小波变换在指数粗糙表面电磁散射中的应用

研究了小波变换在指数粗糙表面电磁散射中的应用.在用矩量法研究电磁散射问题时,基函数的选择是一个非常重要的步骤.不同的基函数对问题的求解规模影响很大.利用小波变换中二尺度方程关系,通过对大尺度基函数和小波基函数求解相应的矩阵方程,然后由小尺度基函数与大尺度基函数以及小波基函数的关系,求出对应于小尺度基函数的矩量法解.该方法的优点是减少了矩阵方程求解的规模.     

金属-各向异性介质体组合目标频域体表积分方程矩量法

利用体表积分方程矩量法求解了具有任意的介电常数张量和磁导率张量的各向异性介质与金属的组合目标的电磁散射问题.给出了基于RWG面基函数和SWG体基函数的体表积分方程阻抗矩阵元素表达式并详细推导了阻抗矩阵元素所涉及的各种积分运算的计算方法;通过数值计算实例与解析解或其它数值方法的详细对比分析,证明了计算公式的正确性.     

二维多导体柱电磁散射特性的特征基函数法分析

特征基函数法是近两年提出来的一种求解电磁散射问题的有效方法,该方法使用的特征基函数不受传统矩量法离散尺寸的限制,因而可以大大减小要求解的矩阵方程。应用特征基函数法分析了二维多导体柱的电磁散射特性,计算了多个无限长导电椭圆柱和方柱的雷达散射截面,结果表明特征基函数法的计算结果与传统矩量法的计算结果吻合良好,而计算量却大为减少。     

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.     

磁场积分方程矩量法中基函数的立体角修正

本文通过考察电磁散射问题矩量法求解中电场积分方程和磁场积分方程的公式 ,分析了在使用三角屋顶基函数情况下传统的磁场积分方程在计算带有棱角的电小尺寸金属物体雷达截面时存在的不足 ,提出了一种基函数的立体角修正技术 ,从而达到了减小计算误差的目的。计算结果表明了算法的有效性。     

多层自适应交叉近似加速的旋转对称体矩量法

为了更有效地分析旋转对称电大物体的电磁散射问题,提出了一种针对旋转对称矩量法的多层自适应交叉近似加速方法,并分别应用于基于三角形基函数和3阶Hermite基函数的旋转对称矩量法.使用所提方法加速混合场积分方程下旋转对称体矩量法的单模式与多模式阻抗矩阵的构建过程时,计算得到的远场雷达散射截面积与传统旋转对称矩量法的结果吻合良好,且计算效率明显提高.     

位积分方程组矩量法用于精确计算非均匀介质柱的电磁散射

位积分方程组的主要特点是以电磁位为未知函数,这些未知函数在具有不同电磁参数的介质分界面处是连续的,因而在矩量法的实现过程中能够非常方便地应用高阶插值基函数来展开未知函数,以便获得高精度的解。但是,经典的点匹配方案使该模型的数值稳定性较差。本文用位积分方程组矩量法模型计算任意截面非均匀介质柱的电磁散射,采用三角形离散方案和高阶插值基函数,在测试过程中应用新提出的测试方法,克服了原位方程组矩量法模型的数值不稳定性。对矩量法矩阵中自阻抗元素的奇异性处理方法也作了详细介绍。文中提供的数值结果表明,该方法是精确、稳定的。     

利用高阶矢量基函数求解时域磁场积分方程

本文利用一种新的高阶矢量基函数求解了三维时域磁场积分方程,该基函数定义在一个曲边三角形贴片上并用拉格朗日插值多项式来表示每一个贴片内的未知电流密度.该基函数的实质就是将拉格朗日插值多项式的插值点选为高斯积分结点,极大地简化和加快了时域积分方程矩量法的繁琐的时间和空间积分运算;另外,该基函数不要求网格为规范网格,给复杂目标的网格剖分带来很大方便.在空间上利用点匹配方法求解了时域磁场积分方程,数值计算结果表明了该方法求解时域积分方程的精确性和高效性.     

结合P-FFT算法和特征基函数分析大型阵列散射

特征基函数方法利用特征值分解提取目标散射特征,构造基于特征向量的基函数可以高效的缩减矩量法分析所需的未知量数目,有利于分析有限周期阵列电磁散射或辐射问题。然而,对于电大尺寸电磁阵列散射问题,直接求解由特征基函数组成的矩阵方程,仍然面临着计算量较大等问题,难以适用于单机计算。本文结合特征基函数和预修正傅里叶快速算法求解体面结合积分方程,分析了大型金属介质混合有限周期阵列的散射特性,该算法有效减少了计算量和计算时间,并且改善了迭代求解收敛性能。     

电波传播

0100421一维随机粗糙面电磁散射的小波矩量解[刊]/郭立新//西安电子科技大学学报.—2000.27(5).—585～589(D)粗糙面的电磁散射问题可以归结为一个电场积分方程。采用小波基函数将积分算子展开,利用矩量法求解矩阵方程,得到一维随机粗糙面的等效电流分布,并进一步得到散射场,所得结果与有关文献的结果基本一致。参8     

利用时域电场积分方程分析天线辐射问题

研究了基于矩量法和RWG三角基函数的隐式电场积分方程的时域算法,引入了一种激励源的时域设置方法.利用直接在时域加激励源的方法来分析天线辐射问题,所得时域数据经傅立叶变换可得到很宽频带的频域数据,与在频域逐个频点求解相比大大节省了计算时间.通过对几种典型天线的分析计算,验证了方法的正确性和算法的稳定性.     

