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Mathematical simulation of Metamaterial Solar Cells

Advances in Applied Mathematics and Mechanics 2011年第6期3卷 702-715页

作者： Jichun Li Yitung Chen Yang Liu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityHunan 411105China Department of Mathematical Sciences University of Nevada Las VegasLas VegasNevada 89154-4020USA Department of Mechanical Engineering University of Nevada Las VegasLas VegasNevada 89154-4027USA

In this paper,we propose several solar cell designs based on *** numerical simulations of various designs with different materials are carried *** tests show that metamaterial solar cells are quite efficient,and over ... 详细信息

关键词： Maxwell’s equations metamaterial solar cell finite element method

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Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

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Communications in computational Physics 2011年第7期10卷 339-370页

作者： Yunqing Huang Hengfeng Qin Desheng Wang Qiang Du Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityHunan 411105China Department of Mechanical and Electronic Engineering School of Mechanical EngineeringXiangtan UniversityHunan 411105China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore 637371Singapore Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA

We present a novel adaptive finite element method(AFEM)for elliptic equations which is based upon the Centroidal Voronoi Tessellation(CVT)and superconvergent gradient *** constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation(CVDT)are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional *** with finite element solutions on such high quality triangulations,superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be *** a seamless integration of these techniques,a convergent adaptive procedure is *** demonstrated by the numerical examples,the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

关键词： Finite element methods superconvergent gradient recovery Centroidal Voronoi Tessellation adaptive methods.

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Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

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Advances in Applied Mathematics and Mechanics 2010年第1期2卷 56-75页

作者： Yanping Chen Li Dai Zuliang Lu School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdongChina Mathematics Teaching and Research Group Xiguan Foreign Language SchoolGuangzhouGuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtanHunanChina

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element *** use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control *** obtain the superconvergence of O(h^(1+s))(0

关键词： Constrained optimal control problem linear elliptic equation mixed finite element methods rectangular partition superconvergence properties

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Analysis theory of random energy of train derailment in wind

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science China(Physics,Mechanics & Astronomy) 2010年第4期53卷 751-757页

作者： CHEN RuiLin 1,2,3 , ZENG QingYuan 3 , HUANG YunQing 1 , XIANG Jun 3 , WEN Ying 3 , GUO XiaoGang 2 , YIN ChangJun 2 , DONG Hui 2 & ZHAO Gang 4 1 hunan key laboratory for computation and simulation in science and engineering, Xiangtan University, Xiangtan 411105, China 2 School of Civil engineering & Mechanics, Xiangtan University, Xiangtan 411105, China 3 School of Civil Architecture, Central South University, Changsha 410075, China 4 AMEC, Toronto M5A5G7, Canada 1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China2. School of Civil Engineering & Mechanics Xiangtan University Xiangtan 411105 China3. School of Civil Architecture Central South University Changsha 410075 China4. AMEC Toronto M5A5G7 Canada

Based on the analysis theory of random energy of train derailment, an analysis theory of random energy of train derailment in wind is suggested. Two methods are proposed -the time domain method and the frequency domain method of analysis theory of random energy of train derailment in wind. The curves of σ pw -v under various wind speeds are obtained through the computation. The original curve of σ p -v is expanded, which turns the analysis theory of random energy of train derailment into the all-weather theory. Train derailment condition has been established under wind action. The first and second criterions of train derailment have been proposed in light of wind action. The analysis of train derailment cases at home or abroad is made, in- cluding the first analysis of Xinjiang train derailment case encountered 13-level of gale, which explained the inevitability of train derailment. The analysis theory of random energy of train derailment in wind shows its validity and accuracy. The input energy σ pw of the transverse vibration of train-track(bridge)-wind system is linked to train speed. With the establishment of the analysis theory of random energy of train derailment in wind, It is likely to initiate an all-weather speed limit map for a train or any high-speed train.

