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A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations

Numerical Mathematics(Theory,Methods and Applications) 2022年第1期15卷 68-90页

作者： Guanrong Li Yanping Chen Yunqing Huang School of Mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048GuangdongP.R.China School of Mathematical Science South China Normal UniversityGuangzhou 510631GuangdongP.R.China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanP.R.China

In this paper,a robust modified weak Galerkin(MWG)finite element method for reaction-diffusion equations is proposed and *** advantage of this method is that it can deal with the singularly perturbed reaction-diffusion *** advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries *** is worth pointing out that,in our method,the test functions space is the same as the finite element space,which is helpful for the error *** error estimates are established for the corresponding numerical approximation in various *** numerical results are reported to confirm the theory.

关键词： Reaction-diffusion equations singular perturbation modified weak Galerkin finite element methods discrete gradient

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Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1440-1458页

作者： Xingfa Yang Yin Yang Yanping Chen Jie Liu State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan UniversityChangsha 410082HunanChina 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 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Center for Research on Leading Technology of Special Equipment School of Mechanical and Electric EngineeringGuangzhou UniversityGuangzhou 510006GuangdongChina

In this paper,we study a class of nonlinear fractional integro-differential equations,the fractional derivative is described in the Caputo *** the properties of the Caputo derivative,we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel,then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra *** provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.

关键词： Spectral method nonlinear fractional derivative Volterra integro-differential equations Caputo derivative

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Convergence Analysis for the Chebyshev Collocation Methods to Volterra Integral Equations with a Weakly Singular Kernel

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1506-1524页

作者： Xiong Liu Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtanHunan 411105China School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdong 510631China School of Mathematics and Statistics Lingnan Normal UniversityZhanjiangGuangdong 524048China

In this paper,a Chebyshev-collocation spectral method is developed for Volterra integral equations(VIEs)of second kind with weakly singular *** first change the equation into an equivalent VIE so that the solution of the new equation possesses better *** integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation *** convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials,approximation theory for orthogonal polynomials,and the operator *** spectral rate of convergence for the proposed method is established in the L^(∞)-norm and weighted L^(2)-*** results are presented to demonstrate the effectiveness of the proposed method.

关键词： Chebyshev collocation method Volterra integral equations spectral rate of convergence H¨older continuity

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Efficient Synthesis of Isoquinolines by AgNO3-Catalyzed Sequential Imination-Annulation of 2-Alkynyl Aldehydes with Ammonium Bicarbonate

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Chinese Journal of Chemistry 2016年第9期34卷 857-860页

作者： Yunhui Zhao Mingjian Luo Yubo Li Xiong Liu Zilong Tang Keqin Deng Gang Zhao Hunan Province College Key Laboratory of QSAR/QSPR School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan Hunan 411201 China Key Laboratory of Synthetic Chemistry of Natural Substances Shanghai Institute of Organic Chemistry Chinese Academy of Sciences Shanghai 200032 China Key Laboratory of Theoretical Chemistry and Molecular Simulation Ministry of Education Xiangtan Hunan 411201 China

An operationally simple approach for the tandem synthesis of isoquinolines by the reaction of o-alkynylalde- hydes with ammonium bicarbonate via Ag-catalyzed 6-endo-dig ring closure is described. The reaction conditions and the scope of the reaction are examined, and a variety of substituted isoquinolines are prepared in moderate to excellent yields.

关键词： isoquinolines annulation imination silver nitrate o-alkynyl aldehydes

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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

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Advances in Applied Mathematics and Mechanics 2023年第6期15卷 1631-1654页

作者： Jiaqi Zhang Yin Yang Zhaojie Zhou School of Mathematics and Computational Science Xiangtan UniversityHunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan 411105HunanChina School of Mathematics and Computational Science Xiangtan UniversityNational Center for Applied Mathematics in HunanHunan International Scientific and Technological Innovation Cooperation Base of Computational ScienceXiangtan 411105HunanChina School of Mathematics and Statistics Shandong Normal UniversityJinan 250014ShandongChina

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is *** deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is *** first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is *** experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

关键词： Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials

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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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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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Recent progress in quantifying substituent effects

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science China Chemistry 2013年第7期56卷 883-910页

作者： CAO ChenZhong WU YaXin Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Key Laboratory of QSAR/QSPR of Hunan Provincial University School of Chemistry and Chemical Engineering Hunan University of Science and Technology School of Chemistry and Chemical Engineering University of South China

This paper summarizes significant progress in quantifying organic substituent effects in the last 20 years. The main content is as follows：（1） The principle of electronegativity equalization has gained wide acceptance, and has been used to calculate the intramolecular charge distribution and inductive effect of groups. A valence electrons equalization method was proposed to compute the molecular electronegativity on the basis of geometric mean method, harmonic mean method, and weighted mean method. This new calculation method further extended the application of the principle of electronegativity equalization. （2） A scale method was established for experimentally determining the electrophilic and nucleophilic ability of reagents, in which benzhydryliumions and quinone methides were taken as the reference compounds, and the research field was extended to the gas phase conditions, organometallic reaction and radicals system. Moreover, the nucleophilicity parameters N and electro- philicity parameters E for a series of reagents were obtained. The definition and quantitative expression of electrophilicity in- dex co and nucleophilicity index co were proposed theoretically, and the correlation between the parameters from experimental determination and the indexes from theoretical calculation was also investigated. （3） The polarizability effect parameter was initially calculated by empirical method and further developed by quantum chemistry method. Recently, the polarizability ef- fect index of alkyl （PEI） and groups （PEIx） were proposed by statistical method, and got wide applications in explaining and estimating gas-phase acidity and basicity, ionization energy, enthalpy of formation, bond energy, reaction rate, water solubility and chromatographic retention for organic compounds. （4） The excited-state substituent constant Crcc obtained directly from the UV absorption energy data of substituted benzenes, is different from the polar constants in molecular ground state an

