粗糙海面及其上方导体目标复合电磁散射的混合算法研究

利用基于电流计算的矩量法结合高频算法基尔霍夫近似的混合算法,分析了一维PM谱粗糙海面及其上方二维无限长任意截面导体目标的双站复合电磁散射特性.混合算法将粗糙面和目标分别划分到KA区域和MOM区域,由于无需数值求解粗糙海面区域的表面极化电流,该算法的运算时间和对计算机内存的需求主要取决于粗糙面上方目标的网格划分情况.数值结果以无限长导体圆柱为例计算了其与一维下垫PM谱粗糙海面的复合双站散射截面,并将计算结果与经典MOM结果进行了比对和验证,结果表明混合方法具有较高的计算效率.最后应用混合方法讨论了不同极化状态、海上不同风速以及目标不同尺寸和位置对复合散射截面的影响. 关键词： 粗糙海面 电磁散射 混合算法 矩量法     

金属纳米柱天线的快速电磁分析

基于分段正弦基函数和矩量法,通过求解离散电流节点格林函数的封闭解得到金属纳米柱天线激发表面等离子体的阻抗矩阵.与使用其它基函数矩量法相比,该方法可以减少矩阵方程的维数.仿真结果表明:使用此方法只需求解很小的矩阵方程就可以求解出纳米天线表面极化电流,从而实现对纳米天线的散射特征及谐振模式的快速分析;其结果与时域有限差分仿真结果吻合良好且速度具有显著的优势,尤其在计算斜入射问题时计算优势更加明显.本文的方法对文中计算的模型有效,同样为其他形状纳米柱天线和碳纳米管器件散射特性仿真提供了快速有效的电磁分析方法.     

基于压缩感知的目标频空电磁散射特性快速分析

矩量法是求解目标电磁散射问题的一种常用数值方法,因其精度较高而被广泛应用.应用矩量法求解目标频空电磁散射特性时,随着入射波的角度和频率的变化,需要间隔很小的角度和频率步长反复求解矩量法生成的矩阵方程,运算量极大.为解决此类问题,本文结合压缩感知理论和渐近波形估计形成一种新的有效计算方法.首先,基于压缩感知理论引入一种富含空间信息的新型入射源,其次,在该入射源照射下应用渐近波形估计技术求解,从而快速实现目标频空电磁散射特性分析.     

新型压缩感知计算模型分析三维电大目标电磁散射特性

为提高基于压缩感知技术的矩量法在三维电大目标双站电磁散射问题中的计算效率和稳定性,提出新的稀疏、测量和重构方法,构建一种新型压缩感知计算模型.不同于基于欠定方程的传统的压缩感知计算模型,新型计算模型首先采用按行均匀抽取阻抗矩阵的方法构造测量矩阵以获得稳定的计算结果;然后,基于Foldy-Lax方程生成多阶特征基函数并作为稀疏基对感应电流进行稀疏转换;再依据少数低阶特征基函数足以近似表征感应电流的先验条件,将恢复算法简化为最小二乘法;最后,将矩阵方程转换为一个超定系统并采用最小二乘法解出电流系数.与传统的计算模型相比,新型计算模型不仅可以获得更加稳定的精确解,还可以显著提高电大目标双站散射问题的求解效率和计算精度.数值仿真结果证明了新方法的可行性和高效性.     

压缩感知理论在矩量法中的应用

矩阵填充与线性方程组求解是矩量法中最耗计算资源的环节.为提高计算效率,提出了一种基于压缩感知理论的矩量法的改进方法.通过引入稀疏变换矩阵实现对待求响应的稀疏表示,从而可在压缩感知理论框架下构造欠定方程,并优化求解.数值仿真实验结果表明:该方法不仅可以减小矩阵填充计算量,还可以有效提高解的求解效率.     

应用压缩传感求解宽角度电磁散射问题

基于矩量法中阻抗矩阵与电磁波入射方向的无关性,引入压缩传感技术,构建一种全新的含有丰富角度信息的入射源.在该入射源照射下利用矩量法获得感应电流的测度,在数次测度之后,通过快速正交匹配追踪算法可恢复各个角度入射下的激励电流.与传统的矩量法相比,计算结果保持很高的精度,且计算时间减少为原来的三分之一,从而降低了宽角度电磁响应分析的计算复杂度.     

