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Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay

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Advances in Applied Mathematics and Mechanics 2022年第6期14卷 1333-1356页

作者： Zhenrong Chen Yanping Chen Yunqing Huang School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdong 510631China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtanHunan 411105China

In this paper,the piecewise spectral-collocation method is used to solve the second-order Volterra integral differential equation with nonvanishing *** this collocation method,the main discontinuity point of the solution of the equation is used to divide the partitions to overcome the disturbance of the numerical error convergence caused by the main discontinuity of the solution of the *** approximation in the sense of integral is constructed in numerical format,and the convergence of the spectral collocation method in the sense of the L¥and L2 norm is proved by the Dirichlet *** the same time,the error convergence also meets the effect of spectral accuracy *** numerical experimental results are given at the end also verify the correctness of the theoretically proven results.

关键词： Second-order Volterra type integro-differential equation delay function piecewise spectral-collocation method.

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Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

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Advances in Applied Mathematics and Mechanics 2015年第1期7卷 74-88页

作者： Yin Yang Yanping Chen Yunqing Huang Wei Yang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China School ofMathematical Sciences South China Normal UniversityGuangzhou 510631China

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second *** provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently *** results are presented,which confirm the theoretical prediction of the exponential rate of convergence.

关键词： Spectral method nonlinear Volterra integral equations

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Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems

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Numerical Mathematics(Theory,Methods and Applications) 2012年第4期5卷 573-591页

作者： Yuelong Tang Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina

This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise control *** time discretization is based on the backward Euler *** state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant *** derive the superconvergence properties of finite element *** using the superconvergence results,we obtain recovery type a posteriori error *** numerical examples are presented to verify the theoretical results.

关键词： General convex optimal control problems fully discrete finite element approximation a posteriori error estimates superconvergence recovery operator

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A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

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Numerical Mathematics(Theory,Methods and Applications) 2011年第4期4卷 439-458页

作者： Tianliang Hou Yanping Chen Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina

In this paper,we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic *** state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant *** derive a posteriori error estimates for both the state and the control *** estimates,which are apparently not available in the literature,are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

关键词： A posteriori error estimates quadratic optimal control problems parabolic equations mixed finite element methods

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The parallel generation of 2-D Hilbert Space-filling Curve on GPU

The parallel generation of 2-D Hilbert Space-filling Curve o...

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201. 5th International Conference on Biomedical engineering and Informatics, BMEI 201.

作者： Feng, Chunsheng Shu, Shi Wang, Junxian Li, Zheng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan China

ISBN: (纸本)9781467311816

In this paper, we propose two parallel Hilbert Space-filling Curve(HSFC) generation algorithms BMIMp and SDDMp based on block matrix iteration method(BMIM) and state diagrams driver method(SDDM) in the CUDA parallel programming mode. Numerical results show that both of them obtain high parallel speedup. Especially, the speedup of BMIMp and SDDMp can reach 207 and 290 respectively for the 1.-order HSFC. Furthermore, BMIMp outperforms SDDMp when considering the total computation time. © 201. IEEE.

关键词： Iterative methods

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Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

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Advances in Applied Mathematics and Mechanics 2012年第6期4卷 751-768页

作者： Yanping Chen Tianliang Hou Weishan Zheng School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina

In this paper,we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control *** state and co-state are approximated by the lowest order Raviart-Thomas mixed fi-nite element spaces and the control variable is approximated by piecewise constant *** derive L^(2) and L^(∞)-error estimates for the control ***,using a recovery operator,we also derive some superconvergence results for the control ***,a numerical example is given to demonstrate the theoretical results.

关键词： Elliptic equations optimal control problems superconvergence error estimates mixed finite element methods

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Superconvergence and L^(∞)-Error Estimates of RT1.ixed Methods for Semilinear Elliptic Control Problems with an Integral Constraint

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Numerical Mathematics(Theory,Methods and Applications) 2012年第3期5卷 423-446页

作者： Yanping Chen Tianliang Hou School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina

In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral *** state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear *** derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant ***,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear ***,some numerical examples are given to demonstrate the theoretical results.

关键词： Semilinear elliptic equations optimal control problems superconvergence L∞-error estimates mixed finite element methods postprocessing

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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 Finite Element Variational Multiscale Method for Stationary Incompressible Magnetohydrodynamics Equations

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Advances in Applied Mathematics and Mechanics 2023年第5期15卷 1142-1165页

作者： Huayi Huang Yunqing Huang Qili Tang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of IntelligentComputing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China

In this paper,we propose a variational multiscale method(VMM)for the stationary incompressible magnetohydrodynamics *** method is defined by large-scale spaces for the velocity field and the magnetic field,which aims to solve flows at high Reynolds *** provide a new VMM formulation and prove its stability and ***,some numerical experiments are presented to indicate the optimal convergence of our method.

关键词： Variational multiscale method stationary incompressible magnetohydrodynamics large-scale spaces stability and convergence high Reynolds numbers

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An Iterative Two-Grid Method of A Finite Element PML Approximation for the Two Dimensional Maxwell Problem

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Advances in Applied Mathematics and Mechanics 2012年第2期4卷 175-189页

作者： Chunmei Liu Shi Shu Yunqing Huang Liuqiang Zhong Junxian Wang Hunan Key Laboratory for Computation&Simulation in Science and Engineering and Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education Xiangtan UniversityHunan 411105China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two ***,we use a fine space to solve a discrete saddle-point system of H(grad)variational problems,denoted by auxiliary system ***,we use a coarse space to solve the original saddle-point ***,we use a fine space again to solve a discrete H(curl)-elliptic variational problems,denoted by auxiliary system ***,we develop a regularization diagonal block preconditioner for auxiliary system 1.and use H-X preconditioner for auxiliary system *** we essentially transform the original problem in a fine space to a corresponding(but much smaller)problem on a coarse space,due to the fact that the above two preconditioners are efficient and *** with some existing iterative methods for solving saddle-point systems,such as PMinres,numerical experiments show the competitive performance of our iterative two-grid method.

关键词： Maxwell scattering edge finite element PML iterative two-grid method

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