General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

Low-order Wavefront Error Compensation for Multi-field of Lithography Projection Objective Based on Interior Point Method

Low-order wavefront error account for a large proportion of wave aberrations.A compensation method for low order aberration of projection lithography objective based on Interior Point Method is presented.Compensation model between wavefront error and degree of movable lens freedom is established.Converting over-determined system to underdetermined system,the compensation is solved by Interior Point Method(IPM).The presented method is compared with direct solve the over-determined system.Then,other algorithm GA,EA and PS is compared with IPM.Simulation and experimental results show that the presented compensation method can obtained compensation with less residuals compared with direct solve the over-determined system.Also,the presented compensation method can reduce computation time and obtain results with less residuals compare with AGA,EA and PS.Moreover,after compensation,RMS of wavefront error of the experimental lithography projection objective decrease from 56.05 nm to 17.88 nm.

The Error Estimates of Direct Discontinuous Galerkin Methods Based on Upwind-Baised Fluxes

In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that L2 norms error estimates can reach to order k + 1 by using time discretization methods.

Discontinuous element pressure gradient stabilizations for compressible Navier-Stokes equations based on local projections

A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.

Projected gradient trust-region method for solving nonlinear systems with convex constraints

In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.

Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second‑Order Elliptic Problems on Cartesian Grids

This paper is concerned with convergence and superconvergence properties of the local discontinuous Galerkin(LDG)method for two-dimensional semilinear second-order elliptic problems of the form−Δu=f(x,y,u)on Cartesian grids.By introducing special GaussRadau projections and using duality arguments,we obtain,under some suitable choice of numerical fuxes,the optimal convergence order in L2-norm of O(h^(p+1))for the LDG solution and its gradient,when tensor product polynomials of degree at most p and grid size h are used.Moreover,we prove that the LDG solutions are superconvergent with an order p+2 toward particular Gauss-Radau projections of the exact solutions.Finally,we show that the error between the gradient of the LDG solution and the gradient of a special Gauss-Radau projection of the exact solution achieves(p+1)-th order superconvergence.Some numerical experiments are performed to illustrate the theoretical results.

基于彩色交叉条纹的相机标定

针对相位标靶标定相机需采集多幅条纹图获取相位的问题,提出了一种基于彩色交叉条纹的相机标定方法。本方法在每个标定位置仅需一幅条纹图就可以完成特征标识点的提取;通过液晶显示屏显示一幅红蓝交叉条纹图像,由相机拍摄,采用傅里叶变换和多频外差法分别得到水平和垂直方向的绝对相位;根据相位标靶的空间位置与图像中绝对相位的精确对应关系,标定相机内参,采用非线性最小二乘法优化。基于重投影误差的实验结果表明,本方法可以快速精确的实现相机标定。

非定常微极流体方程的速度校正投影方法

研究了二维和三维非定常微极流体方程的速度校正投影方法.采用一阶和二阶后向差分格式进行时间离散及协调有限元进行空间离散,给出了一阶和二阶时间半离散速度校正投影方法的无条件稳定性和一阶时间半离散格式的误差估计以及相应的全离散格式,证明了一阶全离散格式的无条件稳定性.最后,通过数值算例验证了该方法的有效性.

希尔伯特空间中的广义松弛余强制变分不等式体系及带误差的三步投影方法

给出了希尔伯特空间H中一类带误差的三步投影方法,借助投影方法的收敛性证明了由该算法生成的迭代序列强收敛于此类广义松弛余强制变分不等式体系问题的精确解,并推广了最近文献的一些主要结果.

高轨道目标电离层折射修正方法研究

为了满足高轨道目标高精度测控的需要,提出了基于双频GNSS的空间投影法和自适应网格法两种电离层距离折射误差修正方法,并对比分析了两种方法在不同仰角、角径时电离层距离折射误差修正精度.分析结果显示:对于2.0 GHz电波信号而言,在较高仰角(仰角>45°)处,空间投影法和自适应网格法修正精度较高,均优于0.2 m;在低仰角和大角径时,空间投影法修正剩余快速增大,修正精度快速降低恶化,达到米量级,而自适应网格法修正精度则不受仰角和角径的影响.这表明:自适应网格法电离层距离修正精度高,适用性强,且便于工程应用,可为提高高轨道目标的测控精度提供有力支撑.

基于三维最小二乘方法的空间直线度误差评定

空间直线度误差是评定机械产品精度的一项重要指标,实际工程中对空间直线度误差评定算法的精度要求越来越高.为了准确评定空间直线度误差,参照国家标准(GB/T 11336—2004),采用三维最小二乘方法建立了空间直线拟合的数学模型,并给出了该数学模型的精确解.基于最小二乘拟合中线,采用空间投影、坐标变换和格点法求得最小二乘中线包容圆柱面直径.采用数值算例验证了新方法的有效性.提出的空间直线度误差评定方法精度高、鲁棒性好且易于编程实现.

