle that correction derivatives (i.e., three derivatives in time) can be converted into vector spatial derivatives. From the error analysis and phase-velocity data, it is argued that this approach will significantly minimize the dispersion errors while still maintaining minimal memory requirements. This claim is also supported by data obtained from FDTD simulations. Using a one-dimensional plasma slab problem as the test case, we show that the bandwidth and dynamic range associated with this fourth-order scheme are significantly improved with respect to its second-order counterpart. The impact of other error mechanisms, namely material boundary-related errors, is also discussed     

A Finite Volumes-Based 3-D Low Dispersion FDTD Algorithm

An algorithm extension to three dimensions is developed and presented for the highly phase-coherent modified second-order in time, fourth-order in space (or M24) finite-difference time-domain (FDTD) algorithm. A finite-volumes approach in conjunction with Yee's standard FDTD lattice is used for algorithm development. The corresponding dispersion relation is also developed, analyzed and compared to both the standard second-order and fourth-order FDTD algorithms as well as to two closely related high-order phase-coherent algorithms. Wideband algorithm attributes are also presented as well as sets of ready to use optimized algorithm coefficients.     

A higher order (2,4) scheme for reducing dispersion in FDTDalgorithm

A finite-difference time-domain (FDTD) scheme with second-order accuracy in time and fourth-order in space is discussed for the solution of Maxwell's equations in the time domain. Compared with the standard Yee (1966) FDTD algorithm, the higher order scheme reduces the numerical dispersion and anisotropy and has improved stability. Dispersion analysis indicates that the frequency band in which the higher order scheme yields an accurate solution is widened on the same grid, this means a larger space increment can be chosen for the same excitation. Numerical results show the applications of the scheme in modeling wide-band electromagnetic phenomena on a coarse grid     

A higher order FDTD method in Integral formulation

We present a fourth-order (4, 4) finite-difference time-domain (FDTD)-like algorithm based on the integral form of Maxwell's equations. The algorithm, which is called the integro-difference time-domain (IDTD) method, achieves its fourth-order accuracy in space and time by taking into account the spatial and temporal variations of electromagnetic fields within each computational cell. In the algorithm, the electromagnetic fields within each cell are represented by space and time integrals (or integral averages) of the fields, i.e., the electric and magnetic fluxes (D,B) are represented by the surface-integral average, and the electric and magnetic fields (E,H) by the line and time integral average. In order to relate the integral average fields in the staggered update equations, we have obtained constitutive relations for these fields. It is shown that the IDTD update equations combined with the constitutive relations are fourth-order accurate both in space and time. The fourth-order correction terms are represented by the modified coefficients in the update equations; the numerical structure remains the same as the conventional second-order update equations and more importantly does not require the storage of field variables at the previous time steps to obtain the fourth-order accuracy in time. Furthermore, the Courant-Friedrichs-Lewy (CFL) stability criteria of this fourth-order algorithm turns out to be identical to the stability limits of conventional second-order FDTD scheme based on differential formulation.     

A low-dispersion 3-D second-order in time fourth-order in space FDTD scheme (M3d/sub 24/)

A second-order in time fourth-order in space modified finite-difference time-domain (FDTD) scheme for three dimensional electromagnetic problems "M3d/sub 24/" is presented. The algorithm enables the numerical phase error to be minimized, so that it leads to high accuracy with low resolution grids. The advantage of this method is demonstrated by considering the long distance propagation of the wave radiated from a time harmonic elementary dipole using a low resolution grid, and comparing the results with other FDTD schemes.     

Relative accuracy of several finite-difference time-domain methodsin two and three dimensions

A comparison of the accuracy of several orthogonal-grid finite-difference-time-domain (FDTD) schemes is made in both two and three-dimensions. The relative accuracy is determined from the dispersion error associated with each algorithm and the number of floating-point operations required to obtain a desired accuracy level. In general, in both 2-D and 3-D, fourth-order algorithms are more efficient than second-order schemes in terms of minimizing the number of computations for a given accuracy level. In 2-D, a second-order approach proposed by Z. Chen et al. (1991) is much more accurate than the scheme of K.S. Yee (1966) for a given amount of computation, and can be as efficient as fourth-order algorithms. In 3-D, Yee's algorithm is slightly more efficient than the approach of Chen et al. in terms of operations, but much more efficient in terms of memory requirements     

Higher-order FDTD(2,4) scheme for accurate simulations in lossy dielectrics

A finite-difference time-domain (FDTD)(2,4) scheme with second-order accuracy in time and fourth-order accuracy in space for the precise solution of Maxwell's equations in lossy dielectrics is presented. Compared with the ordinary FDTD method the novel technique reduces lattice reflection errors, increases the overall accuracy and provides significant computational savings. Numerical results for a waveguide problem indicate the efficiency and robustness of the proposed formulation.     

A Highly Accurate FDTD Model for Simulating Lorentz Dielectric Dispersion

A highly accurate and numerically stable model of Lorentz dielectric dispersion for the finite-difference time-domain (FDTD) method is presented. The coefficients of the proposed model are optimally derived based on the Maclaurin series expansion (MSE) method and it is shown that the model is much better than the other four reported models in implementing the Lorentz dielectric dispersion with error of relative permittivity several orders lower. The model's stability and performance are also analyzed when it is incorporated into the practical second- and fourth-order accurate FDTD algorithms for an exemplified Lorentz medium. Interestingly, we find that all the mentioned models show nearly the same performance in the second-order algorithm due to its large intrinsic numerical dispersion and the superiority of the proposed MSE model begins to be manifested in the higher-order, say, fourth-order FDTD algorithms as implied by the governing numerical dispersion equations.      

A modified FDTD (2, 4) scheme for modeling electrically largestructures with high-phase accuracy

A new fourth-order finite-difference time-domain (FDTD) scheme has been developed that exhibits extremely low-phase errors at low-grid resolutions compared to the conventional FDTD scheme. Moreover, this new scheme is capable of combining with the standard Yee (1966) scheme to produce a stable hybrid algorithm. The problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford. With this new development, the FDTD method can now be used to successfully model structures that are thousands of wavelengths large, using the present day computer technology     

Finite-Difference Time-Domain Algorithm for Dispersive Media Based on Runge-Kutta Exponential Time Differencing Method

The electromagnetic propagation in dispersive media is modeled using finite difference time domain (FDTD) method based on the Runge-Kutta exponential time differencing (RKETD) method. The second-order RKETD-FDTD formulation is derived. The high accuracy and efficiency of the presented method is confirmed by computing the transmission and reflection coefficients for a nonmagnetized collision plasma slab in one dimension. The comparison of the numerical results of the RKETD and the exponential time differencing (ETD) algorithm with analytic values indicates that the RKETD is more accurate than the ETD algorithm.