检索结果-内蒙古大学图书馆

An Augmented Two-Scale Finite Element Method for Eigenvalue Problems

Communications on Applied mathematics and Computation 2025年第2期7卷 663-688页

作者： Xiaoying Dai Yunyun Du Fang Liu Aihui Zhou LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049China School of Statistics and Mathematics Central University of Finance and EconomicsBeijing102206China

In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product *** a correction step,the augmented two-scale finite element solution is obtained by solving an eigenvalue problem on a low-dimensional augmented *** analysis and numerical experiments show that the augmented two-scale finite element solution achieves the same order of accuracy as the standard finite element solution on a fine grid,but the computational cost required by the former solution is much lower than that demanded by the *** augmented two-scale finite element method also improves the approximation accuracy of eigenfunctions in the L^(2)(Ω)norm compared with the two-scale finite element method.

关键词： Two-scale Finite element Augmented subspace method Eigenvalue problem Partial differential equation

来源：评论

学校读者我要写书评

暂无评论

A VARIATIONAL ANALYSIS FOR THE MOVING FINITE ELEMENT METHOD FOR GRADIENTFLOWS

引用

Journal of computational mathematics 2023年第2期41卷 191-210页

作者： Xianmin Xu LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow *** show that the discretized problem has the same energy dissipation structure as the continuous *** enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise *** show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to *** global minimizer,once it is detected by the discrete scheme,approximates the continuous stationary solution in optimal *** examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.

关键词： Moving finite element method Convergence analysis Onsager principle

来源：评论

学校读者我要写书评

暂无评论

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

引用

Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for Mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

来源：评论

学校读者我要写书评

暂无评论

METRICALLY REGULAR MAPPING AND ITS UTILIZATION TO CONVERGENCE ANALYSIS OF A RESTRICTED INEXACT NEWTON-TYPE METHOD

引用

Journal of computational mathematics 2022年第1期40卷 44-69页

作者： Mohammed Harunor Rashid Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Faculty of ScienceUniversity of RajshahiRajshahi-6205Bangladesh

In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed *** establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of ***,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically *** application of this method to variational inequality is *** addition,a numerical experiment is given which illustrates the theoretical result.

关键词： Generalized equation Restricted inexact Newton-type method Metrically regular mapping Partial Lipschitz-like mapping Semilocal convergence.

来源：评论

学校读者我要写书评

暂无评论

A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

引用

Communications on Applied mathematics and Computation 2023年第1期5卷 3-30页

作者： Kunlei Zhao Yulong Du Li Yuan State Key Laboratory of Scientific and Engineering Computing(LSEC)and Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beihang UniversityBeijing 100191China

In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

关键词： Global smoothness indicator Linear weights Sixth-order accuracy WENO

来源：评论

学校读者我要写书评

暂无评论

NVERSE CONDUCTIVITY PROBLEM WITH INTERNAL DATA

引用

Journal of computational mathematics 2023年第3期41卷 482-500页

作者： Faouzi Triki Tao Yin Laboratoire Jean Kuntzmann UMR CNRS 5224Université Grenoble-Alpes700 Avenue Centrale38401 Saint-Martin-d’HèresFrance Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of ScienceBeijing 100190China

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal *** problem finds applications in multi-wave imaging,greedy methods to approximate parameter-dependent elliptic problems,and image treatment with partial differential *** first show that the inverse problem for smooth coefficients can be rewritten as a linear transport *** that the coefficient is known near the boundary,we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin *** propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization *** finally provide numerical examples for the inversion assuming a lower regularity of the coefficient,and using synthetic data.

