MLFMA分析复杂载体平台上天线问题

该文分析了导体介质复合结构平台上线天线的辐射问题。利用等效原理建立EFIE-PMCHW表面积分方程组,定义线、面和连接基函数描述复杂结构上电流分布,分析了导体介质分界面处基函数的处理：利用多层快速多极子方法（MLFMA）21速迭代求解过程中的矩阵矢量相乘运算,并用于有耗媒质求解。MLFMA的运用极大地提高了求解实际电大问题的能力。数值计算结果验证了方法的正确性和高效性。     

MLFMA分析复杂载体平台上天线问题

该文分析了导体介质复合结构平台上线天线的辐射问题。利用等效原理建立EFIE-PMCHW表面积分方程组,定义线、面和连接基函数描述复杂结构上电流分布,分析了导体介质分界面处基函数的处理;利用多层快速多极子方法(MLFMA)加速迭代求解过程中的矩阵矢量相乘运算,并用于有耗媒质求解。MLFMA的运用极大地提高了求解实际电大问题的能力。数值计算结果验证了方法的正确性和高效性。     

基于多层快速多极子算法分析平面多层结构

由于多层平面结构空域闭式格林函数难以用加法定理展开,因此,将多层快速多极子算法推广到该类问题的分析存在一定困难.采用二级离散复镜像技术,获得了多层介质空域格林函数,通过对其表达形式做简单的改写,提出针对多层平面结构的多层快速多极子算法,详细讨论了加法定理展开条件对离散复镜像系数的影响及处理办法.数值算例验证了本文方法的准确性和有效性.     

三维导体介质复合结构电磁辐射与散射的MLFMA分析

利用多层快速多极子方法(MLFMA)分析三维导体介质复合结构的电磁辐射与散射特性.根据等效原理,介质表面构造Poggio-Miller-Chang-Harrington-Wu(PMCHW)方程,导体表面建立电场积分方程(EFIE).分析了含介质目标MLFMA算法中远区组矩阵矢量相乘运算以及有耗媒质空间中格林函数的平面波展开.利用该方法研究了涂敷目标电磁散射特性以及天线罩对直线阵天线辐射特性的影响.MLFMA的应用降低了计算量和存储量,实现了对电大尺寸目标快速、准确的求解.     

基于固定实镜像平面波展开的快速多极子方法计算微带结构问题

将快速多极子算法应用于微带结构的一个关键技术是将矩量法中描述远区单元相互作用的Green函数用加法定理进行平面波展开.本文提出用固定实镜像方法拟合微带结构谱域Green函数进行平面波展开,对比目前常用的复镜像闭式平面波展开方法,该方法具有展开收敛性好,物理概念清晰,Green函数宽频插值方便等特点.计算实例表明了该方法的有效性和可靠性.     

三维导电目标电磁散射的高阶多层快速多极子方法

为进一步提高电大尺寸目标散射求解能力,采用了基于多层快速多极子方法的高阶方法.与低阶相比,该方法所需未知量数目大大减少,而计算精度不变,因而具有比传统多层快速多极子方法更高的计算效率.给出的典型计算结果充分说明了高阶多层快速多极子方法的高效性.     

基于多层快速多极子方法的三维目标RCS高效数值求解技术

随着工程应用的不断深入,复杂三维目标雷达截面积(RCS)的高效计算越来越受关注.本文介绍了我们所发展的基于多层快速多极子方法的几种高效数值方法:后期近似迭代多层快速多极子方法、自适应射线传播多层快速多极子方法、快速远场近似多层快速多极子方法、高阶多层快速多极子方法.作为数值方法,这些方法通用性强,适于任意形状目标RCS·计算.它们不仅具有很好的计算精度,也具有优良的计算性能.对于未知量数目为N的三维电磁散射,计算量为O(NlogN)量级,存储量为O(N)量级,特别适合求解复杂三维目标RCS,有望在将来的雷达工程领域得到更深入的应用.     

三维电大目标散射求解的多层快速多极子方法

为进一步提高对电大尺寸目标散射求解的能力,详细研究了多层快速多极子方法.重点设计了用于多层快速多极子方法的各种优化方法包括Morton编号、转移因子修正内插技术与外向波重复存储策略.对于未知量数目为N的三维电磁散射,数值实验显示多层快速多极子方法具有O(NlogN)量级的计算量、O(N)量级的存储量,特别适合求解三维电大尺寸目标的电磁散射.利用该方法在单机(内存1Gb)上成功计算了未知量为25万的电大尺寸目标散射.     

