高阶矢量基函数在腔体本征值问题中的应用

基于四面体有限单元,采用高阶叠层矢量基函数分析腔体本征值问题,通过若干数值算例验证了在相同计算精度指标下,采用高阶基可以使用尺寸更大的网格,降低未知量个数,提高计算效率;并且通过加密网格,高阶基能够更快地收敛到真解。     

高阶叠层渐近相位基函数结合快速多级子分析电大物体散射特性

由入射波与面电流的关系,引出了渐近相位(AP)在高阶叠层基函数(HO-RWG)中的应用,并运用到矩量法(MOM)中,与快速多级子方法(MLFMA)结合,分析了电大尺寸复杂目标的电磁散射特性。与高阶叠层基函数和零阶相位基函数(AP-CRWG)相比,在相同的计算精度下,都可以大大减少未知量数量,从而可以节省大量内存和计算时间。计算实例表明,该方法有较高的精确性和有效性。     

基于高阶叠层基函数的加速迭代求解方法

研究了高阶叠层矢量基函数的尺度因子对迭代法求解矩阵方程收敛性的影响,选择了可以有效降低矩阵条件数的尺度因子;在此基础上,详细阐述了求解基于高阶叠层矢量基函数阻抗矩阵方程的叠层共轭梯度方法(HCGM),并从理论上分析了叠层共轭梯度算法的收敛性能.通过计算实例表明,与共轭梯度方法(CGM)相比.使用HCGM可以大幅度减少矩阵方程的迭代求解时间.     

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.     

矩量法中阻抗矩阵的稀疏化研究

将高阶叠层矢量基函数及最大正交高阶矢量基函数应用于电磁场积分方程方法,提出将阻抗矩阵按稀疏阵处理的方法.通过文中的处理,使得存储阻抗矩阵的内存需求量和求解矩阵方程的迭代求解时间大为降低.本文还结合适当算例,分析了判断门限的选取对阻抗矩阵的存储量与迭代法求解的计算量的影响.     

介质目标电磁散射特性的多层特征基函数法分析

特征基函数法是近几年提出的一种基于分块和高阶基函数概念求解电磁散射问题的快速算法.为了更有效地分析电大尺寸多目标的电磁散射问题,将基于Foldy-Lax多径散射方程的特征基函数法扩展为多层特征基函数法,通过对子域进行多层划分来控制生成矩阵维数的大小和计算精度.应用多层特征基函数法计算了介质目标的远区散射场,数值结果与传统特征基函数法的计算结果吻合良好,且计算效率明显提高.     

一种高阶矩量法迭代求解的预处理技术

频域高阶矩量法越来越多地用于求解目标散射问题.但高阶矩量法得到的矩阵方程中,系数矩阵条件数较差,并且一般为非对角占优阵,通常用计算效率较低的直接方法求解.本文针对叠层高阶基函数的特点,提出了一种函数空间域分解的加性Schwarz预处理技术.通过数值计算,给出了最优分解方案,并数值验证了预处理技术的有效性.     

用高阶叠层矢量有限元法计算随钻测井的三维电磁响应

用矢量有限元方法对随钻测井的三维地层电磁响应进行了数值仿真。为了提高随钻测井响应的计算效率和精度,采用了高阶叠层矢量基函数,根据场变化快慢的情况,在不同的剖分单元和同一单元的不同方向采用了不同阶数的基函数,有助于减少剖分网格和未知量。采用了基于圆柱坐标下六面体剖分,从而提高了发射、接收线圈、钻铤和井眼边界的几何建模精度。用解析法和数值模式匹配法对有限元计算的结果进行了验证,显示了非常好的吻合,最后仿真了地层倾角对随钻测井响应的影响。     

