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Optimal convergence analysis of an energy dissipation property virtual element method for the nonlinear Benjamin-Bona-Mahony-Burgers equation

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Computers and Mathematics with Applications 2025年 192卷 37-53页

作者： Chen, Yanping Liu, Wanxiang Qin, Fangfang Liang, Qin School of Science Nanjing University of Posts and Telecommunications Nanjing210023 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China

A novel arbitrary high-order energy-stable fully discrete schemes are proposed for the nonlinear Benjamin-Bona-Mahony-Burgers equation based on linearized Crank-Nicolson scheme in time and the virtual element discretization in space. Two skew-symmetric discrete forms are introduced to preserve energy dissipation of the numerical scheme. Furthermore, by utilizing the L2 projection to approximate the nonlinear term and estimating the error of the discrete bilinear forms carefully, the optimal error estimate of the numerical scheme in the H1-norm is obtained. Finally, several numerical examples on various mesh types are provided to demonstrate the energy stability, optimal convergence and high efficiency of the method. © 2025 Elsevier Ltd

关键词： Convergence of numerical methods

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THE A POSTERIORI ERROR ESTIMATOR OF SDG METHOD FOR VARIABLE COEFFICIENTS TIME-HARMONIC MAXWELL'S EQUATIONS

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Journal of Computational Mathematics 2023年第2期41卷 263-286页

作者： Wei Yang Xin Liu Bin He Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Department of Mathematics Lanzhou Jiaotong UniversityLanzhou 730070China

In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the other is the residual-type *** first propose the curl-recovery method for the staggered discontinuous Galerkin method(SDGM),and based on the super-convergence result of the postprocessed solution,an asymptotically exact error estimator is *** residual-type a posteriori error estimator is also proposed,and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's *** efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.

关键词： Maxwell’s equations A posteriori error estimation Staggered discontinuous Galerkin

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Isotropic Cloak Materials Design Based on the Numerical Optimization Method of the Inverse Medium Problem

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 442-468页

作者： Wei Yang Tiancheng Wang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China

In recent years,various kinds of cloak devices were designed by transforma-tion optics,but these cloak metamaterials are anisotropic and difﬁcult to *** this paper,we designed the isotropic cloak metamaterials based on the numeri-cal method of the optimization theory to the inverse medium *** method has universality,and it is not limited by the shape and type of the cloak *** isotropic material is easier to manufacture in practice than anisotropic material.A large number of numerical results show the effectiveness of the method.

关键词： Inverse medium problem isotropic cloak materials ﬁnite element simulations.

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Fast solution to the free return orbit's reachable domain of the manned lunar mission by deep neural network

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Journal of Systems engineering and Electronics 2024年第2期35卷 495-508页

作者： YANG Luyi LI Haiyang ZHANG Jin ZHU Yuehe College of Aerospace Science and Engineering National University of Defense TechnologyChangsha 410073China China Astronauts Research and Training Center Beijing 100094China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha 410073China

It is important to calculate the reachable domain(RD)of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly evaluated and calculated via the classification and regression neural networks. An efficient databasegeneration method is developed for obtaining eight types of free return orbits and then the RD is defined by the orbit’s inclination and right ascension of ascending node(RAAN) at the perilune. A classify neural network and a regression network are trained respectively. The former is built for classifying the type of the RD, and the latter is built for calculating the inclination and RAAN of the RD. The simulation results show that two neural networks are well trained. The classification model has an accuracy of more than 99% and the mean square error of the regression model is less than 0.01°on the test set. Moreover, a serial strategy is proposed to combine the two surrogate models and a recognition tool is built to evaluate whether a lunar site could be reached. The proposed deep learning method shows the superiority in computation efficiency compared with the traditional double two-body model.

关键词： manned lunar mission free return orbit reachable domain(RD) deep neural network computation efficiency

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Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations

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Advances in Applied Mathematics and Mechanics 2022年第6期14卷 1276-1301页

作者： Hongliang Liu Yameng Zhang Haodong Li Shoufu Li School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical ***, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.

