Fast Solution of Scattering From Conducting Structures by Local MLFMA Based on Improved Electric Field Integral Equation

In this paper, a local multilevel fast multipole algorithm (LMLFMA) based on an improved electric field integral equation (IEFIE) is developed to achieve fast and efficient solution of electromagnetic scattering from 3-D conducting structures. The IEFIE is used to reduce iteration number, and LMLFMA is applied to further accelerate the computation of matrix-vector multiplications in iteration, in which only the local interactions between subscatterers are taken into account. Numerical results show that the present method attains faster iterative convergence than traditional EFIE and less computational cost than MLFMA. The speedup can achieve at least 4–5 times while keeping an rms error of less than 2 dB.      

A Regularized Combined Field Integral Equation for Scattering from 2-D Perfect Electrically Conducting Objects

A novel regularized combined field integral equation pertinent to the analysis of scattering from 2-D perfect electrically conducting objects is presented. The equation is immune from ill-conditioning due to dense spatial discretizations and appears free from internal resonances. The regularization is achieved via analytical inversion of the hypersingular part of the combined field integral equation, without negative repercussions on computational complexity. Numerical results are presented that show the effectiveness of the proposed formulation.     

高效求解任意非常规目标电磁散射的修正电场积分方程方法

本文研究了一种可以高效求解任意非常规目标电磁散射的修正电场积分方程方法.借助磁场积分方程主值项的提取,加入到传统电场积分方程中,将传统的一次迭代求解过程转变成逐渐逼近真解的内外两层迭代.其外层迭代不断刷新电流,最终得到精确解.加入磁场主值项的修正电场积分方程显著降低了条件数,同时保留了原电场积分方程普适性强,可用于处理任意非常规目标的优点.对于每一外层迭代步中电流的求解,本文采用了加速矩阵矢量相乘的多层快速非均匀平面波算法,形成高效的内层迭代求解.数值结果表明,该方法在保证精度的同时,可以显著降低问题的求解时间.     

混合场积分方程结合MLFMA分析导体介质复合目标电磁散射问题

针对组合目标电磁散射问题,采用一类新的混合场积分方程进行分析.通过合理选择比例系数组合表面电场和磁场积分方程,构造出具有良好收敛性的阻抗矩阵.MLFMA的迭代求解采用广义最小残差方法(GMRES),结合预条件技术进一步减少迭代次数,加速计算并提高处理电大尺寸导体介质复合目标的能力.研究了几类典型目标电磁散射特性并比较了计算效率,数值算例验证了该方法的准确性和高效性.     

一种改进稳定性的时域电场积分方程法

研究了时域电场积分方程隐式MOT算法中时间基函数对其稳定性的影响,由理论分析和数值结果得出了选用高频分量较少的时间基函数不利于隐式MOT算法稳定性的结论.在此基础上,将一种多项式时间基函数与新的时间平均方法相结合,提出了一种改进稳定性的隐式MOT算法,计算实例表明比先五步后三步平均法更加精确,比以前的隐式MOT算法更加稳定.     

基于时域混合场积分方程求解目标瞬态散射特性

当入射平面波的频谱包含目标的谐振频点时,时域电场积分方程和时域磁场积分方程求解的表面电流不稳定,会出现后期震荡现象。通过线性组合时域电场积分方程和时域磁场积分方程,可以获得一种混合场积分方程。数值结果显示,这种混合场积分方程消除了因内部谐振引起的后期震荡,得到了稳定的表面电流分布和远区散射场。     

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.     

High-Order Discrete Helmholtz Decompositions for the Electric Field Integral Equation

We develop a differential form based formalism to address the problem of low-frequency breakdown of the electric field integral equation (EFIE). Note, in this formalism we approximate the surface magnetic field, not the surface current as is conventionally the case. A discrete Helmholtz decomposition is achieved for both triangular and quadrilateral curvilinear meshes based on a star-cotree decomposition. These decompositions are based upon the construction of a canonical basis which ab-initio possess the required separation into irrotational and nonirrotational spaces. This makes the process of construction clear and generally applicable. The construction of appropriate bases is demonstrated for a range of interpolation orders. The effects of these constructions is demonstrated on a simple flat PEC plate problem     

Efficient 2-D Integral Equation Approach for the Analysis of Power Bus Structures With Arbitrary Shape

A 2-D contour integral-equation method for the frequency-domain analysis of arbitrarily shaped power bus structures is presented. The numerically efficient approach allows the rapid and accurate computation of the frequency-dependent transfer parameters between an arbitrary number of ports, as required for embedding the power plane structure into network simulation. A formulation is developed for calculating the voltage distribution between the planes, as well as for determining the resulting radiated fields based on the field-equivalence principle. The method is applied for several test boards including a populated board with a surface-mount decoupling-capacitor network. The suggested approach is well confirmed by an analytical solution for the rectangular structure, by measurement and 3-D full-wave simulation results.      

Full-Periphery Surface Impedance for Skin-Effect Approximation in Electric Field Integral Equation

A new surface impedance model for RL-extraction in lossy two-dimensional (2-D) interconnects of rectangular cross section is presented. The model is derived directly from the volumetric electric field integral equation under the approximation of the unknown volumetric current density as a product of the exponential factor describing the skin-effect and the unknown surface current density on the conductor's periphery. By proper accounting for the coupling between the boundary elements situated on the top and bottom surfaces of conductor with the elements located on the side-walls, the model maintains accuracy from dc to multi-GHz frequencies as well as for conductors with both large and small thickness/width ratios.     

