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.     

利用时间步进算法精确稳定求解时域积分方程

 时域阻抗矩阵元素的计算需要分别计算场单元和源单元上的空时积分,由于时间基函数的分域性以及时间基函数(如三角型时间基函数)导数的不连续性,使得采用高斯积分方法计算源单元上空时积分的计算精度较差且误差随着时间步长的减小而增大.本文通过将源单元上空时积分转变成为1D时间卷积分和1D空间解析积分来精确计算时域阻抗矩阵元素,并在此基础上利用时间步进算法求解了时域电场、磁场和混合场积分方程.通过计算实例表明该方法在较大的时间步长取值范围内均能确保时域积分方程时间步进算法求解的精度和后时稳定性.     

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.     

时域积分方程MOT算法的推迟位时间卷积数值积分新方法

通过变量代换平滑三角形上推迟位（标量位函数和矢量位函数）并消除推迟矢量位旋度的奇异性,使得采用数值积分法就能够精确快速地计算任意正则时间基函数与推迟位函数及推迟矢量位旋度之间的时间卷积运算,可用于基于任意类型时间基函数的时域电场、时域磁场及其混合场积分方程时间步进（MOT ）算法。与时间卷积运算的解析法对比分析表明,该时间卷积数值积分方法能够精确快速地计算基于任意类型时间基函数和不同时间步长条件下时域积分方程MOT算法的阻抗矩阵元素;而具体的计算实例也表明,阻抗矩阵的精确计算显著地提升了时域积分方程MOT算法的后时稳定性和求解精度。     

导体目标瞬态电磁散射的时空矩量法研究

时域积分方程的矩量法是求解瞬态电磁散射的方法之一。研究了基于加权Lagurre函数和RWG基函数分别作为时间、空间基函数的时空矩量法,给出了时域磁场积分方程时空矩量法的全部计算公式,编制了相应串行和并行计算程序。计算结果表明：该方法具有很好的时域稳定特性,为宽带电磁散射分析提供了可能,同时也指出了其应用的局限性,为改进其方法提供了参考。     

GPU加速混合场积分方程求解导体目标散射问题

利用图形处理单元（GPU）加速混合场积分方程（CFIE）分析导体目标电磁散射问题。较电场积分方程（EFIE）和磁场积分方程（MFIE）,CFIE消除了内谐振问题,并且具有更好的条件数。求解的数值方法为基于 RWG基函数的矩量法（MoM）。所有计算步骤均在 GPU上实现,包括：阻抗元素填充、电压向量填充、矩阵方程的共轭梯度（CG）求解、雷达散射截面（RCS）计算。在保证数值精确度的前提下获得了数十倍的速度提升。     

求解电小尺寸目标散射特性的时域磁场积分方程

在计算电大尺寸光滑目标散射问题时,通常采用的时域磁场积分方程计算简单、快速、准确;但是当处理电小尺寸目标时,通常的磁场积分方程不再准确,必须精确考虑磁场积分方程中包含的立体角信息.通过在测试三角形区域进行特殊的采样,并充分计算测试区的立体角,修正了时域磁场积分方程以满足电小目标散射计算的需求.计算结果与时域电场积分方程的结果相一致,说明了方法的有效性.     

介质散射的双线性高阶叠层基函数矩量法分析

提出了一种基于双线性思想的高阶基函数降低矩量法分析介质目标电磁散射问题时的未知量.论文给出了双线性高阶叠层基函数的构造过程, 并将其应用于介质的面积分方程分析中.数值算例比较了不同阶数时所需未知量以及计算精度, 表明该高阶叠层基函数在满足相同积分方程的计算精度时能比低阶基函数节省未知量.     

双位积分方程在分析地面上线天线中的应用

导出了任意取向线天线在基于sommerfeld积分的反射系数近似条件下的双位积分方程,采用多项式基函数和点匹配的矩量法对该方程求解,给出阻抗元素计算的一般表达式.计算结果表明了该方法的有效性.     

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.     