关键词： substituent effect electronic effect steric effect molecular equalized electronegativity electrophilicity index nucleo-philicity index polarizability effect parameter excited-state substituent constant steric shielding effect

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A two-dimensional numerical wave flume based on SA-MPLS method

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Acta Oceanologica Sinica 2012年第3期31卷 18-30页

作者： HUANG Xiaoyun LI Shaowu State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072China School of Hydraulic Engineering Changsha University of Science and TechnologyChangsha410114China Water&Sediment Science and Water Hazard Prevention Hunan Provincial Key Laboratory Changsha University of Science and TechnologyChangsha 410114China

A spatially adaptive (SA) two-dimensional (2-D) numerical wave flume is presented based on the quadtree mesh system,in which a new multiple particle level set (MPLS) method is proposed to solve the problem of interface tracking,in which common intersection may be traversed by multiple *** using the adaptive mesh technique and the MPLS method,mesh resolution is updated automatically with time according to flow characteristics in the modeling process with higher resolution around the free surface and the solid boundary and lower resolution in less important *** model has good performance in saving computer memory and CPU time and is validated by computational examples of small amplitude wave,second-order Stokes wave and cnoidal *** results also indicate that standing wave and wave overtopping are also reasonably simulated by the model.

关键词： spatially adaptive quadtree mesh system multiple particle level set method numerical wave flume

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DeePMD-kit v3: A Multiple-Backend Framework for Machine Learning Potentials

arXiv

引用

arXiv 2025年

作者： Zeng, Jinzhe Zhang, Duo Peng, Anyang Zhang, Xiangyu He, Sensen Wang, Yan Liu, Xinzijian Bi, Hangrui Li, Yifan Cai, Chun Zhang, Chengqian Du, Yiming Zhu, Jia-Xin Mo, Pinghui Huang, Zhengtao Zeng, Qiyu Shi, Shaochen Qin, Xuejian Yu, Zhaoxi Luo, Chenxing Ding, Ye Liu, Yun-Pei Shi, Ruosong Wang, Zhenyu Bore, Sigbjørn Løland Chang, Junhan Deng, Zhe Ding, Zhaohan Han, Siyuan Jiang, Wanrun Ke, Guolin Liu, Zhaoqing Lu, Denghui Muraoka, Koki Oliaei, Hananeh Singh, Anurag Kumar Que, Haohui Xu, Weihong Xu, Zhangmancang Zhuang, Yong-Bin Dai, Jiayu Giese, Timothy J. Jia, Weile Xu, Ben York, Darrin M. Zhang, Linfeng Wang, Han School of Artificial Intelligence and Data Science Unversity of Science and Technology of China Hefei China AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing China Baidu Inc. Beijing China Department of Computer Science University of Toronto TorontoON Canada Department of Chemistry Princeton University PrincetonNJ08540 United States University of Chinese Academy of Sciences Beijing100871 China State Key Laboratory of Physical Chemistry of Solid Surfaces iChEM College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China College of Integrated Circuits Hunan University Changsha410082 China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing Center for Smart Materials and Device Integration School of Material Science and Engineering Wuhan University of Technology Wuhan430070 China College of Science National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Extreme Matter and Applications National University of Defense Technology Changsha410073 China ByteDance Research Beijing100098 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China College of Materials Science and Opto-Electronic Technology University of Chinese Academy of Sciences Beijing100049 China Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education College of Chemistry Beijing Normal University Beijing100875 China Department of Geosciences Princeton University PrincetonNJ08544 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States IKKEM Fujian Xiamen361005 China Graduate

In recent years, machine learning potentials (MLPs) have become indispensable tools in physics, chemistry, and materials science, driving the development of software packages for molecular dynamics (MD) simulations and related applications. These packages, typically built on specific machine learning frameworks such as TensorFlow, PyTorch, or JAX, face integration challenges when advanced applications demand communication across different frameworks. The previous TensorFlow-based implementation of DeePMD-kit exemplified these limitations. In this work, we introduce DeePMD-kit version 3, a significant update featuring a multi-backend framework that supports TensorFlow, PyTorch, JAX, and PaddlePaddle backends, and demonstrate the versatility of this architecture through the integration of other MLPs packages and of Differentiable Molecular Force Field. This architecture allows seamless backend switching with minimal modifications, enabling users and developers to integrate DeePMD-kit with other packages using different machine learning frameworks. This innovation facilitates the development of more complex and interoperable workflows, paving the way for broader applications of MLPs in scientific research. Copyright © 2025, The Authors. All rights reserved.

关键词： Molecular dynamics

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