时域积分方程MOT算法的推迟位时间卷积数值积分新方法

通过变量代换平滑三角形上推迟位（标量位函数和矢量位函数）并消除推迟矢量位旋度的奇异性,使得采用数值积分法就能够精确快速地计算任意正则时间基函数与推迟位函数及推迟矢量位旋度之间的时间卷积运算,可用于基于任意类型时间基函数的时域电场、时域磁场及其混合场积分方程时间步进（MOT ）算法。与时间卷积运算的解析法对比分析表明,该时间卷积数值积分方法能够精确快速地计算基于任意类型时间基函数和不同时间步长条件下时域积分方程MOT算法的阻抗矩阵元素;而具体的计算实例也表明,阻抗矩阵的精确计算显著地提升了时域积分方程MOT算法的后时稳定性和求解精度。     

一种稳定的时域电场积分方程求解方法

提出了一种求解任意形状理想导体目标时域散射的稳定时域电场积分方程(TDIE)方法,此方法能非常有效地消除后期振荡。利用显式MOT方法求解二阶时间微分的电场积分方程,矢量位随时间的变化关系采用边缘中心近似,标量位随时间的变化关系则采用三角面元重心近似,然后运用先五步后三步的平均方法。数值结果表明,本文方法能够有效地提高TDIE方法的收敛性和稳定性。     

精确稳定求解时域电场积分方程的一种新方法

时域电场、磁场和混合场积分方程已被广泛用来分析散射体的时域散射响应.基于适当的空间积分方法和隐式的时间步进算(MOT)法在求解时域磁场和混合场积分方程时总是稳定的,然而在求解TDEFIE时则是不稳定的.在本文中,时域电场积分方程的非奇异性积分采用标准的高斯求积法来计算;而利用参数坐标变换和极坐标变换将其奇异性积分转换成为可以分区域精确快速计算的非奇异性积分.通过数值实验表明,利用该方法可以非常精确稳定地求解时域电场积分方程,即使是在时间迭代后期也不必采用任何求平均的过程;另外,该方法可以用于任意时间基函数并可以推广到高阶空间基函数的情形.     

基于高阶叠层矢量基函数的时域电磁场 积分方程方法

本文将准正交高阶叠层矢量基函数用于时域电磁场积分方程(TDIE),求解了三维金属目标的时域电磁散射问题.准正交高阶叠层矢量基函数定义在曲面四边形单元上,并且不要求网格为规范网格,给复杂目标的几何建模和电磁建模带来很大方便.在空间上利用伽略金方法、时间上采用点匹配法求解时域电磁场积分方程,并采用隐式时间步进算法,数值计算结果表明了该方法求解时域积分方程的精确性、高效性与稳定性.     

利用时间步进算法精确稳定求解时域积分方程

 时域阻抗矩阵元素的计算需要分别计算场单元和源单元上的空时积分,由于时间基函数的分域性以及时间基函数(如三角型时间基函数)导数的不连续性,使得采用高斯积分方法计算源单元上空时积分的计算精度较差且误差随着时间步长的减小而增大.本文通过将源单元上空时积分转变成为1D时间卷积分和1D空间解析积分来精确计算时域阻抗矩阵元素,并在此基础上利用时间步进算法求解了时域电场、磁场和混合场积分方程.通过计算实例表明该方法在较大的时间步长取值范围内均能确保时域积分方程时间步进算法求解的精度和后时稳定性.     

时域推进算法中TPM模型的奇异性研究

三角贴片模型(TPM)常用于研究电磁散射的时域推进算法中。但在计算矢量位函数和标量位函数的微分过程中,TPM模型将产生奇异点。本文详细分析了TPM模型奇异性问题的产生,并提出了处理奇异点的方法,给出的算例证明了该处理方法的有效性。     

求解时域电场积分方程的稳定时间步进算法

利用面积坐标变换、相对坐标变换、积分区域分解和广义Duffy坐标变换将时域电场积分方程中奇异性积分(共面、共边和共单结点的场源三角形单元上)转化成可精确计算的非奇异性积分.在不同时间基函数(导数连续和导数不连续)、不同时间步长情况下对比分析了该方法和现有的常用方法计算奇异性积分的精度.计算实例表明:时域阻抗矩阵的精确计算有效地改善了时间步进算法的后时稳定性.     