关键词： Inverse problems Multi-wave imaging Static transport equation Internal data Diffusion coeffcient Stability estimates Regularization

来源：评论

学校读者我要写书评

暂无评论

Rigorous biaxial limit of a molecular-theory-based two-tensor hydrodynamics

引用

Journal of Differential Equations 2023年第1期366卷 862-911页

作者： Li, Sirui Xu, Jie School of Mathematics and Statistics Guizhou University Guiyang 550025 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences Beijing China

We consider a two-tensor hydrodynamics derived from the molecular model, where high-order tensors are determined by closure approximation through the maximum entropy state or the quasi-entropy. We prove the existence and uniqueness of local in time smooth solutions to the two-tensor system. Then, we rigorously justify the connection between the molecular-theory-based two-tensor hydrodynamics and the biaxial frame hydrodynamics. More specifically, in the framework of Hilbert expansion, we show the convergence of the solution to the two-tensor hydrodynamics to the solution to the frame hydrodynamics. © 2023 Elsevier Inc.

关键词： Biaxial limit Frame hydrodynamics Liquid crystals Two-tensor hydrydynamics

来源：评论

学校读者我要写书评

暂无评论

DISCRETE ENERGY ANALYSIS OF THE THIRD-ORDER VARIABLE-STEP BDF TIME-STEPPING FOR DIFFUSION EQUATIONS

引用

Journal of computational mathematics 2023年第2期41卷 325-344页

作者： Hong-lin Liao Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

This is one of our series works on discrete energy analysis of the variable-step BDF *** this part,we present stability and convergence analysis of the third-order BDF(BDF3)schemes with variable steps for linear diffusion equations,see,e.g.,[SIAM ***.,58:2294-2314]and[***.,90:1207-1226]for our previous works on the BDF2 *** this aim,we first build up a discrete gradient structure of the variable-step BDF3 formula under the condition that the adjacent step ratios are less than 1.4877,by which we can establish a discrete energy dissipation ***-robust stability and convergence analysis in the L^(2) norm are then *** the mesh robustness means that the solution errors are well controlled by the maximum time-step size but independent of the adjacent time-step *** also present numerical tests to support our theoretical results.

关键词： Diffusion equations Variable-step third-order BDF scheme Discrete gradient structure Discrete orthogonal convolution kernels Stability and convergence

来源：评论

学校读者我要写书评

暂无评论

An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions

引用

Numerical mathematics(Theory,Methods and Applications) 2023年第2期16卷 410-432页

作者： Xiaoqiang Yue Zekai Zhang Xiaowen Xu Shuying Zhai Shi Shu National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100094China School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China.

The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the threedimensional multi-group radiation diffusion *** key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing *** spectral property of the preconditioned matrix is then *** practical strategy is considered sequentially and in ***,numerical results illustrate the numerical robustness,computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems,showing its competitiveness with many existing block preconditioners.

关键词： Radiation diffusion equations physical factorization preconditioning algebraic multigrid parallel and distributed computing

来源：评论

学校读者我要写书评

暂无评论

A Derivative-free Trust-region Method for Optimization on the Ellipsoid

A Derivative-free Trust-region Method for Optimization on th...

引用

2023 International Conference on Advances in Computer Science and engineering Technology, ACSE 2023

作者： Xie, Pengcheng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences ZhongGuanCun East Road No. 55 Beijing China

Optimization methods play a crucial role in various fields and applications. In some optimization problems, the derivative information of the objective function is unavailable. Such black-box optimization problems need to be solved by derivative-free optimization methods. At the same time, optimization problems with ellipsoidal constraints are important and have widespread applications in various fields as well. Following the development of the late professor M. J. D. Powell's efficient derivative-free trust-region optimization methods, this paper considers solving derivative-free optimization problems on the ellipsoid. Our new optimization solver EC-NEWUOA for problems on the ellipsoid in ., n is designed based on Powell's derivative-free software NEWUOA for unconstrained optimization problems. The proposed techniques for our new method mainly include using the Courant penalty function, the augmented Lagrangian method, and the projection technique. Details about the method and theoretical analysis are included in this paper. We also compare our new method with other algorithms by solving test problems and then show the numerical advantages of our new method. © Published under licence by IOP Publishing Ltd.

关键词： Lagrange multipliers

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：