On the testing of the magnetic field integral equation with RWGbasis functions in method of moments

For electromagnetic analysis using method of moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor Ω₀ equal to the solid angle external to the surface at the testing points, which is 2π everywhere on the surface of the object, except at the edges or tips that constitute a set of zero measure. However, the standard formulation of the MFIE with Ω₀=2π leads to inaccurate results for electrically small sharp-edged objects. This paper presents a correction to the Ω₀ factor that, using Galerkin testing in the MFIE, gives accuracy comparable to the electric field integral equation (EFIE), which behaves very well for small sharp-edged objects and can be taken as a reference     

Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects

We present a novel method of moments (MoM)-magnetic field integral equation (MFIE) discretization that performs closely to the MoM-EFIE in the electromagnetic analysis of moderately small objects. This new MoM-MFIE discretization makes use of a new set of basis functions that we name monopolar Rao-Wilton-Glisson (RWG) and are derived from the RWG basis functions. We show for a wide variety of small objects -curved and sharp-edged-that the new monopolar MoM-MFIE formulation outperforms the conventional MoM-MFIE with RWG basis functions.     

Linear-Linear Basis Functions for MLFMA Solutions of Magnetic-Field and Combined-Field Integral Equations

We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can be mitigated by using the LL functions for discretization. This is achieved without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions     

Observed Baseline Convergence Rates and Superconvergence in the Scattering Cross Section Obtained From Numerical Solutions of the MFIE

The scattering cross section data obtained from numerical solutions of the magnetic field integral equation (MFIE), using a variety of basis functions and both Galerkin and non-Galerkin testing schemes, are compared to study the convergence rates of the results. For the basis functions considered, apparent superconvergence is observed in the MFIE scattering cross section when linear tangential/linear normal vector basis functions are used with Galerkin testing, but not with other basis functions.      

Improved testing of the magnetic-Field integral equation

An improved implementation of the magnetic-field integral equation (MFIE) is presented in order to eliminate some of the restrictions on the testing integral due to the singularities. Galerkin solution of the MFIE by the method of moments employing piecewise linear Rao-Wilton-Glisson basis and testing functions on planar triangulations of arbitrary surfaces is considered. In addition to demonstrating the ability to sample the testing integrals on the singular edges, a key integral is rederived not only to obtain accurate results, but to manifest the implicit solid-angle dependence of the MFIE as well.     

On the discretization of the integral equation describingscattering by rough conducting surfaces

Numerical simulations of scattering from one-dimensional (1-D) randomly rough surfaces with Pierson-Moskowitz (P-M) spectra show that if the kernel (or propagator) matrix with zeros on its diagonal is used in the discretized magnetic field integral equation (MFIE), the results exhibit an excessive sensitivity to the current sampling interval, especially for backscattering at low-grazing angles (LGAs). Though the numerical results reported in this paper were obtained using the method of ordered multiple interactions (MOMI), a similar sampling interval sensitivity has been observed when a standard method of moments (MoM) technique is used to solve the MFIE. A subsequent analysis shows that the root of the problem lies in the correct discretization of the MFIE kernel. We found that the inclusion of terms proportional to the surface curvature (regarded by some authors as an additional correction) in the diagonal of the kernel matrix virtually eliminates this sampling sensitivity effect. By reviewing the discretization procedure for MFIE we show that these curvature terms indeed must be included in the diagonal in order for the propagator matrix to be represented properly. The recommended current sampling interval for scattering calculations with P-M surfaces is also given     

Contamination of the Accuracy of the Combined-Field Integral Equation With the Discretization Error of the Magnetic-Field Integral Equation

We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary.     

High-order numerical solutions of the MFIE for the linear dipole

The magnetic field integral equation (MFIE) was applied to a dipole using three different discretization methods and high-order basis functions. For moderate-order, and higher, basis functions it was found that the different discretization methods produced essentially the same results. Continuity of current and its first derivative was observed at cell boundaries even though continuity of current was not explicitly enforced there. The MFIE provided lower condition numbers than the Hallen equation over the range of dipole radii examined. In close proximity to surface discontinuities, including hidden ones, residual errors could not be significantly reduced by increasing the order of the basis functions, implying the need for better modeling at discontinuities and calling into question the use of faceting to represent curved surfaces.     

The use of curl-conforming basis functions for the magnetic-field integral equation

Divergence-conforming Rao-Wilton-Glisson (RWG) functions are commonly used in integral-equation formulations to model the surface current distributions on planar triangulations. In this paper, a novel implementation of the magnetic-field integral equation (MFIE) employing the curl-conforming n~/spl times/RWG basis and testing functions is introduced for improved current modelling. Implementation details are outlined in the contexts of the method of moments, the fast multipole method, and the multilevel fast multipole algorithm. Based on the examples of electromagnetic modelling of conducting scatterers, it is demonstrated that significant improvement in the accuracy of the MFIE can be obtained by using the curl-conforming n~/spl times/RWG functions.