TD‐CFIE Formulation for Transient Electromagnetic Scattering from 3‐D Dielectric Objects

In this paper, we present a time domain combined field integral equation formulation (TD‐CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space‐time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.     

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.     

A stable solution of time domain electric field Integral equation for thin-wire antennas using the Laguerre polynomials

In this paper, a numerical method to obtain an unconditionally stable solution of the time domain electric field integral equation for arbitrary conducting thin wires is presented. The time-domain electric field integral equation (TD-EFIE) technique has been employed to analyze electromagnetic scattering and radiation problems from thin wire structures. However, the most popular method to solve the TD-EFIE is typically the marching-on in time (MOT) method, which sometimes may suffer from its late-time instability. Instead, we solve the time-domain integral equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically and stable results can be obtained even for late-time. Furthermore, the excitation source in most scattering and radiation analysis of electromagnetic systems is typically done using a Gaussian shaped pulse. In this paper, both a Gaussian pulse and other waveshapes like a rectangular pulse or a ramp like function have been used as excitations for the scattering and radiation of thin-wire antennas with and without junctions. The time-domain results are compared with the inverse discrete Fourier transform (IDFT) of a frequency domain analysis.     

Analytical Evaluation of Transient Magnetic Fields Due to RWG Current Bases

A new analytical approach for obtaining the time samples of the magnetic field intensity due to an impulsively excited Rao-Wilton-Glisson (RWG) basis function is presented. The approach is formulated directly in the time domain. It is shown that the magnetic field is related to the arc segments formed by the intersection of the triangular patch of the RWG basis with the sphere that is centered at the observation point and that has a radius of , where is the speed of light. In particular, the magnetic field can be expressed as the variations of two quantities with respect to . The first quantity is the arc segment length, and the second quantity is the bisecting vector of the arc segment. Analytical representations of these quantities are presented. Contrary to previous studies, these representations do not require the calculation of the intersection points of the sphere with the boundaries of the bases. The validity of the obtained time domain formulae is demonstrated through comparison of the results with those obtained in the frequency domain by using numerical quadrature. Finally, it is demonstrated that the derived formulae yield closed-form expressions when convolved with piecewise polynomial temporal basis functions.     

Comparison of a class of subdomain and entire domain basisfunctions automatically satisfying KCL

Accuracy, number of unknowns, and CPU time are compared for piecewise linear subdomain basis functions and polynomial entire domain basis functions. Both types of functions automatically satisfy a continuity equation at wire ends and junctions, according to Kirchoff's current law (KCL). The relative root mean square (RMS) current deviation is chosen as the error metric. An electrically short scatterer, a crossed wire scatterer and an electrically long scatterer are used for comparison. Currents are obtained by solving the electric field integral equation (EFIE), by means of the Galerkin method. It was shown that in most cases, for the same accuracy required, the entire domain approximation uses three to five times less numbers of unknowns and 10-100 times less CPU time than the subdomain approximation. Generally, such efficiency is achieved by using entire domain expansions the order of which is up to n=5 and cannot be significantly improved by using higher order expansions     

An Extension of Parseval's Theorem and Its Use in Calculating Transient Energy in the Frequency Domain

The paper first presents an analysis which leads to an equation useful for calculating energy in the frequency domain. The equation is seen to be an extension of Parseval's theorem and is very useful for calculating the energy content of pulses that are difficult to treat in the time domain. An algorithm based on the equation has been programmed in Fortran. The details of the algorithm and the program were presented elsewhere [1]; only a few details are discussed in this paper. Finally, an application of the method to the calculation of transient energy in power distribution networks is discussed.     

MoM/BI-RME analysis of boxed MMICs with arbitrarily shapedmetallizations

In this paper, we propose a novel approach for the analysis of shielded microstrip circuits, composed of a number of thin metallic areas with arbitrary shapes and finite conductivity, embedded in a multilayered lossy medium. The analysis is based on the solution of an integral equation (IE) obtained by enforcing the proper boundary condition to the electric field on the metallic areas. The IE is solved by using the method of moments with entire domain basis functions, which are numerically determined by the boundary integral-resonant-mode expansion (BI-RME) method. The use of the BI-RME method allows for the efficient calculation of the basis functions independently on the shape of the domain, thus permitting the analysis of a wide class of circuits. Two examples demonstrate the accuracy, rapidity, and flexibility of the proposed method     

Analysis of two dimensions sparse multicylinder scattering problem using DD-FDTD method

An algorithm of two-dimensional (2-D) domain decomposition finite-difference time-domain (DD-FDTD) using in sparse multicylinders scattering problem is proposed in this paper. The idea of domain decomposition is introduced to divide the sparse problem domain into several subdomains. All of subdomains are connected by means of the 2-D time domain Green's function. As a result, a great deal of meshes memory between cylinders is removed, especially when the distances between cylinders become large. Furthermore, the coupling between cylinders can be regarded as the equivalent cylindrical wave irradiations. The incident signals of the equivalent cylindrical waves are expressed as cylindrical wave input field array (CWIFA) according to Huygens principle. Then the calculation time is significantly reduced. The near-field to far-field transformation is used to obtain the equivalent cylindrical wave; as a result, the calculation time can be reduced further. The new method has been demonstrated in 2-D multicylinders scattering problem. Numerical results are in good agreement with the results obtained using classical FDTD method and moment of methods (MM).     

基于Laguerre多项式的边界积分方程时域求解

针对时域积分方程中存在的晚时震荡问题,介绍了基于Laguerre多项式的电场、磁场和混合场积分方程,求解了导体球和导体圆柱的时域电流分布和后向散射场以及单站RCS。结果表明,3种积分方程很好地解决了晚时震荡问题,混合场积分方程具有更高的计算精度。