粗糙海面与其上方多目标复合散射的混合算法

针对粗糙海面与其上方多目标复合的情形,常用算法存在计算量过大、计算时间太长等缺点,本文采用基尔霍夫近似法与矩量法结合的混合算法可以大大简化计算量、节省时间.本文首先通过蒙特卡罗的方法模拟一维PM粗糙海面,并与粗糙海面上方多目标建立复合模型;然后对矩量法结合基尔霍夫近似法的混合算法做了详细的公式推导,得到了复合散射系数,并且分析了不同入射角、目标高度、目标间距、目标尺寸、风速等参数对复合电磁散射特性的影响.实验结果表明,针对粗糙海面与其上方多目标复合的情形,采用矩量法结合基尔霍夫近似法的混合算法不但可以保证准确性,而且可以大幅度减少计算所用时间(混合算法用时占矩量法的19%),对大尺寸粗糙面和复杂的复合模型优势尤为明显.     

时域混合算法在一维海面与舰船目标复合电磁散射中的应用

采用时域积分方程(TDIE)与时域基尔霍夫近似(TDKA)的混合算法研究粗糙海面与舰船目标的复合瞬态电磁散射.该方法将舰船目标及其近邻海面划分为TDIE区域,用TDIE方法精确求解;将剩余电大尺寸的粗糙海面划分为TDKA区域,采用高效的TDKA电流近似求解.通过混合算法和传统TDIE算法结果的对比,表明TDIE-TDKA混合算法能保证计算的精度,同时具有较高的计算效率.最后,讨论了海面上方有无目标、海面上方风速、电磁脉冲入射角、舰船目标尺寸、吃水深度对后向散射磁场的影响.     

非均匀流体介质内部散射声场重建的逐层计算方法*

入射声波激励下非均匀流体介质内部散射声场的重建方法对超声层析成像具有重要意义。以往采用矩量法求解,但该方法全域离散形成的复数满秩矩阵规模随着分辨率与计算精度的提高而急剧增大,对算力具有很高的要求,一定程度上限制了其在实际中的应用。为克服上述缺陷,本文以逐层离散、逐层计算为核心思想,以声散射基本公式与近场声全息理论为基础,推导出逐层计算非均匀流体介质内部散射声场的理论公式并给出对应的几何离散模型。为验证该方法的可行性,以矩量法为参照,对同样的介质模型进行介质内部声场重构仿真。结果表明,逐层算法不仅可以有效地重建非均匀流体介质内部散射声场,且大幅度减小了求解规模。     

基于奇异值分解的数字波前拟合算法

提出了基于奇异值分解、采用泽尼克多项式拟合干涉波前的算法,该算法直接从线性方程组入手,对矩阵进行奇异值分解分解,在求解逆矩阵的过程中,采用阈值法对奇异值的倒数进行非常规的置换(∞→0),可直接得到系数向量。理论分析和实验证明,相对于传统的格拉姆施密特正交法,该算法可首先通过求解条件数判断线性方程矩阵是否奇异,对于解决病态方程组或奇异矩阵的最小二乘问题,有很好的稳定性,避免了由最小二乘构造的法方程组出现病态而引入的计算误差,且易于编程。     

Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

高频电磁干扰对传输线耦合全波建模方法

对于场线耦合问题,经典传输线理论不适用于求解高频电磁干扰辐照下传输线负载上的电压和电流响应。针对这一问题,首先介绍了一种基于天线理论和模拟行为建模（ABM）的时域全波建模方法。该方法利用Harrington矩量法将电流积分方程离散并推导得到宏模型时域表达式,然后利用ABM频域功能实现频变参数的傅里叶逆变换和时域卷积计算。利用电路求解器,该建模方法可直接求解任意结构传输线耦合的负载处瞬态响应;与传统全波算法相比,模型一旦建立便可应用于任意入射场和线性/非线性负载的情况,无需重复耗时地求解电流积分方程。该方法可简化全波算法求解过程,提高仿真计算效率,尤其便于在入射场和负载存在不确定参数时进行高效重复抽样计算以获得统计特性。然后以高频电磁干扰耦合有损大地上的双导体传输线为例,通过与数值电磁代码和传统传输线理论方法的求解结果对比,验证了所提宏模型的有效性以及传输线理论在解决场线耦合问题时的局限性。结果表明,基于全波方法构建的宏模型可在时域内高效准确地求解高频电磁干扰辐照下任意形状传输线负载上的瞬态响应。     

