等离子体中的PLCDRC-ADI-FDTD方法

采用分段线性电流密度递归卷积(Piecewise Linear Current Density Recursive Convolution)方法将交替方向隐式时域有限差分方法(ADI-FDTD)推广应用于色散介质—等离子体中,得到了二维情况下等离子体中的迭代差分公式,为了验证该方法的有效性和可靠性,计算了等离子体涂敷导体圆柱的RCS和非均匀等离子体平板的反射系数,数据仿真结果表明,此算法与传统的FDTD相比,在计算结果吻合的情况下,存储量相当,计算效率更高,时间步长仅仅由计算精度来决定.     

基于OpenMP的色散介质FDTD并行程序设计

分析了色散介质时域有限差分的模型,并针对非磁化等离子体给出了的分层线性递归卷积算法。介绍了OpenMP并行设计的基本模型,并将其应用于非磁化等离子体的计算当中。最终通过验证非磁化等离子体的透射电磁波,验证了将OpenMP并行设计应用于色散介质中的准确性,同时依据计算区域大小不同的3个算例验证了该算法具有较高的并行性能。     

基于非零散度关系的交替方向隐式减缩FDTD算法

该文证明了即使在无源区域,交替方向隐式时域有限差分法(ADI-FDTD)所给出的电磁场量不满足零散度关系,同时推导出了该散度关系的具体表达式。基于该非零散度关系,将不受Courant稳定条件限制的ADI-FDTD法和能节约最多达1/3内存的减缩时域有限差分(R-FDTD)法结合,提出了一种新的交替方向隐式减缩FDTD算法。该算法保留了ADI-FDTD能增大时间步长,缩短计算时间的优点,同时与ADI-FDTD相比节约了最多达1/3(三维)或2/5(二维)的内存。与基于零散度关系的ADI/R-FDTD相比,该算法避免了采用长时间步长计算时的发散现象。应用所提出的ADI/R-FDTD算法计算了二维自由空间波的传播及一维频率选择表面垂直入射的问题,计算结果与ADI-FDTD计算结果完全一致,验证了ADI/R-FDTD的正确性和有效性。     

各向异性介质在三维ADI-FDTD中的应用

该文研究一种减小三维交替方向隐式时域有限差分法(ADI-FDTD)数值色散的新方法。通过在三维空间中合理添加各向异性介质,达到调整相速的目的,从而减小数值色散,使计算结果更加精确。首先对添加各向异性介质后的三维ADI-FDTD迭代公式进行变形,并得到新的数值色散关系,从而求解得到各向异性介质的相对介电常数。以空心波导和具有介质不连续性的波导作为数值算例,分析不同的各向异性介质和添加方法对计算精度的影响,并与传统ADI-FDTD得到的结果和计算资源占用情况进行比较。结果表明通过正确选择各向异性介质和添加方法,可以有效地减小三维ADI-FDTD数值色散。     

一种色散介质中的低误差ADI-FDTD 算法

交变方向隐式时域有限差分（ADI-FDTD）能够克服传统时域有限差分算法中稳定性条件对时间步长的限制,从而提高计算效率,但是在大步长时其误差较大。ER（低误差）-ADI-FDTD 方法通过补偿截断误差项,提高了计算精度,但是目前仅给出二维非色散条件下的形式。在ER-ADI-FDTD 的基础上,提出了一种色散介质中的低误差D-ER-ADI-FDTD 算法,推导出了完整的三维计算公式。最后通过计算和结果比较对算法进行检验。     

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.     

基于ADI-FDTD的混合方法及其快速算法

该文介绍了FDTD与ADI-FDTD相结合的方法,提出了减小因两种不同计算方法在边界引起反射的加权平均的方法,并给出了ADI-FDTD计算线性、无耗、各向同性媒质的快速算法.计算结果表明了该方法的有效性.     

