基于复数帧段特征的语音情感识别方法

在现有的电磁场算法中,时域有限差分法(FDTD)的使用越来越广泛。但是当解决曲面问题时,原有的FDTD方法就不太适用了。而且,大多数的电气设备为多重材料结构和不连续的曲线表面,传统的FDTD算法会产生发散和不稳定现象。由此提出了一种基于非标准曲线算子的三维高阶FDTD算法,用于解决复杂介质结构电气设备的电磁兼容性问题。根据代数拓扑学,将各种不规则形状的网格转化为合适的二重网格用公式表示出来,在优化整体性能的同时降低色散误差。通过计算结果可以看出,高阶非标准FDTD算法的准确度极高,而且没有任何色散情况出现,并且高阶非标准FDTD算法还可以节省大约85%的CPU和内存使用。证明了该FDTD算法能有效提高计算精度并减少计算资源的消耗。     

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.     

一种有效减少ADI-FDTD数值色散的方法

ADI—FDTD算法的数值色散效应较为明显，本文的研究表明一种通过添加各向异性媒质来修正相速误差，从而减少FDTD数值色散的方法，同样适用于ADI-FDTD，且收效更为显著。数值运算结果证明该方法能够简单有效地去除较宽频带范围内的色散。     

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.     

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.     

用Cassinian变换FDTD方法分析几种特殊截面波导传输特性

本文把保角变换应用于紧凑格式2D/FDTD算法,给出了保角变换FDTD算法差分公式,提出了焦点的处理方法.用Cassinian变换分别计算了椭圆波导、茧形波导的截止波长与色散曲线,以及屏蔽平行双线高阶模的截止波长.     

基于Taylor级数展开定理的高阶FDTD的色散分析

时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具.而Taylor级数展开定理是构造差分格式的一种重要方法,例如Yee格式采用二阶Taylor格式,Fang格式采用四阶Taylor格式.本文借助于采样定理,详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差,并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中,严格导出了稳定性条件和数值色散关系的表达式,引入了新的误差定义来衡量算法的好坏.详细地研究了Courant数、网格分辨率CPW和网格长度比率等因素对于数值色散误差的影响,为基于Taylor差分格式的FDTD算法的研究提供了有用的参考.     

基于高阶时域有限差分法与改进节点分析法混合求解复杂传输线网络瞬态响应

该文提出一种用于求解复杂传输线网络瞬态响应的新型混合算法.通过构建混合单端口网络模型将传输线分布参数系统与集总电路分开,分别采用高阶FDTD(2,4)与改进节点电压分析法(MNA)分析传输线与端口电路瞬态响应.与以往暂态分析方法相比,高阶FDTD(2,4)的低数值色散特性,使得求解传输线时可采用粗网格离散,能方便处理电长度较长的传输线.同时直接采用电路分析方法求解端口电路,能够获取电路中各节点的电压电流波过程.通过几组数值实例验证了该方法的有效性及准确性.     

高阶时间空间差分近似对二维ADI-FDTD方法数值色散的影响

本文讨论交替方向隐式时域有限差分法(ADI—FDTD)的数值色散问题，分别对高阶时间空间差分近似，介绍了近似公式，并进行2阶、4阶、6阶、10阶差分数值色散误差的算例计算，对比表明4阶空间差分近似产生的色散误差较小。     

三维最优时域有限差分方法

数值色散是时域有限差分方法(FDTD)中最主要的误差来源,导致数值相速成为频率和方向的函数。文中讨论了一种基于最优有限冲激滤波器设计方法的最优差分格式,从频率空间或者波数空间中实现对理想偏微分算子的逼近,构造一种新的具有低数值色散关系的最优时域有限差分方法。文中导出了其数值色散关系和进行了稳定性分析,并通过与常用的基于泰勒级数展开定理的高阶(2,4)时域有限差分法相比较,发现最优时域有限差分法的数值色散得到了极大的改善。最后通过一个数值例子来验证其有效性。     

A Versatile Split-Field 1-D Propagator for Perfect FDTD Plane Wave Injection

A new staggered field design and formulation for the one-dimensional propagator of the total-field/scattered-field source implementation in finite-difference time domain (FDTD) scattering simulations are presented. The new equations are based on split-field Maxwell's equations and the resulting technique extends the functionality of the multipoint auxiliary propagator to sourcing FDTD lattices hosting extended-stencil high-order algorithms. This technique virtually eliminates numerical dispersion, field location and polarization mismatches between propagator and main grid. The resulting machine accuracy-level leakage error from implementing this technique is confirmed for the standard low and high-order FDTD schemes as well as the M24 high-order algorithm. Normalized field leakage for all three algorithm implementations outside the total-field region was measured at below - 295 dB.     

Dispersion-relation-preserving FDTD algorithms for large-scale three-dimensional problems

We introduce dispersion-relation-preserving (DRP) algorithms to minimize the numerical dispersion error in large-scale three-dimensional (3D) finite-difference time-domain (FDTD) simulations. The dispersion error is first expanded in spherical harmonics in terms of the propagation angle and the leading order terms of the series are made equal to zero. Frequency-dependent FDTD coefficients are then obtained and subsequently expanded in a polynomial (Taylor) series in the frequency variable. An inverse Fourier transformation is used to allow for the incorporation of the new coefficients into the FDTD updates. Butterworth or Chebyshev filters are subsequently employed to fine-tune the FDTD coefficients for a given narrowband or broadband range of frequencies of interest. Numerical results are used to compare the proposed 3D DRP-FDTD schemes against traditional high-order FDTD schemes.     

