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A PRIORI AND A POSTERIORI ERROR ESTIMATES OF A REALLY PRESSURE-ROBUST VIRTUAL ELEMENT METHOD FOR THE INCOMPRESSIBLE BRINKMAN PROBLEM

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arXiv 2024年

作者： Xiong, Yu Chen, Yanping School of Science Nanjing University of Posts and Telecommunications Nanjing210023 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the Raviart–Thomas element for the discretization on the right-hand side. The optimal priori error estimates are carried out, which imply the velocity error in the energy norm is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we implement effective mesh refinement strategies and develop a residual-type a posteriori error estimator. This estimator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method. Copyright © 2024, The Authors. All rights reserved.

关键词： Mesh generation

Review on analysis and control technology of curing residual stress in solid motor propellants

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Hangkong Xuebao/Acta Aeronautica et Astronautica Sinica 2025年第8期46卷

作者： Yu, Baoshi Lei, Yongjun Shen, Zhibin Zhang, Dapeng College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China Rocket Force University of Engineering Xi’an710025 China

A certain residual stress will accumulate during the curing and cooling process of Solid Rocket Motor （SRM）grain，which will affect the structural integrity of the SRM. Therefore，it is of great significance to analyze the Cure-induced Residual Stress（CRS）of the propellant grain and explore effective control methods for ensuring the reli⁃ ability of space vehicles and the safety of weapons and equipment. In this paper，the research progress on the gen⁃ eration mechanism，release method，detection technique and inversion prediction of the CRS of propellant grain is re⁃ viewed. This paper summarizes the current status and shortcomings of the structural integrity research of SRM，con⁃ sidering the CRS of propellant grain，as well as the development of its control methods and engineering applications. Based on the formation causes and release mechanism of the CRS and the release mechanisms in propellant grain structures，corresponding control methods and ideas for engineering application development are proposed. The analysis shows that the co-design method combining curing process control and structural configuration optimization can effectively control the CRS of the propellant grain，and establishing a standard test system is the key to validate the control method. © 2025 Chinese Society of Astronautics. All rights reserved.

关键词： Rocket engines

Investigation of double-gyroid grain boundaries beyond twinning

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arXiv 2024年

作者： Chen, Jing Sun, Zhangpeng Jiang, Kai Xu, Jie 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 Xiangtan411105 China Chinese Academy of Sciences Beijing China

We study four double-gyroid (DG) grain boundaries (GBs) with different orientations numerically using the Landau–Brazovskii free energy, including the (422) twin boundary studied recently, a network switching GB, and two tilt GBs. Topological variations and geometric deformations are investigated. It is found that deviations in strut lengths and dihedral angles from the bulk DG substantially exceed changes in strut angles and nodal coplanarity. We also examine the spectra along the contact plane of two grains and utilize them to evaluate the GB widths. Of the four GBs we study, the network switching GB changes to the least extent topologically and geometrically, meanwhile has the lowest energy and the smallest GB width. Copyright © 2024, The Authors. All rights reserved.

关键词： Grain boundaries

Local averaging type a posteriori error estimates for the nonlinear steady-state Poisson-Nernst-Planck equations

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arXiv 2020年

作者： Yang, Ying Shen, Ruigang Fang, Mingjuan Shu, Shi School of Mathematics and Computational Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin541004 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China School of Mathematics and Computational Science Guilin University of Electronic Technology GuilinGuangxi541004 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan411105 China

The a posteriori error estimates are studied for a class of nonlinear stead-state Poisson-Nernst-Planck equations, which are a coupled system consisting of the Nernst-Planck equation and the Poisson equation. Both the global upper bounds and the local lower bounds of the error estimators are obtained by using a local averaging operator. Numerical experiments are given to confirm the reliability and efficiency of the error estimators. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method

Error analysis of SAV finite element method to phase field crystal model

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arXiv 2019年

作者： Wang, Liupeng Huang, Yunqing Jiang, Kai School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan Hunan411105 China Key Laboratory of Ministry of Education for Intelligent Computing and Information Processing Xiangtan University Xiangtan Hunan411105 China