关键词： Canonical Euler splitting method nonlinear composite stiff functional differentialalgebraic equations stability convergence.

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Optimal Convergence Rate of q-Maruyama Method for StochasticVolterra Integro-Differential Equations with Riemann-Liouville Fractional Brownian Motion

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Advances in Applied Mathematics and Mechanics 2022年第1期14卷 202-217页

作者： Mengjie Wang Xinjie Dai Aiguo Xiao School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

This paper mainly considers the optimal convergence analysis of the q-Maruyama method for stochastic Volterra integro-differential equations(SVIDEs)driven by Riemann-Liouville fractional Brownian motion under the global Lipschitz and linear growth ***,based on the contraction mapping principle,we prove the well-posedness of the analytical solutions of the ***,we show that the q-Maruyama method for the SVIDEs can achieve strong first-order *** particular,when the q-Maruyama method degenerates to the explicit Euler-Maruyama method,our result improves the conclusion that the convergence rate is H+1/2,H∈(0,1/2)by Yang et al.,***.,383(2021),***,the numerical experiment verifies our theoretical results.

关键词： Stochastic Volterra integro-differential equations Riemann-Liouville fractional Brownian motion well-posedness strong convergence

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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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CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

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Journal of Computational Mathematics 2024年第1期42卷 49-70页

作者： Xiaojing Dong Yinnian He Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.

关键词： Partition of unity method Local and parallel algorithm Finite element method Iteration methods Magnetohydrodynamics

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A study on the effect of cylindrical shell scaled model size on ESCM prediction accuracy

A study on the effect of cylindrical shell scaled model size...

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2024 International Conference on Aerospace and Mechanics, ICAM 2024

作者： Du, Donghai Chen, Chen Wang, Jiachun Li, Daokui Zhou, Lilin College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China

Current research on similitude theory has introduced numerous methods to address the distortion similitude model. However, these methods still encounter some challenges in guiding the design of scale models, such as insufficient accuracy and a limited range of design sizes. In this paper, the Energy Similitude Correction Method (ESCM) is used to analyze the effect of size design on the accuracy of cylindrical shell-scaled models, taking into account distortion factors such as wall thickness and thermal environment. The research shows that the closer the model size is to the prototype size, the higher the prediction accuracy is. Additionally, larger size combinations are more reliable for predicting the prototype frequency in scaled model tests. The research results provide a basis for the reasonable design of the size of the scaled model group and make a positive contribution to improving the prediction accuracy of the scaled model. © 2024 Institute of Physics Publishing. All rights reserved.

关键词： Prediction models

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Multiscale Modeling with Online Correction for Darcy–Forchheimer Flow

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Lobachevskii Journal of Mathematics 2024年第11期45卷 5424-5436页

作者： Spiridonov, D.A. Huang, J. Laboratory of Computational Technologies and Artificial Intelligence North-Eastern Federal University Yakutsk 677000 Russian Federation School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Hunan Xiangtan 411105 China

Abstract: In this research, we present an algorithm of the Online generalized multiscale finite element method (Online GMsFEM) for Darcy–Forchheimer model in fractured media. The mathematical model describes a nonlinear Darcy flow with a high inertial effect and flow speed. The fine grid approximation is carried out by the finite element method (FEM) and to approximate lower dimensional fractures we use a discrete fracture model (DFM). We use a model reduction approach called Online GMsFEM, that is based on local residuals of coarse neighborhoods. The online multiscale basis functions are constructed in each local domain based on residuals. Such online multiscale basis functions make it possible take into account the effects of nonlinear coefficients in the Darcy–Forchheimer equation. We present numerical results in two-dimensional heterogeneous fractured domain. We investigate the accuracy of the method, depending on the influence of nonlinearity. The numerical experiments show that the Online GMsFEM has high accuracy for such nonlinear problems. The accuracy weakly depends on the magnitude of the nonlinear part of the equation. © Pleiades Publishing, Ltd. 2024.

关键词： Darcy–Forchheimer model discrete fracture model finite element method fractured domain multiscale model reduction nonlinear flow problem Online generalized multiscale finite element method

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