ADI-FDTD方法在乳腺癌检测正向计算中的应用

传统的时域有限差分(Finite-Difference Time-Domain, FDTD)算法受到稳定性条件的制约, 时间步长受限于空间网格的尺寸.医学应用讲究即时性, 为提高成像的速度, 文中采用无条件稳定的交替隐式时域有限差分(Alternating-Direction Implicit Finite-Difference Time-Domain, ADI-FDTD)算法替代传统的FDTD算法进行正向计算, 通过实验得出采用ADI-FDTD算法在保证精度的前提下, 计算时间可缩短为FDTD算法的四分之一, 为乳腺癌微波即时成像提供了可能.     

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。     

ADI-FDTD+GRT在波导电路分析中的应用

本文研究时域有限差分法(FDTD)的一种新的时空压缩技术,并应用于波导电路的分析.首先分析了软激励条件下的改进的几何重置技术(GRT),研究了合理选择源面与参考面的放置位置,使GRT不仅减小了吸收边界对计算结果的影响,而且节省了计算空间,还可以精确得到全部散射参量.另外阐述了与交替方向隐式时域有限差分法(ADI-FDTD)相结合,使计算空间和时间同时被压缩,达到节省计算资源的目的.为了衡量ADI-FDTD+GRT算法的计算精度和效率,分析了包含不连续结构的波导作为算例,将其数值计算结果分别与传统FDTD和HFSS作比较,并将端面和参考面不同间距的ADI-FDTD+GRT与传统ADI-FDTD在仿真结果和资源占用方面进行对比,结果表明本文算法是精确和高效的.     

高阶ADI-FDTD算法的数值色散分析

该文给出高阶交替方向隐时域优先差分(ADI-FDTD)算法,即在ADI-FDTD迭代公式的基础上对时间的差分仍然采用二阶中心差分格式,而对空间的差分则采用四阶中心差分格式,并解析地证明了所给出的高阶ADI-FDTD算法仍然满足无条件稳定方程,同时对增长因子相位的分析,得到数值色散关系,最后对其数值色散误差进行了分析,研究表明与普通ADI-FDTD相比,其色散误差较小。     

Finite-difference Time-domain Algorithm for Plasma Based on Trapezoidal Recursive Convolution Technique

The electromagnetic wave propagation in plasma media is modeled using finite-difference time-domain (FDTD) method based on the trapezoidal recursive convolution (TRC) Technique. The TRC Technique requires single convolution integral in the formulation as in the recursive convolution (RC) method, while maintaining the accuracy comparable to the piecewise linear convolution integral (PLRC) method with two convolution integrals. The three dimensional (3-D) TRC-FDTD formulations for plasma are derived. The high accuracy and efficiency of the presented method is confirmed by computing the transmission and reflection coefficients for a unmagnetized collision plasma slab. The backward radar cross section (RCS) of perfectly conducting sphere covered by homogeneous and inhomogeneous plasma is calculated.     

UPML媒质中的包络ADI-FDTD

由于交替方向隐式时域有限差分法(Alternating-Direction Implicit Finite-Difference Time Domain,ADI-FDTD)的数值色散会随着时间步长的增加而增加,文中讨论了单轴各向异性完全匹配层(uniaxial perfectly matched layer,UPML)媒质中包络交替方向隐式时域有限差分法(Envelope ADI-FDTD),推导了二维Envelope ADI-FDTD UPML的迭代公式,并提出一种新的离散方法。与ADI-FDTD UPML相比,改进后的Envelope ADI-FDTD UPML的时间步长可以取得更大,且能有效地修正相速误差,从而减少数值色散,提高计算精度。     

