碰撞等离子体的高阶FDTD算法

给出了电磁波在均匀、碰撞等离子体中传播的四阶时间和四阶空间FDTD算法.该算法比Yee氏FDTD算法每一个网格每一维增加一个存储单元,与常规的二阶等离子体FDTD算法相同.由于采用四阶时间和四阶空间近似,因此该算法能有效地减小数字色散误差,其频带宽度比二阶算法的频带宽度更宽.为了验证该高阶算法的正确性,对均匀、碰撞等离子体平板的电磁波反射系数进行了计算,并与解析结果、二阶FDTD计算结果进行了比较,证明了该算法的高效和精确.     

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     

Development of higher order FDTD schemes with controllable dispersion error

A new methodology that facilitates the control of the inherent dispersion error in the case of higher order finite-difference time-domain (FDTD) schemes is presented in this paper. The basic idea is to define suitable algebraic expressions that reflect numerical inaccuracies reliably. Then, finite-difference operators are determined via the minimization of the error estimators at selected frequencies. In order to apply this procedure, an error expansion in terms of cylindrical harmonic functions is performed, which also enables accuracy enhancement for all propagation angles. The design process produces a set of two-dimensional (2-D) FDTD algorithms with optimized frequency response. Contrary to conventional methodologies, the proposed techniques adjust their reliability range according to the requirements of the examined problem and can be, therefore, more efficient in computationally demanding simulations.     

A higher order electron wave propagation method

A finite-difference propagation scheme for simulating electron currents through arbitrary quantum structures is presented in this paper. It is shown that due to the strong interaction of external fields and electrons, the trajectories predicted using higher order propagation operators are a significant improvement over that of lower order schemes, especially in cases where the longitudinal electron momentum is not accurately known. A novel boundary condition based on the popular transparent boundary condition is used for minimizing unphysical reflections off the computation boundaries even in the presence of strong lateral electric fields. The application of this scheme is illustrated through a few examples     

A novel FDTD formulation for dispersive media

A novel FDTD formulation for dispersive media called piecewise linear JE recursive convolution (PLJERC) finite-different time-domain (FDTD) method is derived using the piecewise linear approximation and the recursive convolution relationship between the current density J and the electric field E. The high accuracy and efficiency of the PLJERC method is confirmed by computing the reflection coefficients of an electromagnetic wave through a collision plasma slab in one dimension.     

A special higher order finite-element method for scattering by deepcavities

A special higher order finite-element method is presented for the analysis of electromagnetic scattering from a large, deep, and arbitrarily shaped open cavity. This method exploits the unique features of the finite-element equations and, more importantly, the unique features of the problem of scattering by a large and deep cavity. It is designed in such a manner that it uses minimal memory, which is proportional to the maximum cross section of the cavity and independent of the depth of the cavity, and its computation time increases only linearly with the depth of the cavity. Furthermore, it computes the scattered fields for all angles of incidence without requiring significant additional time. The technique is implemented with higher order tetrahedral and mixed-order prism elements, both having curved sides to allow for accurate modeling of arbitrary geometries. Numerical results show that higher order elements yield a remarkably more accurate and efficient solution for scattering by three-dimensional (3-D) cavities. Of the two kinds of element, the mixed-order prism is optimal for the proposed special solver     

Comparison of the dispersion properties of higher order FDTD schemes and equivalent-sized MRTD schemes

The dispersion errors of higher order finite-difference time-domain (HO-FDTD) algorithms are compared to those of multiresolution time-domain (MRTD) algorithms that have equivalent spatial stencil sizes. Both scaling-function-based MRTD (S-MRTD) and wavelet-function-based MRTD (W-MRTD) schemes are considered. In particular, the MRTD schemes considered include the Coifman scaling functions and the Cohen-Daubechies-Feauveau (CDF) biorthogonal scaling and wavelet functions. In general, the HO-FDTD schemes are more accurate than their MRTD counterparts.     

Unconditionally stable FDTD formulation with UPML-ABC

A new unconditionally stable finite-difference time-domain (US-FDTD) formulation is established in combination with the uniaxial anisotropic perfectly matched layer absorbing boundary condition. This approach exhibits improved absorbing performance yet maintains unconditional stability. Numerical results show that the reflection error of this scheme is limited even when the time-step size is beyond the Courantndash;Friedrichndash;Levy stability bound, and the absorbing performance is better than that of the US-FDTD with the dispersive boundary condition.     