多层低频快速多极子算法分析电磁散射问题

主要研究了低频条件下目标的散射问题,详细给出了基于Loop-Tree矩量法的多层低频快速多极子方法基本原理。通过对自由空间格林函数进行多极子展开,避免了传统快速多极子方法通过平面波展开格林函数遇到的低频崩溃问题。改进的对角预条件技术显著地减少了预条件矩阵的构造时间和矩阵的迭代求解时间。数值算例证明了算法的有效性。     

曲面共形阵列结构快速数值分析方法

针对曲面共形阵列结构电磁散射特性的高效、精确仿真分析需求,提出了一种并行综合函数矩量法处理方案.该方法是传统电磁经典数值算法——矩量法的一种改进形式,通过几何区域分解处理和综合基函数的方式极大降低了算法的内存消耗,使得单机分析电大尺寸问题和大规模阵列问题成为可能.更为重要的是,针对周期阵列结构,该方法具备综合函数复用特性和多区域并行处理特性,能够大大提高算法的综合处理效率.一个6×11的柱面共形贴片阵列被用于验证所提方法的性能,仿真结果表明,对于周期阵列结构,该方法的计算精度与多层快速多极子算法相当,虽然计算效率略低于多层快速多极子方法,但内存消耗比多层快速多极子方法低一个数量级.     

Fast multipole method for scattering from an arbitrary PEC targetabove or buried in a lossy half space

The fast multipole method (FMM) was originally developed for perfect electric conductors (PECs) in free space, through exploitation of the spectral properties of the free-space Green's function. In the work reported here, the FMM is modified, for scattering from an arbitrary three-dimensional (3-D) PEC target above or buried in a lossy half space. The “near” terms in the FMM are handled via the original method-of-moments (MoM) analysis, wherein the half-space Green's function is evaluated efficiently and rigorously through application of the method of complex images. The “far” FMM interactions, which employ a clustering of expansion and testing functions, utilize an approximation to the Green's function dyadic via real image sources and far-field reflection dyadics. The half-space FMM algorithm is validated through comparison with results computed via a rigorous MoM analysis. Further, a detailed comparison is performed on the memory and computational requirements of the MoM and FMM algorithms for a target in the vicinity of a half-space interface     

Short-pulse plane-wave scattering from buried perfectly conductingbodies of revolution

The method of moments is used to analyze short-pulse plane-wave scattering from perfectly conducting bodies of revolution buried in a lossy, dispersive half space. The analysis is performed in the frequency domain, with the time-domain fields synthesized via Fourier transform. To make this analysis efficient, the method of complex images is used to compute the frequency-dependent components of the half-space dyadic Green's function. Results are presented for short-pulse scattering from buried spheres and cylinders, using measured frequency-dependent soil parameters (permittivity and conductivity)     

一种新型针对快速多极子法(FMM)的预条件技术

提出了一种针对FMM近场作用矩阵块的不完全LU预条件方法。和传统单纯依靠填充参数来控制非零元素个数的ILU分解方法相比，该方法由于引入了数值丢弃阈值，因而可获得性能更好的预条件矩阵。利用该项预条件技术，迭代过程变得更健壮，而且收敛也更快，计算花费的时间也更少。数值实验表明：这种基于双丢弃准则的ILUT预条件技术，是一种非常适合FMM计算的预条件处理方法。     

Multilevel fast multipole algorithm for general targets on a half-space interface

The multilevel fast multipole algorithm (MLFMA) is considered for scattering from an electrically large conducting or dielectric target resting on the interface of a dielectric half-space. We focus on analysis of the half-space Green's function such that it is computed efficiently and accurately, while retaining a form that is applicable to an MLFMA analysis. Attention is also directed toward development of a simple preconditioner to accelerate convergence of the conjugate-gradient solver. The utility of the model is examined for several applications, including scattering from an electrically large vehicle, trees, and rough dielectric interfaces in the presence of a dielectric half-space background.     