关键词： train derailment analysis theory of random energy of train derailment analysis theory of random energy of train de- railment in wind train derailment condition in wind the criterion of train derailment in wind train derailment case

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AN EFFICIENT MOVING MESH METHOD FOR A MODEL OF TURBULENT FLOW IN CIRCULAR TUBES

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Journal of computational Mathematics 2009年第2期27卷 388-399页

作者： Yin Yang Yanping Chen Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China School of Mathematical Sciences South China Normal University Guangzhou China

This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl＇s mixing-length theory. Our algorithm is formed by an outer iterative algorithm for handling the optimal control condition and an inner adaptive mesh redistribution algorithm for solving the singular governing equations. We discretize the nonlinear problem by using a upwinding approach, and the resulting nonlinear equations are solved by using the Newton- Raphson method. The mesh is generated and the grid points are moved by using the arc-length equidistribution principle. The numerical results demonstrate that proposed algorithm is effective in capturing the boundary layers associated with the turbulent model.

关键词： Eddy viscosity Turbulent pipe flow Boundary layer Optimal control Moving mesh

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Legendre spectral Galerkin method for second-kind Volterra integral equations

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中国高等学校学术文摘·数学 2009年第1期4卷 181-193页

作者： Zhengsu WAN Yanping CHEN Yunqing HUANG Department of Mathematics Hunan Institute of Science and TechnologyYueyang 414006China 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 Science Xiangtan UniversityXiangtan 411105China

The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this *** provide a rigorous error analysis for the proposed method,which indicates that the numerical errors (in the L2 norm) will decay exponentially provided that the kernel function and the source function are sufficiently *** examples are given to illustrate the theoretical results.

关键词： Volterra integral equation Legendre spectral Galerkin method convergence

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Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

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Communications in computational Physics 2009年第5期5卷 928-941页

作者： Shan Jiang Yunqing Huang Department of Mathematics Xiangtan UniversityXiangtan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied MathematicsXiangtan UniversityXiangtan 411105China

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale *** key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary *** boundary conditions are chosen to extract more accurate boundary information in the local *** consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base *** examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

关键词： Multiscale finite element method multiscale base functions oscillatory boundary condition periodic coefficient non-periodic coefficient

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A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems

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Advances in Applied Mathematics and Mechanics 2009年第2期1卷 242-256页

作者： Zuliang Lu Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanP.R.China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongP.R.China

In this paper,we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element *** state and co-state are approximated by the order k≤1 RaviartThomas mixed finite element spaces and the control is approximated by piecewise constant *** derive a posteriori error estimates for the coupled state and control approximations.A numerical example is presented in confirmation of the theory.

关键词： Semilinear optimal control problems mixed finite element methods a posteriori error estimates

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Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods

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Advances in Applied Mathematics and Mechanics 2009年第6期1卷 830-844页

作者： Yanping Chen Peng Luan Zuliang Lu School of Mathematical Science South China Normal UniversityGuangzhou 510631GuangdongChina Mathematics Teaching and Research Group Sanshui Experimental High School of Zhongshan UniversityFoshan 528145GuangdongChina Hunan Key Lab for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina

In this paper,we present an efficient method of two-grid scheme for the approximation of two-dimensional nonlinear parabolic equations using an expanded mixed finite element *** use two Newton iterations on the fine grid in our ***,we solve an original nonlinear problem on the coarse nonlinear grid,then we use Newton iterations on the fine grid *** two-grid idea is from Xu's work[SIAM ***.,33(1996),pp.1759–1777]on standard finite *** also obtain the error estimates for the algorithms of the two-grid *** is shown that the algorithm achieve asymptotically optimal approximation rate with the two-grid methods as long as the mesh sizes satisfy h=O(H^((4k+1)/(k+1))).

关键词： Nonlinear parabolic equations two-grid scheme expanded mixed finite element methods Gronwall’s Lemma

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RECOVERY A POSTERIORI ERROR ESTIMATES FOR GENERAL CONVEX ELLIPTIC OPTIMAL CONTROL PROBLEMS SUBJECT TO POINTWISE CONTROL CONSTRAINTS

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Journal of computational Mathematics 2009年第4期27卷 543-560页

作者： Yanping Chen Yao Fu Huanwen Liu Yongquan Dai Huayi Wei School of Mathematical Sciences South China Normal University Guangzhou 510631 China College of Mechanical Engineering Jiangxi Yu Zhou Scientific and Technological Institute Xinyu 338029 China School of Mathematics and Computer Science Guangxi University for Nationalities Nanning 530006 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University

Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.

关键词： General convex optimal control problems Finite element approximation Control constraints Superconvergence Recovery operator.

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