Integral equation analysis for higher order modes and cutofffrequencies of arbitrary profiles

A semianalytical method of analysis for arbitrary weakly guiding circular and noncircular profiles, which has its fundamental basis in perturbation theory and incorporates Green's function and integral equation techniques in a powerful method of analysis possessing extremely high accuracy, is extended to the analysis of higher order modes and cutoff frequencies of arbitrary weakly guiding circular and noncircular profiles. Its accuracy is demonstrated by its application to several weakly guiding profiles, for which the method is found to be extremely accurate (<10^-5%). Furthermore, additional simplifications to the semianalytical method of analysis are presented, which dramatically reduce the number of calculations required for solution     

一种基于高阶累积量的复杂调制样式识别方法

针对卫星数字化视频广播第二代标准（Digital Video Broadcasting-Satellite-Second Generation,DVB-S2）中多进制幅度移相键控（Multiple Amplitude and Phase-Shift Keying,MAPSK）和多进制正交幅度调制（Multiple Quadrature Amplitude Modulation,MQAM）信号的调制识别,提出了基于高阶累积量的识别方法。首先对16QAM、32QAM、16APSK、32APSK信号的高阶累积量及其特征进行分析,进而利用其高阶累积量的不同提取用于信号分类的特征参量进行调制识别。给出了算法的详细流程,并对算法进行了仿真分析,结果表明,当样本数越多时,算法信噪比适应能力越好,而与相位偏差无关;在信号样点数为2 048点且信噪比为10 dB时,算法可实现96%的正确识别率,完全满足实际系统对信号分类的需要。     

自适应交叉近似压缩的高阶矩量法的并行实现

高阶矩量法在计算电磁学中的应用越来越广泛, 为了进一步提高其计算规模, 引入并行的自适应交叉近似压缩算法(Adaptive Cross Approximation algorithm, ACA).该算法首先采用非均匀有理B样条建模(Non-Uniform Rational B-Splines, NURBS)的方法进行面片分组; 然后利用矩量法中远区阻抗矩阵的低秩特性进行ACA压缩; 最后采用稀疏近似逆预条件(Sparse Pattern Approximate Inverse preconditioning, SPAI)的共轭梯度法(Conjugate Gradient method, CG)快速求解矩阵方程.该算法中的ACA压缩过程和迭代求解过程都特别适合并行计算.数值实验表明, 对于电大尺寸问题, ACA压缩后的矩阵占用的内存远远低于原矩阵, 而预条件的共轭梯度法可以很快收敛.此外该算法在大规模并行时的效率较高.     

A generalized higher order finite-difference time-domain method and its application in guided-wave problems

In this paper, a (2M,4) scheme of the finite-difference time-domain (FDTD) method is proposed, in which the time differential is of the fourth order and the spatial differential using the discrete singular convolution is of order 2M. Compared with the standard FDTD and the scheme of (4, 4), the scheme of (2M, 4) has much higher accuracy. By choosing a suitable M/spl ges/2, the (2M, 4) scheme can arrive at the highest accuracy. In addition, an improved approximation of the symplectic integrator propagator is presented for the time differential. On the one hand, it can directly simulate unlimited conducting structures without the air layer between the perfectly matched layer and inner structure; on the other hand, it needs only a quarter of the memory space required by the Runge-Kutta time scheme and requires one third of the meshes in every direction of the standard FDTD method. By choosing suitable meshes and bandwidth M, our scheme not only retains higher accuracy but also saves memory space and CPU time. Numerical examples are provided to show the high accuracy and effectiveness of the proposed scheme.     

A novel dispersive FDTD formulation for modeling transient propagation in chiral metamaterials

Chiral media engineered for applications at microwave frequencies can be described as metamaterials composed of randomly oriented helices (with sizes typically less than a wavelength) embedded within an achiral background that is characterized by its permittivity and permeability. Chiral metamaterials embody properties of magnetoelectric coupling and polarization rotation. Chiral media are also highly dispersive and no effective full-wave time domain formulation has been available to simulate transient propagation through such an important class of metamaterials. A new finite-difference time-domain (FDTD) technique is introduced in this paper to model the interaction of an electromagnetic wave with isotropic dispersive chiral metamaterials, based on the implementation of a wavefield decomposition technique in conjunction with the piecewise-linear recursive convolution method. This formulation represents the first of its kind in the FDTD community. The FDTD model is validated by considering a one-dimensional example and comparing the simulations with available analytical results. Moreover, the FDTD technique is also used to investigate the propagation of electromagnetic waves through multilayered metamaterial slabs that include dispersive chiral and double-negative media. Hence, this model enables the investigation of complex dispersive metamaterials with magnetoelectric coupling and double-negative behavior as well as facilitates the exploitation of their unique properties for a variety of possible applications.     