一种稳定的时域电场积分方程求解方法

提出了一种求解任意形状理想导体目标时域散射的稳定时域电场积分方程(TDIE)方法,此方法能非常有效地消除后期振荡。利用显式MOT方法求解二阶时间微分的电场积分方程,矢量位随时间的变化关系采用边缘中心近似,标量位随时间的变化关系则采用三角面元重心近似,然后运用先五步后三步的平均方法。数值结果表明,本文方法能够有效地提高TDIE方法的收敛性和稳定性。     

用时域积分方程法计算介质目标的电磁散射

本文应用时域积分方程法计算介质目标的散射场，并以球体和带球帽的圆柱体为例给出了沿轴向入射平面波的电磁散射结果，与实际测试结果非常一致，值得指出的是，虽然本文给出的介质目标具有平面对称性，但该方法适用于任意形状的目标。     

A 3-D Spectral Integral Method (SIM) for Surface Integral Equations

An efficient 3-D spectral integral method (SIM) has been proposed to speed up the method of moments (MOM) calculation of induced currents on a cuboid. This method utilizes the Toeplitz structure in the impedance matrix and the fast Fourier transform to accelerate the MOM solution. It reduces the memory and CPU time per iteration from $O(N^2)$ in the MOM to $O(N^{1.5})$ and $O(N^{1.5}log N)$, respectively. Thus, the SIM can be also used as an efficient radiation boundary condition for the finite element method. Numerical results confirm the effectiveness of this method.      

Time Domain Integral Equation Analysis of Scattering From Composite Bodies via Exact Evaluation of Radiation Fields

A novel marching on in time and Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT)-based time domain integral equation solver for analyzing transient scattering from composite multiregion structures comprising homogeneous penetrable volumes and perfectly conducting surfaces is presented. To render the marching on in time procedure stable, observer and source integrals are approximated via multipoint collocation and evaluated in closed form. The proposed scheme avoids the costly evaluation of five dimensional integrals required in full space-time Galerkin schemes, and proves to be stable for all targets investigated, including coated perfect electrically conducting surfaces and multiregion penetrable volumes.      

三维矢量散射积分方程中奇异性的分析

本文研究了电场积分方程（ＥＦＩＥ）中被积函数奇异性的处理方法,特别是三维矢量散射分析中出现的高阶奇异性,给出了两种解决积分方程奇异性的数值方法。一种方法是计算Ｏ（１／Ｒ）阶奇异积分转移法,另一种方法是为解决Ｏ（１／Ｒ＾２）高阶奇异积分的数值计算问题的,它是通过排除一包含奇点的有限小块,而这一小块区域对积分的贡献为零,从而使积分方程在整个积分域变得数值可积。     

求解电场积分方程的高阶矩量法

高阶矩量法越来越多地用于求解目标散射问题。该文对高阶矩量法中的若干问题进行了分析。由于高阶矩量法需处理多重数值积分,该文提出了一种把多重数值积分转化为矩阵乘积的方法。对于矩量法阻抗矩阵的填充,每次只需计算积分节点上格林函数的值,大大缩短矩阵填充时间,提高了高阶距量法的效能。对奇异(准奇异)积分的不同处理方法做了总结,并对其优劣做了评价。     

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.     

Electric Field Integral Equations for Electromagnetic Scattering Problems With Electrically Small and Electrically Large Regions

Numerically stable electric field integral equations (EFIE) are presented for electromagnetic scattering problems that may include both electrically small geometrically complex and electrically large regions. A reduced integrand is achieved by implementing quasi-static assumptions in the electrically small regions, full-wave methods in the electrically large regions, and applying appropriate coupling relations between the regions. Use of the method provides computational efficiency as well as insight into the conditions under which the electromagnetic fields within electrically small regions of the problem can be assumed to be primarily capacitive or inductive in nature. The theoretical development of the method is highlighted in this communication and then applied to examples of electrically small, inductively-loaded, and capacitively-loaded monopole antennas. The accuracy of the results is verified with two independent methods.     

Normally-Integrated Magnetic Field Integral Equations for Electromagnetic Scattering

Modified magnetic field integral equations (MFIEs) are proposed incorporating a testing integration in the direction normal to the boundary of the target surface. The result involves a simpler kernel than the conventional MFIE, facilitating accurate computations. By employing a complex exponential testing function, the equations can be made immune to the interior resonance problem. The influence of the limits of integration, and the overall accuracy, is investigated using high order basis functions.     

基于TDIE精确求解导体面与线天线结合问题

在求解导体面与线天线连接问题中,使用细金属带来模拟细金属导线,把线-面连接问题转换为面-面连接问题,当场点与源点相距很近甚至重合时,阻抗矩阵元素的计算会出现奇异性,推导了一种奇异项解析求解的计算方法。该方法通过坐标轴的平移和旋转,将问题由三维直角坐标系转换到二维极坐标系,解析计算出中间结果后,再通过坐标变换得到原问题中的结果。数值结果表明了改进方法的精确性和有效性。