正则化预条件方法在矩量法中的应用

计算电磁学中矩量法产生的系统矩阵是病态矩阵,使用迭代方法求解时很难收敛,即使采用现有的预条件技术也经常不收敛.本文借用不适定问题求解中的正则化方法的概念,提出采用正则化矩阵作为矩量法中矩阵方程的一个预条件矩阵.这种预条件方法可以直接改善原矩阵的特征值分布,而且不需要额外的空间来存储预条件矩阵.此外,本文提出通过正则化矩阵方程的L曲线的二阶导数的最大值点来确定正则化参数,使得预条件矩阵方程求解的效率最高.数值实验表明,对于高阶矩量法求解电场积分方程或者磁场积分方程时分别产生的矩阵方程,采用常见的预条件迭代方法求解时收敛很慢,但是采用本文的预条件迭代方法却可以较快地收敛.     

多尺度问题电磁特性叠层矩量法分析北大核心CSCD

论文提出了一种叠层矩量法分析多尺度目标电磁特性。论文采用矩量法直接计算强相互作用区域,多层矩阵压缩方法(MLMCM)和多层快速多极子方法(MLFMA)分别用于加速计算低频和高频作用区域。论文通过使用多分辨ILU(MR-ILU)预条件加速迭代求解矩量法离散多尺度目标产生的病态矩阵方程。通过分析实际多尺度目标电磁特性证明论文方法的有效性。     

求解复杂载体天线辐射问题的近场预条件技术

提出了一种近场预条件技术与LDU分解法相结合的新技术,用于加速矩量法(MoM)分析复杂载体上线天线辐射问题中线性方程组的迭代求解.通过LDU分解可将系数矩阵中表示载体上单元相互作用的具有对角占优特性的子阵分离出来,构造一个矩阵分解形式的预条件阵.结合广义最小留数(GMRES)法,分别对装载在两个简单形体和一架大型飞机模型上的线天线的辐射问题进行了求解.数值结果表明,该方法可大大加快线性方程组迭代求解的收敛速度,提高分析计算效率.     

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.     

MLFMA/VIE-MoM大型矩阵方程的快速迭代求解方法

 本文针对体积分方程矩量法(VIE-MoM)分析三维非均匀介质电磁散射问题所导出的大型矩阵方程的求解问题, 基于多层快速极子技术(MLFMA)算法研究了快速近似迭代方法.提出了一种基于MLFMA分组方案对系数矩阵进行重组并提取强耦合元素的近场预条件器的构造方法,有效地提高了广义最小余量法(GMRES)的迭代收敛速度.提出了一种在迭代计算过程中的近似矩阵向量乘积方案,明显降低了单步计算过程中MLFMA远区耦合作用的计算时间.计算实例表明,采用本文的迭代加速技术可使计算速度提高3至5倍,有效地提高了VIE-MoM大型矩阵方程的迭代求解速度.     

基于超级计算机的矩量法性能分析与优化

复杂目标的精确电磁特性分析往往需要巨大的存储和极长的计算时间。针对这一问题,结合国内发展迅速的超级计算机系统,研究了具有精确高效仿真能力的高性能电磁算法——高阶矩量法。提出了单元预选法来消除矩阵并行填充过程中的无效计算,加速矩阵填充过程。提出了一种具有更少的通信次数和通信量的新型并行LU分解算法,加速矩阵方程求解过程。数值测试表明提出的矩阵并行填充算法和矩阵方程并行求解算法在超级计算机平台上都能获得较高的并行性能,大幅提高了矩量法的仿真能力。     

大型波导纵缝阵列天线的分析与设计

本文利用矩量法和等效网络法对矩形波导宽边纵缝阵列进行了精确的理论分析，严格计算阵中缝隙的内部和外部互耦，并利用等效网络法提取阵中缝隙的等效导纳特性。在此基础上，提出模型阵列和模型缝隙的大型波导缝隙阵的设计方法．理论结果与实验比较吻合。     