Incorporation of Conductor Loss in the Unconditionally Stable ADI-FDTD Method

A surface-impedance boundary condition (SIBC) is presented for an unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method. The conformal SIBC formulation based on locally conformal grids is capable of modeling the conductor loss of arbitrarily-shaped lossy metal structures. The work is described in the framework of the finite-integration technique (FIT) formulation of the ADI-FDTD. The paper focuses on the proposed ADI-FDTD SIBC formulation and its extensive validation. For this purpose, cylindrical and spherical cavity resonators are used for numerical tests. The quality factor $Q$ is directly proportional to wall loss and is particularly sensitive to the accuracy of loss calculation. The resonator structure consists only of a vacuum-filled metal cavity and is thus free of additional sources of error that are caused by other extensions to the basic ADI-FDTD algorithm. The formulation is validated by comparison with analytic results and numerical data calculated using CST Microwave Studio (MWS). The convergence rate of the results is of second order, i.e., the error reduces to one quarter as the mesh resolution is doubled.      

Envelope ADI–FDTD Method and Its Application in Three-Dimensional Nonuniform Meshes

The envelope alternating-direction-implicit finite difference time domain (ADI-FDTD) method in 3-D nonuniform meshes was proposed and studied. The phase velocity error for the envelope ADI-FDTD and ADI-FDTD methods in uniform and nonuniform meshes and different temporal increments were studied. A cavity problem was studied using the envelope ADI-FDTD and ADI-FDTD methods in graded meshes and the conventional FDTD method in a uniform mesh. The simulation results show that the envelope ADI-FDTD performs better than the ADI-FDTD in numerical accuracy     

FINITE-DIFFERENCE TIME-DOMAIN ANALYSIS OF UNMAGNETIZED PLASMA PHOTONIC CRYSTALS

The plasma photonic crystal is a periodic array composed of alternating thin unmagnetized (or magnetized) plasmas and dielectric materials (or vacuum). In this paper, the piecewise linear current density recursive convolution finite-difference time-domain method for the simulation of isotropic unmagnetized plasma is applied to model unmagnetized plasma photonic crystal structures. A perfectly matched layer absorbing material is used in these simulations. In time-domain, the electromagnetic propagation process of a Gaussian pulse through an unmagnetized plasma photonic crystal is investigated. In frequency-domain, the reflection and transmission coefficients through unmagnetized plasma photonic crystals are computed and their dependence on plasma frequency, plasma thickness, collision frequency is studied. The results show theoretically that the electromagnetic bandgaps of unmagnetized plasma photonic crystals are tuned by the plasma parameters.     

Nonlinear theory of the isothermal ion-acoustic waves in the warm degenerate plasma

The collisionless unmagnetized degenerate plasma with zero-temperature components is considered. The exact barometric formulas for the electron and ion degenerate gases and the exact expressions for the electron and ion Debye radii are derived. A dispersion relation for the isothermal ion-acoustic waves is obtained and analyzed and an exact solution for the linear velocity of the ion sound is found. The domains of parameters in which the soliton solutions can be found are determined using the analysis of the dispersion relation. The nonlinear theory of the isothermal ion-acoustic waves is developed and employed to obtain and to analyze the exact solution of the original equations. The analysis is based on the method of the Bernoulli pseudopotential. The ranges of the phase velocities of the periodic ion-acoustic waves and the soliton velocities are determined. It is demonstrated that the ranges are not overlapped and that the soliton velocity cannot be less than the linear velocity of the ion sound. The profiles of physical quantities in the periodic wave and soliton are constructed.     

色散媒质中ADI-FDTD的PML

基于交替方向隐式(ADI)技术的时域有限差分法(FDTD)是一种非条件稳定的计算方法,该方法的时间步长不受Courant稳定条件限制,而是由数值色散误差决定。与传统的FDTD相比, ADI-FDTD增大了时间步长, 从而缩短了总的计算时间。该文采用递归卷积(RC)方法导出了二维情况下色散媒质中ADI-FDTD的完全匹配层(PML)公式。应用推导公式计算了色散土壤中目标的散射,并与色散媒质中FDTD结果对比,在大量减少计算时间的情况下,两者结果符合较好。