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Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities

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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 101-118页

作者： Hongliang Liu Jingwen Song Huini Liu Jie Xu Lijuan Li School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China School of Automation and Electronic Information Xiangtan UniversityXiangtanHunan 411105China

In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak ***,the solution interval is divided into multiple subintervals by weak discontinuity ***,Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each ***,the parameters of the neural network are obtained by training with the extreme learning *** numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.

关键词： Convergence delay differential-algebraic equations Legendre activation function,neural network.

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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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Analysis of a two-grid method for semiconductor device problem

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Applied Mathematics and Mechanics(English Edition) 2021年第1期42卷 143-158页

作者： Ying LIU Yanping CHEN Yunqing HUANG Qingfeng LI School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105Hunan ProvinceChina College of Information and Intelligence Hunan Agricultural UniversityChangsha 410128China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin *** estimate the error of the numerical solutions in the sense of the *** linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton *** main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine *** estimation for the two-grid solutions is analyzed in *** is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.

关键词： two-grid method semiconductor device mixed finite element method Galerkin method L^q error estimate

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PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS

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Journal of computational Mathematics 2006年第5期24卷 657-664页

作者： Yun-qing Huang Shi Shu Xi-jun Yu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 411105 China Laboratory of Computational Physics Institute of Applied physics and Computational Mathematics Beijing 100088 China

We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.

关键词： Finite element Algebraic multigrid methods Preconditioned Conjugate Gradient Condition number.

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Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1327-1343页

作者： Bo Tang Yunqing Huang Ning Dong School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan UniversityXiangtan 411105HunanChina School of Science Hunan City UniversityYiyang 413000HunanChina School of Science Hunan University of TechnologyZhuzhou 412000HunanChina

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with *** is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley *** this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special ***,the doubling algorithm based on the proposed generalized transformation is presented and shown to be ***,the convergence result and the comparison theorem on convergent rate are *** numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

关键词： Shift-and-shrink transformation generalized Cayley transformation doubling algorithm nonsymmetric algebraic Riccati equation

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Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations

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Mathematics and Computers in simulation 2023年第1期212卷 289-309页

作者： Wang, Qi Xiang, Kainan Zhu, Chunhui Zou, Lang Hunan Key Laboratory for Computation and Simulation in Science and Engineering & Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education & School of Mathematics and Computational Science Xiangtan University Hunan Province Xiangtan City411105 China National Center for Applied Mathematics in Hunan China

This article introduces a kind of stochastic SEIR models containing virus mutation and logistic growth of susceptible populations, whose deterministic versions have a positively invariant set and globally asymptotically stable equilibrium points. For these stochastic SEIR epidemic models, we prove they have a unique global positive solution, and also obtain sufficient conditions respectively for survival and extinction of the infectious disease. Eventually, we validate our theoretical findings using numerical simulations. © 2023 International Association for Mathematics and Computers in simulation (IMACS)

关键词： Viruses

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Lower Bounds for Eigenvalues of the Stokes Operator

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Advances in Applied Mathematics and Mechanics 2013年第1期5卷 1-18页

作者： Jun Hu Yunqing Huang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China

In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconformin... 详细信息

关键词： Lower bound eigenvalue Stokes operator

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The correction operator for the canonical interpolation operator of the Adini element and the lower bounds of eigenvalues

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science China Mathematics 2012年第1期55卷 187-196页

作者： HU Jun HUANG YunQing LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871Chinal Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China

In this paper,we develop a correction operator for the canonical interpolation operator of the Adini *** use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three *** prove that the discrete eigenvalues are smaller than the exact ones.

关键词： the lower bound the Adini element the eigenvalue problem

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A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation

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International Journal of Modeling, simulation, and Scientific Computing 2020年第2期11卷 115-132页

作者： Yaping Zhang Jiliang Cao Weiping Bu Aiguo Xiao School of Mathematics and Computational Science and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University 411105 HunanP.R.China College of Science Shaoyang University 422000 ShaoyangP.R.China

In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial time.A fast evaluation of the distributedorder time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the *** stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are *** the spatial approximation,the finite element method is *** convergence of the corresponding fully discrete scheme is ***,some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

关键词： Distributed-order fractional derivative fractional reaction-diffusion equation fast evaluation graded mesh finite element method error estimate

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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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