Numerical dispersion of higher order nodal elements in thefinite-element method

The discretization inherent in the finite-element method results in numerical dispersion. This dispersion is investigated for a time-harmonic plane wave propagating through an infinite, two-dimensional, finite-element mesh composed of uniform quadrilateral and triangular elements. The effects on the dispersion due to the propagation direction of the wave, the order of the elements, the node density, and the mesh geometry are studied. Results are given which can serve as a guide in selecting the appropriate element order, node density, and mesh geometry when applying the finite-element method     

A novel implementation of multilevel fast multipole algorithm for higher order Galerkin's method

A new approach is proposed to reduce the memory requirements of the multilevel fast multipole algorithm (MLFMA) when applied to the higher order Galerkin's method. This approach represents higher order basis functions by a set of point sources such that a matrix-vector multiply is equivalent to calculating the fields at a number of points from given current sources at these points. The MLFMA is then applied to calculate the point-to-point interactions. This permits the use of more levels in MLFMA than applying MLFMA to basis-to-basis interactions directly and, thus, reduces the memory requirements significantly.     

A frequency-dependent FDTD method for biological applications

A frequency-dependent finite-difference time-domain (FD)² TD method for calculating the response of pulses in plasma or water has recently been described. This method is an advance over the traditional finite-difference time-domain (FDTD) method in that it allows for the frequency dependence of these two media. The modification of the (FD)²TD method to obtain broadband frequency information in 3D biological applications is discussed. The implementation of this method is described, and its accuracy is verified by comparison with analytic solutions using the Bessel function expansion. The use of this method is illustrated by an example of the 3D simulation of a hyperthermia treatment using two applicators over a frequency range of 40 to 200 MHz     

A multiwire formalism for the FDTD method

The thin-wire formalism is a widely used subcell model that allows the finite-difference time-domain (FDTD) method to take account of wires thinner than the cell size. In this paper, the original formalism is generalized to a multiwire formalism that allows the FDTD method to take account of bundles composed of arbitrarily close wires     

A new well-conditioned Integral formulation for Maxwell equations in three dimensions

We present a new boundary integral equation dedicated to the solution of the boundary problem of a perfectly electrically conducting surface for the harmonic Maxwell equations in unbounded domains. Any solution of the harmonic Maxwell equations is represented as the electromagnetic field generated by a combination of electric and magnetic potentials. These potentials are those appearing in the classical combined field integral equation (CFIE), but their coupling is realized by an operator Y/spl tilde//sup +/ instead of a coefficient. Therefore, the integral equation obtained can be viewed as a generalization of the CFIE. In this paper, we propose an explicit construction of the coupling operator Y/spl tilde//sup +/ which is designed to approximate the exterior admittance operator of the scattering obstacle. A local approximation by the admittance operator of the tangential plane seems to be relevant thanks to the localization effects related to high-frequency phenomena. The provided numerical simulations show that this formulation leads to linear systems that are better conditioned compared to more classical integral equations, which speeds up the resolution when solved with iterative techniques.     

Higher order formulation of absorbing boundary conditions for finite-difference time-domain method

A simple formulation of absorbing boundary conditions with higher order approximation is proposed for the finite-difference time-domain (FD-TD) method. Although this formulation is based on the third order approximation of the one-way wave equations the authors have succeeded in reducing it to an equation in a form quite similar to the second order approximation.<>     

A nonparametric phase estimation method for SIMO systems based onsecond-order and higher order statistics

We present a nonparametric phase estimation algorithm for linear single-input multiple-output (SIMO) channels. Given an unknown stationary input signal with known statistics, our approach is to obtain the joint minimum mean square phase estimation based on the polyspectra and the cross-spectra of the SIMO channel outputs. By utilizing both higher order and second-order statistics of the channel outputs, our approach is shown to be more accurate and reliable than methods based on higher order statistics alone. It can be applied to SIMO channels with common zeros