可压缩Navier-Stokes方程的压力梯度局部投影间断有限元法

将压力梯度投影与间断有限元法相结合,对可压缩线性化N-S方程提出了一种稳定化间断有限元格式.证明了此格式在速度和压力有限元空间无需满足B-B型条件的情况下,解的存在性和唯一性,以及相应的误差估计.

我国体育公共事业经济评价探析——对定位、方法及计量误区的研究

运用文献资料法、逻辑分析法、案例分析法等,通过分析我国体育公共事业经济评价研究的发展历程,找出以往研究中存在的定位误区、评价方法误区、计量误区。引用第29届北京奥运会经济评价为标准案例,分析其在定位、评价方法、计量中的科学性,成为我国体育公共事业经济评价的重要参考依据,这对于结合我国体育赛事的具体情况,提高经济评价正确性,具有理论和现实的意义。

广义松弛余强制变分不等式体系及二步投影方法

设H为希尔伯特空间,〈.,.〉,‖.‖分别表示希尔伯特空间H中的内积和范数。K为H中的闭凸子集,T∶K×K→H为K×K上的任一映象。本文将重点讨论下面一类非线性变分体系(SNVI)问题:求x*,y*∈K使得〈ρT(y*,x*)+x*-y*,y-x*〉≥0,y∈K,ρ>0,〈ηT(x*,y*)+y*-x*,z-y*〉≥0,z∈K,η>0。文章中首先给出了希尔伯特空间H中一类带误差的二步投影方法,然后借助于投影方法的收敛性证明了由该算法生成的迭代序列强收敛于此类广义松弛余强制变分不等式体系(SNVI)问题的精确解。文中结果主要推广了Verma和S.S.Chang等的主要结论。

实验室环境下三维重建系统的误差模型分析及设计

针对实验教学中三维场景重建过程存在的误差扰动问题,在研究不同参数对误差影响的基础上,提出一种锥体相交几何误差模型,并利用线-圆投影法对该模型进行简化,以此估计出多摄像机立体视觉系统中由量化误差引起的物点定位误差。仿真实验测试表明,该方法具有模型简单、计算量小等优点,适用于多摄像机视觉系统下场景的三维重建。对该模型的仿真实验由学生在实验室中完成,目的是培养学生的创新思维与实际动手能力。

基于相位法的三维测量系统的相移误差分析

采用投影栅相位法进行三维测量时,光栅移动的精密控制是整个测量系统的基础。针对相移误差,对硬件系统进行设计,通过步进电机细分控制实现更小、更平稳的相移误差;并对传统的四步相位提取算法进行优化,在优化算法中,稳定的相移误差项可以作为中间变量,即其大小随机变化不再对相位计算结果产生影响。实验结果表明:设计的硬件系统调试简单,步进电机可以实现最小1/128细分;优化后的算法有效地抑制了相移误差对测量结果的影响,进一步提高了表面微观形貌的测量精度和可靠性;从而使得测量系统的整体性能指标得到提升。

2360 aBP 古洪水对小浪底设计洪水的作用

根据我国频率计算中广泛采用的Ｐ－Ⅲ型分布，应用统计试验方法，分别对仅由历史调查洪水和实测洪水组成的不完全系列，以及加入考虑流量误差情况下的古洪水资料后的系列进行了计算，得到后者比前者抽样误差大为减小的结论。运用黄河小浪底２３６０ａＢＰ古洪水的资料加入后的计算结果，论证了增加设计洪水的可靠性，并认为重要水利工程的设计洪水频率计算应在现代技术允许的条件下加入古洪水资料。

基于MATLAB的抵偿坐标系工程实践

在高速铁路、高速公路等工程项目中为限制长度变形,对坐标系的选择提出了更高的要求,有时须建立抵偿坐标系。通过对椭球膨胀法建立的抵偿坐标系与普通坐标系进行实验数据验证,发现抵偿坐标系得到的变形值更小,精确度更高,但面临计算量大、易出错等问题的困扰。基于MATLAB平台的抵偿坐标的实现,不仅能够对数据进行批量化处理,还具有速度快、精度高的优势。

固端法:二维有限元先验定量误差估计与控制

该文基于有限元超收敛计算的单元能量投影(Element Energy Projection,简称EEP)法,尝试将一维有限元中新近提出的先验定量误差估计的“固端法”拓展到二维有限元分析,以Poisson方程为例,用EEP公式预先估算出各单元的误差,可以不经有限元求解计算而直接给出满足精度要求的网格划分。该文给出的初步数值算例验证了该法的有效性。