精确快速计算时域积分方程中奇异性积分的新方法

该文首先利用参数坐标和广义Duffy坐标变换将时域电场积分方程(TDEFIE)的奇异性积分转换成非奇异性积分,然后根据时间基函数的特点将该积分转换成可以快速精确计算的分区域积分。数值计算实例表明,该方法可以大幅度提高求解TDEFIE的后时稳定性和解的精度,而不必采用任何求平均的过程。该方法适用于任意类型的时间基函数并可方便地推广到高阶曲面拟合和高阶空间基函数情形。     

衍射微柱透镜焦深和焦移特性的矢量分析

当衍射光学元件的特征尺寸可以与照射光波长比拟时,必须考虑光波矢量衍射特性。利用矢量分析方法——二维时域有限差分法(FDTD)对有限口径衍射微柱透镜的焦深和焦移特性进行严格矢量分析,与传统标量分析方法的结果进行了详细比较。分析给出TE波垂直入射情况下衍射微柱透镜焦深和焦移与透镜F数的关系,结果表明,微柱透镜的焦移量要大于标量分析结果,而二者得出的焦深量基本一致,这些结论对衍射微透镜的设计和实际应用有一定指导意义。同时分析了透镜面型量化对焦深和焦移的影响,讨论了矢量分析方法的数值色散、计算空间吸收边界的设置和FDTD计算区稳定电磁场向观察面的传播算法。     

一种高阶辛时域有限差分法的研究

从电磁场方程的Hamilton函数出发,提出了一种基于辛时域积分技术的高阶时域有限差分方法.该方法对时域的离散采用了能够保证系统的相空间体积不变和总能量不变的辛格式,对于空间的离散采用中心差分格式.计算结果表明与传统的时域高阶差分方法--Runge-Kutta法比较,该方法计算速度和计算精度都有较大的提高.     

Accurate solutions of Maxwell's equations around PEC corners andhighly curved surfaces using nodal finite elements

A method is presented for computing accurate solutions of Maxwell's equations in the presence of perfect electrical conductors (PECs) with sharp corners and highly curved surfaces using conventional nodal finite elements and a scalar/vector (S/V) potential formulation. This technique approximates the PEC with an impedance boundary condition (IBC) where the impedance is small. Critically, it couples both potentials through this boundary condition, rather than setting the scalar potential to zero. This permits cancellation of the tangential components of the vector potential, resulting in an accurate normal electric field. The cause for the inaccuracies that nodal methods experience In the presence of sharp PEC corners or highly curved PEC surfaces is elucidated. It is then shown how the inclusion of the scalar potential cures these deficiencies permitting accurate solutions. Spectral analysis of the resulting finite element matrices are shown validating the boundary conditions used. Examples are presented comparing a benchmark solution, conventional PEC and IBC boundary conditions, and the new S/V potential IBC on a PEC wedge and PEC ellipse. In both cases the new S/V IBC produces superior results     

Recursive Image Enhancement--Vector Processing

A new approach to design of a recursive image enhancer is introduced when the image is characterized statistically by its mean and correlation function. A vector linear dynamical model is derived to represent the statistics of the processor output when several lines of the picture are processed simultaneously. Based on the vector model, a Kalman filter is designed and utilized to recursively enhance the image. The vector processing results in a simpler and more accurate image enhancement algorithm in comparison with scalar processing. Two examples, one with very low signal-to-noise ratio, are used to illustrate the effectiveness of the procedure. Finally, the performance of the vector and scalar estimators is compared.     

Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.     

