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 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.     

Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

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.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

刻蚀波导粗糙面散射的矩量法数值分析

用矩量法对刻蚀波导粗糙面的散射特性做出了精确的数值分析基于MonteCarlo方法建立高斯粗糙面数学模型,证明矩量法在分析刻蚀波导散射问题时,是可以应用于不同起伏高度、不同入射角的一种精确而高效的数值方法对不同起伏高度的两种偏振态,分别在小角度入射和大角度入射两种情况的随机散射特性应用矩量法做出了分析并以基于二氧化硅波导的EDG器件为例,分析了由于波导壁粗糙对于器件频谱响应特性的影响.     

Analysis of Millimeter Wave Microstrip Circulator with a Magnetized Ferrite Sphere by FDTD Method with Modified Matrix Pencil Method

In this paper, the modified matrix pencil (MMP) method is used in the finite difference time domain (FDTD) method to eliminate the late time instability of time domain responses when analyzing the novel microstrip circulator with a magnetized ferrite sphere. The frequency dependent scattering parameters: reflection, isolation and insertion parameters of the microstrip circulator calculated over a wide band of frequencies with this hybrid method are compared with that obtained by direct FDTD method which agree well with the experimental results.     

复杂含核粒子对贝塞尔波束散射特性的影响

基于面积分方程的矩量法及其快速算法研究了复杂含核粒子对任意入射贝塞尔波束的散射特性.将零阶贝塞尔束的矢量解和坐标系旋转理论相结合,推导出任意入射贝塞尔波束电磁场分量的数学表达式.根据等效原理,建立了求解具有任意形状和复杂内部结构含核粒子散射问题的面积分方程.对贝塞尔波束任意入射下一些复杂含核粒子的散射进行了数值模拟,结果表明:贝塞尔波束入射时的微分散射截面要小于平面波入射时的微分散射截面,且随着半锥角的减小而增大;当波束中心的位置远离粒子中心时,微分散射截面会减小;微分散射截面对波束的入射角非常敏感.这为激光对微粒的探测、诊断以及操纵技术提供有益帮助.     

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.     

Topographic Analysis of Ocular Fundus Using the Fourier Transform Method for Projected Grating Images

In topography measurements of a local ocular fundus of the human eye using a grating-pattern projection technique, a pre-processing method to detect fringes accurately and a generalized Fourier transform method to analyze the fringe deformations are proposed. The method of analysis compensates for fringe deformations caused by instrumental characteristics. By combining the two methods, depth information can be determined with high accuracy. It is shown that the topographic parameters of the optic disc and the fundus slopes in the rim area are obtained with good reproducibility.     

Analysis of FSS with Dielectric Losses at Millimeter Wave Band Using the Transverse Transmission Line Method

The analysis of periodic structures on isotropic substrates with dielectric losses is presented. Frequency selective surface structures composed by an array of conducting patch elements are considered. This analysis uses the Galerkin method in combination with the transverse transmission line method, in the Fourier domain, to determine the reflection and transmission characteristics of the considered structures. The analysis provides very accurate results compared to those presented by other authors.     

迈克尔逊干涉仪测定金属线胀系数实验分析——升温测量和降温测量

利用迈克尔逊干涉仪可精确测量微小长度这一特性来测定金属在一定温度变化范围内,热胀冷缩的微小长度变化,从而得到一种更加精确测量金属线胀系数的新方法。并分别进行了升温测量和降温测量。后经对实验结果及实验误差的对比分析,结果显示,降温测量相比升温测量,可极大地减小实验误差,提高实验精度。