Electromagnetic analysis of an antenna embedded in a compositeenvironment

This paper addresses the problem of an antenna embedded in a hole dug in the ground. The composite medium configuration consists of a half-space dielectric (representing the Earth-air interface) containing a cylindrical hole filled with a different dielectric medium. The wire antenna resides within this hole, on the axis. The solution strategy is based on decomposing the problem into simpler subproblems, which are treated sequentially. First we calculate a numerical dyadic Green's function for the composite medium by solving an integral equation formulated over a background consisting of the unperturbed dielectric half space (for which the Green's functions are known in a spectral integral form). This integral equation is solved via the fictitious currents method, which is a special case of the method of moments. We then solve the integral equation for the antenna currents using this numerical Green's function and determine the input impedance and radiation pattern     

Error analysis for the truncation of multipole expansion of vectorGreen's functions [EM scattering]

One of the most important mathematical formulas in fast multipole algorithms (FMA) is the addition theorem. In the numerical implementation of the addition theorem, the infinite series should be truncated. In this paper, the number of terms needed for the scalar Green's function is derived, and the error analysis for the truncation error in the multipole expansion of the vector Green's functions is given. We have found that the error term in vector Green's functions is proportional to 1/R. If the scalar Green's function is truncated at the L-th term and the relative error is ϵ, then the relative error in the dyadic Green's function is ϵ/4, if it is truncated at the (L+2)-th term. For the vector Green's function related to MFIE, the relative error is ϵ/2 if it is truncated at the (L+1)-th term     

Wide-band electromagnetic scattering from a dielectric BOR buriedin a layered lossy dispersive medium

A method of moments (MoM) analysis is developed for electromagnetic scattering from a dielectric body of revolution (BOR) embedded in a layered medium (the half-space problem constituting a special case). The layered-medium parameters can be lossy and dispersive, of interest for simulating soil. To make such an analysis tractable for the wide-band (short-pulse) applications of interest here, we have employed the method of complex images to evaluate the Sommerfeld integrals characteristic of the dyadic layered-medium Green's function. Example wide-band scattering results are presented, wherein fundamental wave phenomenology is elucidated. Of particular interest, we consider wide-band scattering from a model plastic mine, buried in soil, with the soil covered by a layer of snow     

Scale Model Experimental Validation and Calibration of the Half-Space Green's Function Born Approximation Model Applied to Cross-Well Radar Sensing

Efficient forward models that describe the physical nature of the geophysical problem are desired for subsurface sensing and reconstruction of a contrasting contaminant pool volume. An analytical model to approximate sensing with radar is developed and implemented in the frequency domain in terms of the half-space lossy dyadic Green's function. The Born approximation is employed as a linear forward model, which will eventually be used for tomographic inversion for object detection. The forward model is compared with measurements generated by a cross-well radar (CWR) experiment in a controlled soil test tank using broadband borehole antennas. Soil parameter (dielectric constant and loss tangent) variance with frequency is represented by a quadratic polynomial. Calibration for soil parameters is performed via CWR data using an iterative nonlinear parameterized inversion technique. With the appropriate calibration, good agreement is obtained with wideband experimental measurements for several different borehole antenna placements, confirming the accuracy of the model.     

A numerical formulation of dyadic Green's functions for planarbianisotropic media with application to printed transmission lines

An integral equation (IE) method with numerical solution is presented to determine the complete Green's dyadic for planar bianisotropic media. This method follows directly from the linearity of Maxwell's equations upon applying the volume equivalence principle for general linear media. The Green's function components are determined by the solution of two coupled one-dimensional IE's, with the regular part determined numerically and the depolarizing dyad contribution determined analytically. This method is appropriate for generating Green's functions for the computation of guided-wave propagation characteristics of conducting transmission lines and dielectric waveguides. The formulation is relatively simple, with the kernels of the IE's to be solved involving only linear combinations of Green's functions for an isotropic half-space. This method is verified by examining various results for microstrip transmission lines with electrically and magnetically anisotropic substrates, nonreciprocal ferrite superstrates, and chiral substrates. New results are presented for microstrip embedded in chiroferrite media     

Dyadic Green's function of multilayer cylindrical closed and sector-structures for waveguide, microstrip-antenna, and network analysis

A clear and systematic method to derive the spectral- and space-domain dyadic Green's function of arbitrary cylindrical multilayer and multiconductor structures is proposed. The derivation is either done for a circumferentially closed or a cylindrical sector structure, which is bounded by electric or magnetic walls in an azimuthal direction. The solution for the dyadic Green's function in the spectral domain is obtained via an equivalent circuit. Relations between the spectral and space domains for the dyadic Green's functions are derived using eigensolution expansions. Finally, the dyadic Green's function is applied to the problem of finding the propagation constants of the two-layer dielectric rod.