Application of SSOR Preconditioning Technique to Method of Lines for Millimeter Wave Scattering

In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps.     

An Effective Multigrid Preconditioned CG Algorithm for Millimeter Wave Scattering by an Infinite Plane Metallic Grating

An effective multigrid based preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using multigrid technique we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the initial guess for the conjugate gradient (CG) method. Numerical results show that our developed method can reach five times improvement of computational complexity.     

Analysis of Millimeter Wave Scattering by an Electrically Large Metallic Grating Using Wavelet-Based Algebraic Multigrid Preconditioned CG Method

An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background.     

Application of Robust Incomplete Cholesky Factorizations Preconditioned CG Algorithms for FEM Analysis of Millimeter Wave Filters

The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for Complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures.     

Analysis of Millimeter Wave Scattering by the Infinite Plane Metallic Grating Using PCG-FFT Technique

In this paper, both fast Fourier transformation (FFT) and preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Electromagnetic wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation. For arbitrary incident wave, Helmholz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by FFT technique. As a result, this Topelitz impedance matrix only requires O(N) memory storage for the conjugate gradient FFT method to solve the current distribution with the computational complexity O(N log N) . Our numerical results show that circulate matrix preconditioner can speed up CG-FFT method to converge in much smaller CPU time than the banded matrix preconditioner.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence ten times faster than GMRES. The reflection and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence 19 times faster than GMRES. The isolation and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

Efficient Analysis of Millimeter Wave Ferrite Circulators by the GMRES Iterative Algorithm

The finite element method (FEM) combined with the perfectly matched layers (PML) is given for simulation of waveguide ferrite circulators. The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. The formulation of FEM and the algorithm of GMRES method are described in detail. The reflection and insertion losses of millimeter wave waveguide circulator are analyzed and the results are compared with those obtained from literature.     

Analysis of Frequency Selective Surfaces with Metallic and Dielectric Losses at Millimeter Wave Range

In this paper, a theoretical analysis of scattering from a doubly frequency selective surfaces (FSS) with dielectric and metallic losses in the millimeter wave range is presented. The theoretical analysis involves the solution of the electric field integral equation relating the induced current in the FSS in the presence of anisotropic dielectric layers. The method of moment is employed to obtain numerical results. The frequency selective surface structure considered is composed by conducting patch elements sandwiched between two anisotropic dielectric layers. Three different anisotropic materials are considered: Epsilam-10, Alumina, and Sapphire. The sapphire presents low losses when compared with the other two dielectric materials. The most common metals, as copper and aluminum, are considered in this analysis. None significant metallic losses were observed for any considered metal. Numerical results are presented for the scattering characteristics and for dielectric and metallic losses parameters.     

Fast Stimulation of Millimeter Wave Waveguide Filters by Boundary Marching Method

The boundary marching method is applied for the analysis of the waveguide bandpass filers. The vector finite element method with the perfectly matched layers (PML) as the matching load is given for parameter extraction of millimeter wave filters. The implementation of the fast boundary marching method is described in detail. The reflection and insertion losses of millimeter wave filters are obtained and compared with those obtained from literature.     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

表面粗糙度的变波矢光散射测量方法的研究

提出了表面粗糙度变波矢光散射测量方法，通过散射光强中心亮点光能量的参数ｌｎ，Ｅ随变化的线性关系来确定粗糙度ｗ，对６块粗糙度不同的硅片背面样品进行了实验测量。     

单根电极或沟槽形成的栅格对声表面波的散射*

该文借鉴汪承灏先生研究栅格声表面波散射的技术路线,提出一种既不限制基片和栅格形状、类型,也不限制声波入射方向,可精确计算栅格对SAW散射的有限元通用模型。作为对《超声学》第六章"声表面波"中栅格对声表面波的反射和体波散射一节部分结论的进一步阐释和说明,计算了YZ-Li Nb O3和128?YX-Li Nb O3单晶上厚度为200 nm、宽度为1μm的单根悬浮铝栅条以及沟槽在不同频率下的反射系数曲线。提出的计算方法今后可推广应用于层状结构基底、应用到非规则指条、沟槽、金属点阵、基片端面、台阶等的反射的精确分析,为优化设计新型声表面波器件奠定理论基础。     

