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Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

Communications in computational Physics 2022年第8期32卷 829-849页

作者： Xiaoqiang Yue Jianmeng He Xiaowen Xu Shi Shu Libo Wang 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 411105P.R.China Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100094P.R.China College of Information Science and Technology JinanUniversityGuangzhou 510632P.R.China

We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high *** this article,motivated by[***,***,***,SIAM *** ***.33(2012)653–680]and[***,***,***,***.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear ***,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

关键词： Radiation diffusion equations Schwarz methods algebraic multigrid parallel and distributed computing

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A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 57-86页

作者： Yin Yang Jianyong Tao Shangyou Zhang Petr V.Sivtsev 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 UniversityXiangtanHunan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing Ammosov North Eastern UniversityKulakovskogo677013YakutskRussia

In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.

关键词： The fractional Ginzburg-Landau equation Jacobi collocation method convergence

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Mathematical analysis of a PML model obtained with stretched coordinates and its application to backward wave propagation in metamaterials

Mathematical analysis of a PML model obtained with stretched...

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作者： Huang, Yunqing Li, Jichun Yang, Wei Hunan Key Laboratory for Computation and Simulation in Science Engineering Xiangtan University Hunan 411105 China Department of Mathematical Sciences University of Nevada Las Vegas Las Vegas NV 89154-4020 United States

We investigate the well-posedness of a perfectly matched layer model developed by Cohen and Monk [Comput Methods Appl Mech Eng 169 (1999), 197-217]. A new time-domain finite element method is proposed to solve the model. A novel feature of the scheme is that the number of unknowns is reduced to two from four in the original form. The scheme's effectiveness is demonstrated through numerical experiments. © 2013 Wiley Periodicals, Inc.

关键词： Maxwell equations

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Protein folding kinetic order prediction from amino acid sequence based on horizontal visibility network

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Current Bioinformatics 2016年第2期11卷 173-185页

作者： Zhao, Zhi-Qin Yu, Zu-Guo Anh, Vo Wu, Jing-Yang Han, Guo-Sheng Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University XiangtanHunan411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQ4001 Australia School of Science Xi’an Shiyou University 18 Second Dianzi Road Yanta District Xi’anShaanxi710065 China

Protein folding is one of the most important problems in molecular biology. The kinetic order of protein folding is one of the main aspects of the folding process. Previous methods for predicting protein folding kinetic order require to use the information on tertiary or predicted secondary structure of a protein. In this paper, based on physicochemical properties of amino acids, we propose an approach to predict the protein folding kinetic order from the primary structure of a protein using support vector machine combined with principal component analysis. The horizontal visibility network, Hilbert-Huang transform, global descriptor, and Lempel-Ziv complexity are used to extract features in our approach. To evaluate our approach, the leave-one-out cross-validation test is employed on two widely-used data sets ("IvankovData" and "ZhengData" data sets) consisting of two-state and multi-state proteins. The overall accuracies of prediction can reach 83.87% for "IvankovData" data set and 85% for "ZhengData" data set respectively. Comparisons with the existing methods show that the present approach performs better on the "IvankovData" data set. These results indicate that the present approach is effective and valuable for predicting protein folding kinetic order. Based on factor analysis, we find that the length of protein sequence, hydrophobicity and hydrophilicity of amino acids are important features in our approach. © 2016 Bentham science Publishers

关键词： Hilbert-Huang transform

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Quorum sensing regulation methods and their effects on biofilm in biological waste treatment systems: A review

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Frontiers of Environmental science & engineering 2022年第7期16卷 47-59页

作者： Zhuqiu Sun Jinying Xi Chunping Yang Wenjie Cong Environmental Simulation and Pollution Control State Key Joint Laboratory School of EnvironmentTsinghua UniversityBeijing100084China State Environmental Protection Key Laboratory of Microorganism Application and Risk Control(SMARC) Beijing100084China Guangdong Provincial Key Laboratory of Petrochemical Pollution Processes and Control School of Environmental Science and EngineeringGuangdong University of Petrochemical TechnologyMaoming525099China College of Environmental Science and Engineering Hunan University and Key Laboratory of Environmental Biology and Pollution Control(Hunan University)Ministry of EducationChangsha410082China

Quorum sensing (QS) plays an important role in microbial aggregation control. Recently, the optimization of biological waste treatment systems by QS regulation gained an increasing attention. The effects of QS regulation on treatment performances and biofilm were frequently investigated. To understand the state of art of QS regulation, this review summarizes the methods of QS enhancement and QS inhibition in biological waste treatment systems. Typical QS enhancement methods include adding exogenous QS molecules, adding QS accelerants and cultivating QS bacteria, while typical QS inhibition methods include additions of quorum quenching (QQ) bacteria, QS-degrading enzymes, QS-degrading oxidants, and QS inhibitors. The specific improvements after applying these QS regulation methods in different treatment systems are concluded. In addition, the effects of QS regulation methods on biofilm in biological waste treatment systems are reviewed in terms of biofilm formation, extracellular polymeric substances production, microbial viability, and microbial community. In the end, the knowledge gaps in current researches are analyzed, and the requirements for future study are suggested.