“邻居单元”为基础的预条件方法及其应用

该文提出了一种具有物理意义的预条件方法--"邻居单元"为基础的预条件方法。该方法充分考虑了矩阵元素中的"主要"信息量,可以有效加快迭代收敛速度。在构造预条件因子时,采用从目标的"几何结构剖分"出发,而不是从"矩阵元素"出发确定"基权函数之间的作用量关系",这样保证了构造预条件矩阵的计算复杂度仅为O(N)。作为实例,该文将这种预条件方法与共轭梯度方法结合应用于矩量法基站天线分析所得方程的求解,数值结果表明了该文方法的有效性。     

结合P-FFT算法和特征基函数分析大型阵列散射

特征基函数方法利用特征值分解提取目标散射特征,构造基于特征向量的基函数可以高效的缩减矩量法分析所需的未知量数目,有利于分析有限周期阵列电磁散射或辐射问题。然而,对于电大尺寸电磁阵列散射问题,直接求解由特征基函数组成的矩阵方程,仍然面临着计算量较大等问题,难以适用于单机计算。本文结合特征基函数和预修正傅里叶快速算法求解体面结合积分方程,分析了大型金属介质混合有限周期阵列的散射特性,该算法有效减少了计算量和计算时间,并且改善了迭代求解收敛性能。     

自适应交叉近似压缩的高阶矩量法的并行实现

高阶矩量法在计算电磁学中的应用越来越广泛, 为了进一步提高其计算规模, 引入并行的自适应交叉近似压缩算法(Adaptive Cross Approximation algorithm, ACA).该算法首先采用非均匀有理B样条建模(Non-Uniform Rational B-Splines, NURBS)的方法进行面片分组; 然后利用矩量法中远区阻抗矩阵的低秩特性进行ACA压缩; 最后采用稀疏近似逆预条件(Sparse Pattern Approximate Inverse preconditioning, SPAI)的共轭梯度法(Conjugate Gradient method, CG)快速求解矩阵方程.该算法中的ACA压缩过程和迭代求解过程都特别适合并行计算.数值实验表明, 对于电大尺寸问题, ACA压缩后的矩阵占用的内存远远低于原矩阵, 而预条件的共轭梯度法可以很快收敛.此外该算法在大规模并行时的效率较高.     

矩形波导纵缝阵列的矩量法分析与设计

利用矩量法对矩形波导宽边纵缝阵列进行了理论计算。首先利用等效原理及切向磁场的连续性给出了求解阵列纵缝口面磁流的积分方程，对一实际阵列进行了计算，计算结果与测试结果吻合良好。     

混合ACA和MLFMA方法计算复合目标电磁散射

采用矩量法(MoM)计算电大尺寸的复合目标的电磁散射。为了能够高效快速地计算电大尺寸三维复合目标的电磁散射,提出一种新的混合方法,将自适应交叉近似(ACA)算法和多层快速多级子(MLFMA)算法相结合,共同加速矩量法的计算。其中,MLFMA用于加速目标与自身的作用,ACA用于加速目标与其他目标的相互作用。提出的混合算法在计算复合目标电磁散射时,可降低运算存储,缩短阻抗矩阵填充时间,并且能够加快矩阵矢量乘,且不影响计算精确度。数值算例表明,所提快速算法能够在保证电磁散射计算精确度前提下,比传统方法更高效。     

矩形波导纵缝阵列的理论计算

利用矩量法对矩形波导宽边纵缝阵列进行了理论计算。首先利用等效原理及切向磁场的连续性给出了求解阵列纵缝口面磁流的积分方程．后对一实际阵列进行了计算．计算结果与测试结果吻合良好。     

The design of large waveguide arrays of shunt slots

It is shown that the method of moments (MM) solution can determine the active admittance of each slot in a finite array and that the infinite array model is quite accurate for the design of large waveguide arrays of shunt slots. Active admittances computed by an infinite array model agree favorably with that of slots in sufficiently large finite arrays. Measured results verify the MM solution, thereby validating the infinite array model accuracy     

