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。     

TDEFIE的奇异性积分的精确快速计算

利用时域积分方程(TDIE)法模拟时域散射现象越来越受到学者们的关注.用于求解TDIE的时间步进(MOT)算法的后时不稳定性严重阻碍了TDIE法的广泛应用和发展.本文首先利用参数坐标和Duffy坐标变换将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.数值结果表明,该方法大幅提高了利用MOT算法求解TDE-FIE的MOT算法的后时稳定性和计算精度.     

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.     

高阶矩量法求解MFIE 时近奇异性提取*

采用高阶矩量法求解磁场积分方程时,相邻面片之间的互阻抗是一个难以算准的奇异性四重积分,因为内层面积分和外层面积分中同时包含有奇异性.本文对于内层的近奇异积分采用sinh (x)函数作积分变换,而对于外层的弱奇异性积分采用Duffy变换进行处理,使得被积式变成能够直接数值积分的连续光滑函数.数值结果表明该方法计算近奇异积分时精度远高于直接高斯积分方法,求得的雷达散射截面与电场积分方程所得的结果完全一致,验证了方法的准确性和有效性.     

非均匀介质结构中线天线辐射问题的有限元-边界积分方法

采用有限元边界积分方法,通过把所求解区域分成内外两部分,内场用有限元计算,外场用边界积分计算,分析了线天线辐射问题.边界积分采用伽略金方法处理,并用变换解决了积分方程的奇异性问题,最后给出了仿真结果.     

RWG 基伽略金矩量法自/ 互阻抗计算中两个关键问题的评述

为了快速获得RWG基伽略金矩量法自/互阻抗精确值,一般采用数值方法与解析技术相结合的求积策略。求积策略中的数值积分方法采用三角形高斯求积,而解析技术则普遍采用奇异值提取技术。针对这两个关键问题在应用过程中容易忽视的几个细节进行了评述,包括三角形高斯求积规则选取、求积公式应用条件以及奇异性积分被积函数改造等。采用新近提出的奇异性积分精确快速算法对自/互阻抗计算涉及的两类积分进行了推导计算,同时给出了场、源三角形完全重合和具有公共边两种情形下,采用常规奇异值提取技术和精确快速算法对这两类积分的计算结果。     

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.     

单环频率选择表面的传输系数分析

简要介绍了利用谱域伽略金法计算平面频率选择表面传输系数的方法。该方法以平面波谱展开和傅里叶变换为基础,在谱域中应用弗洛凯定理建立方程。采用屋顶基函数作为子域基函数表示感应电流,通过矩量法求解频率选择表面上的感应电流,进而求得传输系数。给出了某工程使用的单环频率选择表面的设计,计算结果与测试结果一致。     

用于平面多层介质结构的全波算法

提出一种平面多层介质带线结构的新型全波算法.该方法基于电场积分方程,由伽略金法求解相应的矩阵方程,从而容易获得表征电路特性的网络参数(如散射参数、导纳).以低温共烧陶瓷(LTCC)带通滤波器为数值算例,并采用Momentum仿真对比,结果表明该方法准确、速度快,可以大大提高格林函数的计算效率.     

Numerical evaluation of singular and near-singular potential Integrals

A simple and efficient numerical procedure using a singularity cancellation scheme is presented for evaluating singular and near-singular potential integrals with 1/R singularities. The procedure not only has several advantages over singularity subtraction methods, but also improves on some aspects of other singularity cancellation methods such as polar and Duffy transformations. A theoretical analysis is presented for triangles, quadrilaterals, tetrahedrons, bricks, and prisms, and numerical results are presented for triangles and prisms.     

Accurate and efficient numerical integration of weakly singular integrals in Galerkin EFIE solutions

A Galerkin descretization of the electric field integral equation for perfectly conducting surfaces using Rao-Wilton-Glisson (1982) basis functions requires the numerical evaluation of integrals with singular kernels over triangular regions. These singularities have been traditionally handled by utilizing a "singularity extraction" procedure to produce a regular integral and an analytic function to replace the original singular integral. A new approach is presented here in which the four-dimensional (4-D) weakly singular integrals unique to the Galerkin Rao-Wilton-Glisson electric field integral equation solution for perfectly conducting surfaces are transformed into integrals with regular integrands. The transformations allow some of the integrations to be performed analytically, in some cases reducing the original 4-D integral into a 1-D numerical integration. The accuracy and convergence properties of the new method are demonstrated by evaluating the scalar potential function over a unit triangle.     

An accurate approach for the calculation of MoM matrix elements

The method of moments solution on integral equations for electromagnetic scattering and radiation problems with Rao-Wilton-Glisson (RWG) and n/spl times/RWG basis functions requires the calculation of singular double surface integrals over triangular subdomains. In this paper, an approach is presented to deal with the singularity and almost singularity in which the triangle subdomain is divided into several subtriangles and then the singular or almost singular integral is calculated over each of the subtriangles. This approach is mainly based on the projection process and the local polar frame. It can be used to deal with the singular double surface integrals of order 1/R and 1/R/sup 2/, in which vector functions may be of zeroth-order and higher order. Numerical examples are provided to verify the validity of the method presented in this paper for dealing with the singularity and almost singularity.     

导体线面连接问题中奇异函数积分的计算

在线面连接问题中，电流展开函数包含体展开函数、线展开函数和连接点展开函数三类。求解电场积分方程的积分项是电流基函数及其散度分别与自由空间格林函数的乘积，由于连接点展开函数含有一个奇异点，所以被积函数中含有两个奇异点。本文通过积分变换消除了奇异点，并将二重积分化为一重积分，使计算精度得到提高。计算实例验证了本文方法的正确性。     

Computational cost estimations and comparisons for three methods of applied electromagnetics (MoM, MAS, MMAS)

The computational costs of three numerical techniques used in electromagnetics, namely the moment method (MoM), the method of auxiliary sources (MAS), and its modified version (MMAS), are estimated for various calculation schemes and configurations. Both surface and volumetric problems are considered. The number of multiplications required for the system-matrix fill is calculated and added to the algorithmic cost of the matrix inversion. The Green's function singularity extraction is also taken into account, particularly for the MoM. The original integrals are transformed into the local (area or volume) coordinate systems, and are subsequently evaluated on the basis of standard numerical quadrature schemes. For the surface integral equation (SIE), some calculations using either the well-known Duffy transformations or some analytical-numerical integration schemes are also presented (expressions are available only for the scalar potential integral case). For the MAS and MMAS, the matrix fill is shown to be much faster, since no time-consuming integrations are involved. The analysis is applied to various objects, such as a perfectly conducting (PEC) parallelpiped, a PEC sphere, and a microstrip patch antenna, and useful conclusions are drawn on the relative efficiency of the three methods.     

Evaluation and integration of the thin wire kernel

New approaches for numerically computing the thin wire kernel and wire potential integrals are presented. The singular behavior of the kernel integral is removed by transforming the integration variable to produce a smooth integrand. Subsequent integration of the kernel to obtain potential integrals uses quadrature schemes catering to its behavior. This technique allows standard algorithms for numerical quadrature to be used with updated integration weights that account for the transformed behavior, obviating the need for singularity subtraction techniques. The result is a procedure for evaluating the potential integrals that is independent of the basis functions.