In this paper, we construct and analyze an energy stable scheme by combining the latest developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) for phase field crystal (PFC) model, and show rigorously that the scheme is first-order in time and second-order in space for the L2and H1 gradient ow equations. To reduce eficiently computational cost and capture accurately the phase interface, we give a simple adaptive strategy, equipped with a posteriori gradient estimator, i.e. L2norm of the recovered gradient. Extensive numerical experiments are presented to verify our theoretical results and to demonstrate the efiectiveness and accuracy of our proposed method. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Multifractal analysis and topological properties of a new family of weighted Koch networks

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Physica A: Statistical Mechanics and its Applications 2017年 469卷 695-705页

作者： Da-Wen Huang Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c ) in the limit of large generation t ; the second smallest eigenvalue μ 2 and the maximum eigenvalue μ n are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ 2 is approximately a quartic polynomial of c and μ n = 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c . We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.

关键词： Weighted Koch networks Modified sandbox algorithm Multifractal analysis Topological property

A novel genome signature based on inter-nucleotide distances profiles for visualization of metagenomic data

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Physica A: Statistical Mechanics and its Applications 2017年 482卷 87-94页

作者： Xian-Hua Xie Zu-Guo Yu Yuan-Lin Ma Guo-Sheng Han Vo Anh 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 Xiangtan Hunan 411105 China Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques Gannan Normal University Jiangxi 341000 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

There has been a growing interest in visualization of metagenomic data. The present study focuses on the visualization of metagenomic data using inter-nucleotide distances profile. We first convert the fragment sequences into inter-nucleotide distances profiles. Then we analyze these profiles by principal component analysis. Finally the principal components are used to obtain the 2-D scattered plot according to their source of species. We name our method as inter-nucleotide distances profiles (INP) method. Our method is evaluated on three benchmark data sets used in previous published papers. Our results demonstrate that the INP method is good, alternative and efficient for visualization of metagenomic data.

关键词： Alignment-free method Inter-nucleotide distance Metagenome Visualization

Adaptive tetrahedral mesh generation by constrained centroidal voronoi-delaunay tessellations for finite element methods

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Adaptive tetrahedral mesh generation by constrained centroid...

作者： Chen, Jie Huang, Yunqing Wang, Desheng Xie, Xiaoping School of Mathematics and Statistics Xi'An Jiaotong University Xi'an 710049 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411005 China Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637616 Singapore School of Mathematics Sichuan University Chengdu 610064 China

This article presents a tetrahedral mesh adaptivity algorithm for three-dimensional elliptic partial differential equations (PDEs) using finite element methods. The main issues involved are the mesh size and mesh quality, which have great influence on the accuracy of the numerical solution and computational cost. The first issue is addressed by a posteriori error estimator based on superconvergent gradient recovery. The second issue is solved by constrained centroidal Voronoi-Delaunay tessellations (CCVDT), which guarantees good quality tetrahedrons over a large class of mesh domains even, if the grid size varies a lot at any particular refinement level. The CCVDT enjoys the energy equidistribution property so that the errors are very well equidistributed with properly chosen sizing field (density function). And with this good property, a new refinement criteria is raised which is different from the traditional bisection refinement. © 2013 Wiley Periodicals, Inc.

关键词： Finite element method

computationally efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

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Physical Review E 2021年第4期103卷 043303-043303页

作者： Yuemin Ding Jin-Long Liu Xiaohui Li Yu-Chu Tian Zu-Guo Yu Department of Energy and Process Engineering Norwegian University of Science and Technology 7049 Trondheim Norway School of Computer Science Queensland University of Technology Brisbane QLD 4000 Australia Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China School of Information Science and Engineering Wuhan University of Science and Technology Wuhan Hubei 430081 China

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

关键词： Network formation & growth Fractals Fractal dimension characterization