耦合纵缝馈电的短路波导宽边纵缝阵的分析与设计

基于三层结构（馈电缝、耦合缝、辐射缝）平面缝隙阵天线设计的需要,用场分析法对由耦合纵缝馈电的两端短路波导宽边直线纵缝阵进行了分析和综合。该法考虑了所有的互耦、高次模及波导壁厚的影响,得到了耦合纵缝馈电的两端短路波民宽边纵缝直线阵在辐射缝偏心距相同和缝长相同时直线缝阵口径分布等幅同相的结论。利用所得结论并结合泰勒线阵综合法提出了适合于对文中系统进行综合的有效方法。     

A hybrid moment method solution for TEz scattering fromlarge planar slot arrays

This paper develops a hybrid moment method (MM) based numerical model for electromagnetic scattering from large finite-by-infinite planar slot arrays. The model incorporates the novel concept of a physical basis function (PBF) to reduce dramatically the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance to tailor the array's edge currents. An individual slot column is represented by equivalent magnetic scattering currents on an unbroken perfectly conducting plane. Floquet theory reduces the currents to a single reference element. In the array's central portion, where the edge perturbations are negligible, the slot column reference elements are combined into a single basis function. Thus, one PBF can represent an arbitrarily large number of slot columns. A newly developed one-sided Poisson sum formula is used to calculate the mutual coupling between the PBF and the slot columns in the presence of a stratified dielectric media. The array scanning method (ASM) gives the mutual coupling between the individual slot columns. The hybrid method is validated using both numerical and experimental reference data. The results demonstrate the method's accuracy as well as its ability to handle array problems too large for traditional MM solutions     

Analysis of Slot Characteristics in Slotted Single-Mode Semiconductor Lasers Using the 2-D Scattering Matrix Method

We use the two-dimensional (2-D) scattering matrix method (SMM) to analyze the slot characteristics in slotted single-mode semiconductor lasers and compare the results with those calculated by the one-dimensional transfer matrix method (TMM). The analysis shows that the 2-D SMM is required to accurately account for the measured results. Using the 2-D SMM simulation, we find that there is almost no reflection at the interface from slot to waveguide while a large reflection exists at the interface from waveguide to slot, and the power loss is much larger than the power reflected. For a single slot, the slot width has little influence on the slot reflectivity, which coincides with the measured results. The reflection and transmission of the slot are found to be exponentially dependent on the slot depth     

Analytic design of conformal slot arrays

A completely analytic design process has been developed for small slot arrays which accounts for the varying effect of mutual coupling as a function of element position. A previously developed theory for the design of small arrays has been extended to include conformal dielectric-filled waveguide slot arrays. Computer software has been assembled which enables calculation of the slot geometries required to implement a specified aperture distribution and input impedance condition. The slot self- and mutual admittances are calculated numerically, thus eliminating the traditional measured slot data from the design process. This design technique has been applied to conformalX-band slot arrays on cylinders of a few wavelengths diameter. The arrays consist of multiple dielectric-filled waveguides, each of which is a narrow-band standing-wave linear array of longitudinal shunt slots. The computerized design process adjusts the length and offset of each slot in the total array until the desired aperture distribution and impedance match are achieved. A flow diagram of the design program and test results from experimental arrays are presented.     

An Improved Weak-Form BCGS-FFT Combined With DCIM for Analyzing Electromagnetic Scattering by 3-D Objects in Planarly Layered Media

Fast algorithms for electrically large objects buried in layered media are mainly hindered by two time-consuming processes. One is the table filling of Green's function, and the other is the solving of the impedance matrix equation. For the first, to accelerate the evaluation of the time-consuming Sommerfeld integral in the dyadic Green's function (DGF), the discrete complex image method (DCIM) is introduced to get a closed-form DGF. To further accelerate the calculation of DGF for the volume electric field integral equation (EFIE), DGF is split before applying DCIM. For the second, the iterative solver stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) is combined with DCIM for solving the matrix equations. Meanwhile, the closed-form DGF enables the "spherical-mean" Green's function, which eliminates the singularity of Green's function. Numerical results show that the weaker singularity results in a faster and steadier convergence rate for iterative solvers