Bistatic electromagnetic scattering from a three-dimensional perfect electric conducting object above a Gaussian rough surface based on the Kirchhoff–Helmholtz and electric field integral equation

A hybrid integral equation is developed to solve the problem of electromagnetic (EM) scattering from a three-dimensional (3D) perfect electric conducting (PEC) object above a two-dimensional (2D) PEC or dielectric Gaussian rough surface. Firstly, the Kirchhoff–Helmholtz (KH) equation is adopted to describe the wave reflection on the rough surface; only one integral operation on the rough surface is needed, and the scattering from the object can be described by solving the electric field integral equation (EFIE) on the surface of the object. Moreover, according to scattering theory, the KH equation and the EFIE are coupled together (KH-EFIE) to describe wave propagation between the object and the rough surface. Then method of moments (MoM) is adopted to solve the KH-EFIE, and the current is obtained to calculate the scattering field. Finally, compared with other methods, the accuracy of the proposed approach is validated, and its efficiency is proved to be much higher than numerical solutions. Furthermore, by calculating the statistic composite radar cross-section (RCS) of the object/surface and the difference radar cross-section (DRCS) of the object, the influence of the rough surface root mean square (rms) height, the correlation length, the medium permittivity, the shape of the object, and the altitude of the object on the scattering characteristic is investigated.     

Efficient Solution to Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Under the theory structure of compressive sensing(CS),an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution(BOR),which will result in a small-scale impedance matrix.In the new linear equation system,the small-scale impedance matrix can be regarded as the measurement matrix in CS,while the excited vector is the measurement of unknown currents.Instead of solving dense full rank matrix equations by the iterative method,with suitable sparse representation,for unknown currents on the surface of BOR,the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations.Numerical results show that the proposed method can greatly improve the computational efficiency and can decrease memory consumed.     

Application of the singularity-subtraction technique to isotropic scattering in a planar layer

A numerical procedure for solving a singular Fredholm integral equation, which describes radiative transfer in an absorbing and isotropically scattering layer exposed to collimated radiation, is studied. The integral equation is solved by subtracting out the singularity and then approximating the integral term by a Gaussian quadrature. Bidirectional and hemispherical properties are found from the source function. Any arbitrary directional distribution of incident radiation can be handled by superimposing the collimated radiation case. In particular, the case of isotropic incident radiation is presented. The method gives accurate results, even for the extreme conditions of large optical thickness and large angle of incidence.     

一种基于压缩感知的三维导体目标电磁散射问题的快速求解方法

提出了一种将压缩感知和特征基函数结合的方法来计算三维导体目标的雷达散射截面.利用压缩感知理论,将随机选择的矩量法阻抗矩阵作为测量矩阵,将激励电压视为测量值,然后再用恢复算法可实现二维或二维半目标感应电流的求解.对于三维导体目标,使用Rao-Wilton-Glisson基函数表示的感应电流在常用的离散余弦变换基、小波基等稀疏基上不稀疏.为此,本文将计算出的目标特征基函数作为稀疏基,用广义正交匹配追踪算法作为恢复算法来加速恢复过程,并应用到三维导体目标的雷达散射截面计算中.数值结果证明了本文方法的准确性与高效性.     

Investigation on scattering from a plasma-coated target over a rough sea surface using a multi-hybrid method

An iterative strategy combining the Kirchhoff approximation (KA) with the hybrid finite element–boundary integral (FE-BI) method is presented to consider electromagnetic scattering from a coated target above a rough sea surface. The multi-hybrid method considers the multiple-scattering interactions between target and underlying surface based on equivalent principle and currents updating scheme. The hybrid FE-BI-KA method, which is an improved and generalized version of a previous KA–Method of Moments (MoM) technique, can deal with an inhomogeneous target. Numerical results are given to evaluate the validity of the multi-hybrid technique, and then the hybrid method is employed to investigate electromagnetic scattering from a plasma-coated airfoil above a rough sea surface, including the effects of several key parameters on stealth performance, such as plasma angular frequency and electron collision frequency.