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A LEGENDRE GALERKIN SPECTRAL METHOD FOR OPTIMAL CONTROL PROBLEMS

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Journal of Systems Science & Complexity 2011年第4期24卷 663-671页

作者： Yanping CHEN Nianshi XIA nianyu yi School of Mathematical Sciences South China Normal University Guangzhou 510631 China. The Faculty of Mathematics Chengyi College Jimei University Xiamen 361021 China. Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematicsand Computational Science Xiangtan University Xiangtan 411105 China.

这份报纸认为 Legendre 是 Galerkin 光谱为非强迫的最佳的控制问题的近似。作者导出 posteriori 错误估计为光谱最佳的控制的近似计划问题。由选择适当基础功能， discretization 方程的生硬矩阵是稀少的。并且作者使用快 Legendre 变... 详细信息

这份报纸认为 Legendre 是 Galerkin 光谱为非强迫的最佳的控制问题的近似。作者导出 posteriori 错误估计为光谱最佳的控制的近似计划问题。由选择适当基础功能， discretization 方程的生硬矩阵是稀少的。并且作者使用快 Legendre 变换改进这个方法的效率。表明我们的理论结果的二个数字实验被介绍。

关键词：最优控制问题 Galerkin Legendre变换后验误差估计刚度矩阵离散方程数值实验谱逼近

VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY PARABOLIC EQUATIONS

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Journal of Systems Science & Complexity 2013年第6期26卷 902-924页

作者： CHEN Yanping HOU Tianliang yi nianyu School of Mathematical Sciences South China Normal University School of Mathematics and Computational Science Xiangtan University

This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic *** state and co-state are approximated by RaviartThomas mixed finite element spaces,and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control.A priori error estimates are derived for the state,the co-state,and the *** numerical examples are presented to confirm the theoretical investigations.

关键词：最优控制问题线性抛物方程离散化有限元空间先验误差估计容许控制状态合作

SomeWeighted Averaging Methods for Gradient Recovery

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Advances in Applied Mathematics and Mechanics 2012年第2期4卷 131-155页

作者： Yunqing Huang Kai Jiang nianyu yi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina

We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in *** results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh.

关键词： Finite element method weighted averaging gradient recovery

RECOVERY BASED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATION IN 2D

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Journal of Computational Mathematics 2020年第1期38卷 84-102页

作者： Yunqing Huang Huayi Wei Wei Yang nianyu yi Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

We design and numerically validate a recovery based linear finite element method for solving the biharmonic *** main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formulation of the biharmonic equation,where G is the recovery operator which recovers the piecewise constant function into the linear finite element *** operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty *** explicit matrix expression of the proposed method is also *** examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method.

关键词： Biharmonic equation Linear finite element Recovery Adaptive

A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations

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Science China Mathematics 2008年第8期51卷 1376-1390页

作者： CHEN YanPing HUANG YunQing yi nianyu School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem... 详细信息

关键词： Legendre Galerkin spectral method optimal control problems parabolic state equations a posteriori error estimates

High order compact schemes for gradient approximation

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Science China Mathematics 2010年第7期53卷 1899-1914页

作者： Huang YunQing Liang Qin yi nianyu Xiangtan Univ Sch Math & Computat Sci Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan 411105 Peoples R China Peking Univ Sch Math Sci Beijing 100871 Peoples R China

In this paper, we propose three gradient recovery schemes of higher order for the linear interpolation. The first one is a weighted averaging method based on the gradients of the linear interpolation on the uniform mesh, the second is a geometric averaging method constructed from the gradients of two cubic interpolation on macro element, and the last one is a local least square method on the nodal patch with cubic polynomials. We prove that these schemes can approximate the gradient of the exact solution on the symmetry points with fourth order. In particular, for the uniform mesh, we show that these three schemes are the same on the considered points. The last scheme is more robust in general meshes. Consequently, we obtain the superconvergence results of the recovered gradient by using the aforementioned results and the supercloseness between the finite element solution and the linear interpolation of the exact solution. Finally, we provide several numerical experiments to illustrate the theoretical results.

关键词： superconvergence gradient recovery compact scheme

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抛物型微分方程的多尺度有限元高效计算

扬州大学学报（自然科学版） 2015年第2期18卷 26-30页

作者：江山易年余孙美玲扬州大学数学科学学院江苏扬州225002 湘潭大学数学与计算科学学院湖南湘潭411105 南通职业大学基础课部江苏南通226007

提出了抛物型微分方程的高效多尺度数值计算方法.与传统有限元基函数相比,多尺度有限元基函数能更好地反映问题自身的强振荡微观信息,结合多尺度有限元格式,可使计算结果在宏观尺度获得很好的数值逼近.对时间采用欧拉向后差分离散化,得... 详细信息

提出了抛物型微分方程的高效多尺度数值计算方法.与传统有限元基函数相比,多尺度有限元基函数能更好地反映问题自身的强振荡微观信息,结合多尺度有限元格式,可使计算结果在宏观尺度获得很好的数值逼近.对时间采用欧拉向后差分离散化,得到稳定且收敛的数值结果.新方法在取得高仿真逼近的同时,节约了大量计算资源和时间,因而更具应用价值.

关键词：抛物型模型多尺度有限元时间离散化欧拉向后差分算法效率

数字微反射镜的RGB三色LED照明系统研究

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照明工程学报 2010年第3期21卷 56-58,63页

作者：张云翠刘龙杨轶曹冠英张竞辉邹念育大连工业大学光子学研究所辽宁大连116034 大连东软信息学院嵌入式系统工程系辽宁大连116023

大功率RGB三色LED的体积小、重量轻,成为投影仪、背投电视等显示仪器的新型光源。本文研究了基于RGB三色LED的数字微反射镜的照明系统的设计方法,给出了光源和照明系统的设计结果,并对照明结果进行了分析。基于该新型光源的数字微反射... 详细信息

大功率RGB三色LED的体积小、重量轻,成为投影仪、背投电视等显示仪器的新型光源。本文研究了基于RGB三色LED的数字微反射镜的照明系统的设计方法,给出了光源和照明系统的设计结果,并对照明结果进行了分析。基于该新型光源的数字微反射镜照明系统与传统照明系统相比,具有结构简单、体积降低、重量减轻、节能环保等优点。

关键词：发光二极管数字微反射镜导光管

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中美道路照明标准及测试方法的解析

照明工程学报 2011年第5期22卷 58-63页

作者：孟令涛邹念育贺晓阳曹冠英杨轶李德胜张竞辉大连工业大学光子学研究所辽宁大连116034

本文对中美两国道路照明标准进行了解析,总结了两国标准中参数设置方面的区别和联系,比较了各自的优劣,进而针对照度、亮度和眩光限制几项重要参数的测试与评价方法提出了改进建议,对提高道路照明的质量有积极的参考意义。

关键词：道路照明标准值评价指标测试方法 LED