基于特征基函数法的一维理想导体粗糙海面电磁散射快速算法研究

针对传统矩量法在处理具有较多未知量的理想导体粗糙海面电磁散射问题时对计算机内存的需求过大, 耗时过长的缺陷, 文中引入了特征基函数法, 并根据Foldy-Lax多径散射方程构造特征基函数, 首先只考虑离散子域本身的自相互作用构造主要特征基函数, 然后考虑各离散子域间的互耦效应构造次要特征基函数, 最后由主要特征基函数和次要特征基函数的加权叠加构造特征基函数.通过与传统矩量法仿真结果的对比, 讨论了不同次要特征基函数的阶数或不同离散子域的个数对计算精度和计算效率的影响.仿真结果表明了本文所采用的算法能够在保证计算精度的前提下, 减少计算时间, 并能够通过离散子域尺寸的选取控制实际操作矩阵的维数.     

高阶四面体矢量元的实现与性能比较

以H1(curl)四面体插值矢最元为例,基于基函数分类和单元矩阵分块技术,完整地给出了高阶矢量元单元矩阵的计算公式,显式给出了积分系数矩阵的计算结果.通过分析一个矩形谐振腔,系统比较了各种矢量元的性能(如计算精度、条件数、面元选择性等),并将其用于分析不均匀腔体的谐振问题.分析方法可有效地推广到任意形式的更高阶、叠层基的分析.     

A nonlinear estimation method in tomographic imaging

A nonlinear estimation approach to solving the inverse scattering problem, and reconstructing the space-varying complex permittivity of unknown objects is considered. The bilinear operator equations governing the scattering are approximated into finite dimensional spaces on the basis of the finite degrees of freedom of data, and on the simple concept that one cannot expect to reconstruct an arbitrary function from a finite number of independent equations. As a consequence, a discrete model, well suited to numerical inversion, is developed. The particular bilinear nature of the equations, and a suitable choice of contrast and field unknowns allows the functional adopted in the estimation to be minimized in an accurate and numerically efficient manner. Numerical experiments show how the method is capable, when a proper number of searched unknowns is adopted, to manage the possible convergence to local minima (which is a typical question in nonlinear inverse problems), and validate the effectiveness of the proposed approach     

An improved MoM model for line-fed patch antennas and printed circuits

In this paper, an improved model is proposed to analyze the edge-connected line-fed patch antennas and printed circuits based on the method of moments (MoM), where the number of unknowns can be significantly reduced using simplified meshes. In the presented model, three types of basis functions are used to describe the currents on the antenna patch and circuit, the feedline and the feedline-patch junction. A new feedline-patch junction basis function is proposed based on the conventional wire-surface junction basis function. Numerical results are given to illustrate the accuracy and efficiency of the improved MoM model.     

The Implementation of Multilevel Green's Function Interpolation Method for Full-Wave Electromagnetic Problems

We extend the multilevel Green's function interpolation method (MLGFIM) developed for quasi-electrostatic problems to full-wave simulations. The difficulty in applying the interpolation approach lies in the additional rapidly changing phase term associated with the full-wave Green's functions. To enhance the efficiency and accuracy of the full-wave Green's function interpolation, a scattered point set consisting of two staggered Tartan grids in conjunction with radial basis function interpolation is employed. To further reduce the computational complexity, the QR factorization technique is applied to compress the low rank Green's function matrices. For electromagnetic scattering from PEC spheres up to a diameter of eight wavelengths, the proposed method compares well with Mie's scattering in accuracy and shows the O(NlogN) efficiency. As the method is "kernel independent", its extension to structures in layered medium is straightforward. In the numerical simulations of finite microstrip patch arrays up to 11 by 11 elements, the proposed method demonstrates very favorable dependencies of CPU time and memory storage requirement versus the number of unknowns     

Problem-matched basis functions for microstrip coupled slot arrays based on transmission line Green's functions (TLGF)

Problem matched basis functions are proposed for the method of moments analysis of printed slot coupled microstrips. The appropriate equivalent currents of the integral equation kernel are represented in terms of two sets of entire domain basis functions. These functions synthesize on one hand the resonant behavior of slots, microstrips or dipoles and on the other hand the field in proximity of the feeding source and of the discontinuities. In order to define these basis functions, canonical geometries are identified, whose Green's functions have been found in semi-analytical form. The accuracy and the effectiveness of the method in terms of convergence rate and number of unknowns is demonstrated by comparison with a standard fine meshing full-wave analysis. The method is extremely convenient for large arrays, where the subwavelength details should be treated together with large global dimensions. Since the proposed solution is independent of the dimensions of these details, it provides dramatic reduction of the number of unknowns and improvement of condition number.     