关键词： Quorum sensing Biological waste treatment Biofilm formation

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Spectral collocation method for a class of fractional diffusion differential equations with nonsmooth solutions

Spectral collocation method for a class of fractional diffus...

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作者： Wang, Junjie Xiao, Aiguo Bu, Weiping Hunan Key Laboratory for Computation and Simulation in Science and Engineering & Key Laboratory for Intelligent Computing and Information Processing of Education Ministry Xiangtan University Hunan China School of Mathematics and Statistics Pu'er University Yunnan China

In this paper, we develop spectral collocation method for a class of fractional diffusion differential equations. Since the solutions of these fractional differential equations usually exhibit singularities at the end-points, it can not be well approximated by classical polynomial basis functions. We first give nonclassical interpolants based on the associated Jacobi-Gauss points and obtain the corresponding fractional differentiation matrices. Second, we prove the convergence for the developed spectral collocation method. Finally, several numerical examples are considered to demonstrate the validity and applicability of the developed basis functions. © 2020 John Wiley & Sons, Ltd.

关键词： Polynomials

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Hybrid Allen-Cahn-based lattice Boltzmann model for incompressible two-phase flows: The reduction of numerical dispersion

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Physical Review E 2019年第2期99卷 023302-023302页

作者： Yang Hu Decai Li Licong Jin Xiaodong Niu Shi Shu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 People's Republic of China

In this work a phase field-lattice Boltzmann model for incompressible two-phase flows is presented. In this model, the interface tracking equation is a linear combination of the local and nonlocal Allen-Cahn equations. We also propose a multiple-relaxation-time lattice Boltzmann model for solving the hybrid Allen-Cahn equation. The second-order convergence rate of the present model in space is validated by simulating the diagonal translation of circular interface. Three other numerical tests, including static bubble immersed in another fluid, bubble rising under gravity, and droplet splashing on a thin liquid film, are simulated to verify the performance of the present model in reducing the numerical dispersion. The numerical results indicate that the order parameter fluctuation can be reduced by one order of magnitude in bulk region.

关键词： Multiphase flows Lattice-Boltzmann methods

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Two classes of implicit–explicit multistep methods for nonlinear stiff initial-value problems

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Applied Mathematics and computation 2014年 247卷 47-60页

作者： Aiguo Xiao Gengen Zhang Xing Yi School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China

The initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications. In order to reduce the computation cost, implicit–explicit (IMEX) methods are often applied to these problems, i.e. the stiff and non-stiff terms are discretized by using implicit and explicit methods, respectively. In this paper, we mainly consider the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems, and present two classes of the IMEX multistep methods by combining implicit one-leg methods with explicit linear multistep methods and explicit one-leg methods, respectively. The order conditions and the convergence results of these methods are obtained. Some efficient methods are constructed. Some numerical examples are given to verify the validity of the obtained theoretical results.

关键词： Stiff problems Singular perturbation problems Implicit–explicit multistep methods One-leg methods Linear multistep methods Convergence

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Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method

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Applied Mathematics 2013年第1期4卷 113-118页

作者： Yin Yang College of Civil Engineering and Mechanics Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.

关键词： Legendre Pseudo-Spectral Method Multi-Order Fractional Differential Equations Caputo Derivative

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Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes

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Numerical Mathematics(Theory,Methods and Applications) 2024年第1期17卷 210-242页

作者： Yu Xiong Yanping Chen Jianwei Zhou Qin Liang School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105P.R.China School of Mathematics and Statistics Linyi University Linyi 276005P.R.China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631P.R.China

In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal *** virtual element method is H1-conforming and exact *** virtue of these properties and the topological degree argument,we rigorously prove the well-posedness of the proposed discrete *** con-vergence analysis is carried out,which imply that the error estimate for the velocity in energy norm does not explicitly depend on the *** experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the asymptotic pressure robustness of the proposed scheme.

关键词： Optimal error estimates divergence-free virtual element nonlinear damping term.

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