Derivation of the Lorentz potentials

The article [Schwab et al., 1996] on semantics of the irrotational component of the magnetic vector potential inspired the following alternative derivation of the expressions for the magnetic field, H, and the electric field, E, in terms of the Lorentz potentials. The artifice of the Lorentz gauge is not used in this derivation. Instead, the Lorentz potentials are required to satisfy differential equations akin to those satisfied by the Coulomb potentials. The Lorentz vector potential, A_L, is constructed by adding what turns out to be an irrotational vector, A_irr, to the Coulomb vector potential, A_C. The Lorentz scalar potential, φ_L, is constructed by adding a scalar, φ, to the Coulomb scalar potential, φ_C     

Optimum design of vector-quantized subband codecs

This article provides an approach for representing an optimum vector quantizer by a scalar nonlinear gain-plus-additive noise model. The validity and accuracy of this analytic model is confirmed by comparing the calculated model quantization errors with actual simulation of the optimum Linde-Buzo-Gray (1980) vector quantizer. Using this model, we form an MSE measure of an M-band filter bank codec in terms of the equivalent scalar quantization model and find the optimum FIR filter coefficients for each channel in the M-band structure for a given bit rate, filter length, and input signal correlation model. Specific design examples are worked out for four-tap filters in the two-band paraunitary case. These theoretical results are confirmed by extensive Monte Carlo simulation     

A hybrid finite element method for 3-D scattering using nodal andedge elements

A hybrid finite element method for three-dimensional scattering is presented and numerical examples shown. This approach, which couples finite element discretization with the method of moments, is particularly well suited for monostatic radar cross section calculations. The method is based on a scalar and vector potential formulation of Maxwell's equations, the use of nodal elements, and a highly efficient body of revolution implementation of the method of moments. Combined nodal and edge elements are employed to accurately model fields around corners and edges. A curvature-based sampling criterion is derived and shown to ensure accurate answers for highly curved scatterers. Numerical results and Cray computer timings are compared with published results for an edge element code using radiation boundary conditions     

An efficient finite-element formulation without spurious modes foranisotropic waveguides

A numerically efficient finite-element formulation is presented for the analysis of lossless, inhomogeneously loaded, anisotropic waveguides of arbitrary shape. The electromagnetic field is described either by the three components of a magnetic vector potential and an electric scalar potential or by the three components of an electric vector potential and a magnetic scalar potential. The uniqueness of the potentials is ensured by the incorporation of the Coulomb gauge and by proper boundary conditions. Owing to the implementation of the solenoidality condition for the vector potential even in the case of zero wavenumber, no spurious modes appear. Variation expressions suited to the finite-element method are formulated in terms of the potentials. Standard finite-element techniques are employed for the numerical solution, leading to a generalized eigenvalue problem with symmetric, sparse matrices. This is solved by means of the bisection method with the sparsity of the matrices fully utilized. Dielectric- and ferrite-loaded waveguides with closed and open boundaries and including both isotropic and anisotropic materials are presented as examples     

A simple and accurate complex image interpretation of verticalantennas present in contiguous dielectric half-spaces

An efficient technique is developed to solve the important problem of vertical antennas located above and penetrating the interface between contiguous dielectric half-spaces. It begins by deriving the spectral expressions of the vector and scalar potential Green functions in terms of the TM wave spectral transmission coefficient. The complex image technique is used to derive simple, accurate, and rapidly convergent expressions of the full-wave spatial Green functions. The spatial Green functions are used in the moment method to model vertical thin-wire antennas residing above the penetrating the interface separating the contiguous dielectric half-spaces with and without loss     

Analysis of microstrip resonators of arbitrary shape

A space-domain approach based on a mixed-potential integral equation formulation is developed for efficient computation of complex resonant frequencies of laterally open microstrip-pitch resonators of arbitrary shape. The effects of the substrate-which may consist of any number of planar, possibly uniaxially anisotropic, dielectric layers-are rigorously incorporated in the formulation by means of the vector and scalar potential Green's functions. The current distribution on the conducting patch is approximated in terms of vector basis functions defined over triangular elements. Computed resonant frequencies, quality factors, modal currents, and far-field radiation patterns are presented for several microstrip resonators. For patches of simple, regular shapes, the results are in agreement with published data obtained by specialized techniques, which, unlike the method presented here, are not easily extendible to arbitrary shapes