Simulation of Millimeter Wave Circulators by FEM with Unifrontal/Multifrontal Technique

The combination of unifrontal and multifrontal techniques is applied for solving a large, sparse, and unsymmetric system of linear equations resulting from the use of edge-based finite element method (FEM) for millimeter wave ferrite devices. The formulation of finite element method combined with the perfectly matched layers (PML) is given and the combined algorithm of unifrontal and multifrontal methods is described. The lower data movement of unifrontal method and the lower fill-in of normal multifrontal methods are combined for an algorithm with their features. The performance of typical waveguide junction circulators is analyzed and the calculated results are compared with those obtained from the literature.     

玫苯胺共振光散射法测定DNA

本文研究了三苯甲烷类碱性染料玫苯胺与DNA作用的共振光散射光谱 ,在 pH =10 5～ 11的范围内 ,DNA的加入导致玫苯胺共振光散射的增强 ,在 4 85nm处 ,存在一共振光散射增强峰 ,其强度与DNA的浓度呈线性关系 ,据此建立了一种测定DNA的共振光散射法。方法的线性范围为 0～ 1 0 0mg·L-1,检测限为14 2ng·mL-1。将该方法用于混合样品中DNA的测定 ,结果令人满意。     

中性红共振光散射法测定脱氧核糖核酸

本文基于脱氧核糖核酸 (DNA)对有机染料中性红的共振光散射的增强效应 ,拟订了一种测定DNA的共振光散射法。在pH 5 0～ 7 0范围内 ,有机染料中性红在DNA分子表面进行长距组装导致共振光散射增强。在 335 0nm处的共振光谱散射增强程度与DNA浓度呈线性关系 ,其线性范围为 0～ 6 0 0ng·mL-1,检出限可达 12 8ng·mL-1。该方法简便、快速 ,具有较高的灵敏度和准确度。将该方法用于混合样品中DNA的测定 ,结果令人满意。     

应用AWE技术和等效偶极子法快速计算目标宽带RCS

将渐近波形估计(AWE)技术结合等效偶极子(EDM)法应用于任意三维导体目标宽带雷达散射截面(RCS)的快速计算.首先利用等效偶极子法实现阻抗矩阵的快速填充及其多阶导数矩阵的快速计算,并利用内外迭代近场预处理技术加速矩阵方程的求解,进而应用渐近波形估计技术实现宽带雷达散射截面(RCS)的快速计算.数值计算表明:本文方法在保证计算精度的前提下,提高了计算效率.     

基于微面斜率法的粗糙表面半透明介质层光谱散射特性分析

对具有一维高斯分布粗糙表面的半透明介质层光谱散射,基于微面斜率法建立了考虑遮蔽效应的粗糙表面光谱辐射传递概率模型,采用蒙特卡罗法模拟光谱辐射能束在粗糙表面、半透明介质层介质与镜反射基底之间的多次反射、折射和吸收等传递过程。通过数值模拟,分析了介质层表面粗糙度、光谱光学厚度、折射率和基底反射率对介质层双向反射分布函数(BRDF)的影响。结果表明,表面粗糙程度不同时,反射峰值随入射角度呈现不同的变化趋势;表面粗糙度增加或折射率增大都将导致漫反射份额增大;介质层光谱光学厚度和基底反射率主要影响BRDF的数值大小,而对BRDF的分布形态影响很小。     

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.     

基于图像处理的频域有限差分法用于实际光子晶体光纤的研究

提出了一种基于图像处理算法和频域有限差分法相结合研究实际光子晶体光纤的数值分析方法.该方法针对实际光子晶体光纤由于结构不规则难以进行数值分析的缺点.采取首先对光子品体光纤的电镜扫描图像使用阈值分割和维纳滤波等图像处理算法获得光纤截面的几何网像.然后使用图像插值及构造均值移动窗口滤波等方法实现了网格划分和介电系数平均等步骤,最后结合频域有限差分法对光纤特性进行分析计算.结果表明,该方法能够精确分析实际光子晶体光纤的色散特性.模拟得到的实际光子晶体光纤的模场分布与实验结果吻合很好.