电磁散射与辐射问题中的混合基函数矩量法

三维散射与辐射问题通常采用电场积分方程(EFIE)结合矩量法(MoM)求解，而基函数是决定矩量法精度和效率的重要因素。本文针对采用三角形网格剖分会引起未知元过多而采用四边形网格剖分会因为网格质量变差而影响计算精度的问题，提出一种基于三角形与四边形混合网格的混合基函数，应用于散射体RCS和天线阻抗特性计算。结果表明，相比于三角形剖分，混合基函数能够在减少未知元个数的同时获得较高的精度；另外也解决了基于单纯四边形网格的基函数在网格质量较差的情况下不能准确模拟表面电荷的问题。     

Acceleration of Fast Multipole Method for Large-Scale Periodic Structures With Finite Sizes Using Sub-Entire-Domain Basis Functions

An acceleration technique to the fast multipole method (FMM) has been proposed to handle large-scale problems of periodic structures in free space with finite sizes based on the accurate sub-entire-domain basis functions. In the proposed algorithm, only nine (or 27) elements in the whole impedance matrix are required to be computed and stored for a two-dimensional (or three-dimensional) periodic structure, and the matrix-vector multiply can be performed efficiently using the combination of fast Fourier transform and FMM. The theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of O(N) with small constants, where N is the total number of unknowns     

复杂目标降维建模方法及其在电磁散射中的应用

任何金属目标结构都可以看作由若干相互连接的平板或弯板所组成,采用若干双线性表面面元来拟合实际目标表面,将目标表面的三维坐标降为双线性表面的二维坐标,从而使得目标表面电流的三个分量简化为双线性表面的二个分量;根据提出的混合域基函数,采用矩量法对目标模型的电磁散射特性进行分析计算.计算结果表明,此方法可以降低对计算机的内存需求,并有利于电磁散射问题的计算机快速求解.     

Method of moments enhancement technique for the analysis of Sierpinski pre-fractal antennas

The numerical analysis of highly iterated Sierpinski microstrip patch antennas by the method of moments (MoM) involves many tiny subdomain basis functions, resulting in a very large number of unknowns. The Sierpinski pre-fractal can be defined by an iterated function system (IFS). As a consequence, the geometry has a multilevel structure with many equal subdomains. This property, together with a multilevel matrix decomposition algorithm (MLMDA) implementation in which the MLMDA blocks are equal to the IFS generating shape, is used to reduce the computational cost of the frequency analysis of a Sierpinski based structure.     

Marching-on-in-Degree Based Time-Domain Magnetic Field Integral Equation Method for Bodies of Revolution

A marching-on-in-degree (MOD) based time-domain magnetic field integral equation method for bodies of revolution (BOR) is proposed and applied to obtain the induced currents on perfectly electric conducting BOR. Before this work, the time-domain integral equation method for BOR based on a marching-on-in-time procedure cannot really reduce the computational cost, since the number of unknowns cannot really be reduced. But it is the unknown reduction that serves as the key point of cost saving in BOR-problems. The method implemented in this letter can really utilize the symmetric property of BOR by applying two sets of entire domain basis functions. One is a set of scaled Laguerre polynomials inherited from common MOD method and used as temporal basis functions. The other is a Fourier series which comes from frequency domain method for solving BOR-problems. The validity, efficiency, and stability of the method are verified by several numerical examples.