非Yee网格的FDTD法分析复杂媒质PBG结构的带阻特性

采用电、磁场各分量均位于网格中心的高阶时域有限差分法计算PBG结构的色散特性。对简单媒质问题的计算结果与采用Yee网格时域有限差分法所得一致，但更适合于分析含复杂媒质的问题。计算了三类磁各向异性PBG结构的色散特性曲线，指出：磁各向异性媒质都可明显增宽第一阻带；对称型磁各向异性还增多色散特性曲线中的阻带数，但旋磁型各向异性则不影响阻带数。     

Analysis of the numerical dispersion of the 2Dalternating-direction implicit FDTD method

The numerical dispersion property of the two-dimensional alternating-direction implicit finite-difference time-domain (2D ADI FDTD) method is studied. First, we notice that the original 2D ADI FDTD method can be divided into two sub-ADI FDTD methods: either the x-directional 2D ADI FDTD method or the y-directional 2D ADI FDTD method; and secondly, the numerical dispersion relations are derived for both the ADI FDTD methods. Finally, the numerical dispersion errors caused by the two ADI FDTD methods are investigated. Numerical results indicate that the numerical dispersion error of the ADI FDTD methods depends highly on the selected time step and the shape and mesh resolution of the unit cell. It is also found that, to ensure the numerical dispersion error within certain accuracy, the maximum time steps allowed to be used in the two ADI FDTD methods are different and they can be numerically determined     

Stability and Numerical Dispersion Analysis of a Fourth-Order Accurate FDTD Method

In order to obtain high-order accuracy, a fourth-order accurate finite difference time-domain (FDTD) method is presented by Kyu-Pyung Hwang. Unlike conventional FDTD methods, a staggered backward differentiation scheme instead of the leapfrog scheme is used to approximate the temporal partial differential operator. However, the high order of its characteristic equation derived by the Von Neumann method makes the analysis of its numerical dispersion and stability very difficult. In automatic control theory, there are two effective methods for the stability analysis, i.e., the Routh–Hurwitz test and the Jury test. The combination of the Von Neumann method with each of the two can strictly derive the stability condition, which only makes use of the coefficients of its characteristic equation without numerically solving it. The method of analysis in this paper is also applicable in the stability and numerical analysis of other high-order accurate FDTD methods.     

高阶FDTD法分析电-大尺寸光波导器件

高阶时域有限差分(FDTD)法用于电-大尺寸平面光波导器件的时域分析,实现了高阶FDTD法的理想匹配层(PML)吸收边界条件;研究了高阶FDTD法的数值色散特性,并对平行介质带定向耦合器进行了数值模拟,所得结果与解析解非常一致。     

有耗介质中时域精细积分方法的数值色散分析

分析了时间步长、空间步长、电导率和电磁波传播方向对时域精细积分(PITD)方法的数值损耗和数值色散的影响。结果表明:PITD的数值损耗大于电磁波的真实损耗,其数值波速可以大于电磁波的真实波速。PITD的数值损耗和数值色散都基本上不受时间步长的影响。随着空间步长的减小,PITD的数值损耗和数值色散的误差都逐步减小。当电导率较小时,PITD的数值损耗和数值色散的误差比时域有限差分(FDTD)方法的大。但当电导率较大时,PITD的数值波速却比FDTD的数值波速更加接近于电磁波的真实波速。PITD的数值损耗和数值色散的各向异性在三维情况下的值要大于其在二维情况下的值。数值算例表明:对良导体而言,PITD比FDTD拥有更高的计算精度和更快的计算速度。     

Three New Unconditionally-Stable FDTD Methods With High-Order Accuracy

Three novel finite-difference time-domain (FDTD) methods based on the split-step (SS) scheme with high-order accuracy are presented, which are proven to be unconditionally stable. In the first novel method, symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell's equations into six sub-matrices. Accordingly, the time step is divided into six sub-steps. The second and third proposed methods are obtained by adjusting the sequence of the sub-matrices deduced in the first method, so all the novel methods presented in the paper have similar formulations, of which the numerical dispersion errors and the anisotropic errors are lower than the alternating direction implicit finite-difference time-domain (ADI-FDTD) method, the initial SS-FDTD method and the modified SS-FDTD method based on the Strang-splitting scheme. Specifically, for the second method, corresponding to a certain cell per wavelength (CPW), there is a Courant number value making the numerical anisotropic error to be zero, while in the third novel method, corresponding to a certain Courant number value, there exists a CPW making the numerical anisotropic error to be zero. In order to demonstrate the high-order accuracy and efficiency of the proposed methods, numerical results are presented.     

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.      

Enlarged cells for the conformal FDTD method to avoid the time step reduction

Recently, the conformal finite-difference time-domain (CFDTD) method has emerged as an efficient FDTD method with a higher order accuracy than the conventional FDTD methods that are degraded by staircasing errors. The only obvious point to further improve on the CFDTD method is its requirement for a smaller time step increment due to the existence of small irregular cells near the boundary. In this letter, an enlarged cell technique is introduced to ensure the stability of the CFDTD method without the time step reduction. The introduction of the enlarged cells therefore makes the CFDTD method much more efficient and suffers from a smaller dispersion error, as shown in several two-dimensional examples.