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A Domain Decomposition Method for Nonconforming Finite Element Approximations of Eigenvalue Problems

Communications on Applied Mathematics and Computation 2025年第2期7卷 606-636页

作者： Qigang Liang Wei Wang Xuejun Xu School of Mathematical Science Tongji UniversityShanghai200092China Key Laboratory of Intelligent Computing and Applications(Tongji University) Ministry of EducationShanghai200092China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

Since the nonconforming finite elements(NFEs)play a significant role in approximating PDE eigenvalues from below,this paper develops a new and parallel two-level preconditioned Jacobi-Davidson(PJD)method for solving the large scale discrete eigenvalue problems resulting from NFE discretization of 2mth(m=1.2)order elliptic eigenvalue *** a spectral projection on the coarse space and an overlapping domain decomposition(DD),a parallel preconditioned system can be solved in each iteration.A rigorous analysis reveals that the convergence rate of our two-level PJD method is optimal and *** results supporting our theory are given.

关键词： PDE eigenvalue problems Nonconforming finite elements(NFEs) Preconditioned Jacobi-Davidson(PJD)method Overlapping domain decomposition(DD)

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A Network Deception Defense Mechanism Based on Virtual Topology Generation

A Network Deception Defense Mechanism Based on Virtual Topol...

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2023 International Conference on Intelligent Systems, Communications, and Computer Networks, ISCCN 2023

作者： Wang, Binghui Lu, Bin State Key Laboratory of Mathematical Engineering and Advanced Computing Information Engineering University Zhengzhou China

ISBN: (纸本)9781510666238

To address the problem that traditional network defense techniques are difficult to cope with scanning attacks launched by internal attackers, this paper proposes a Virtual Network Topology Deception Defense mechanism(VNTDD)based on the idea of deception defense. In order to solve the problem of lack of randomness and security of virtual network topology, we divide the virtual network topology into three categories: forwarding nodes, real nodes and virtual nodes, and analyze their deployment locations and numbers respectively to generate a random virtual network topology, and enables the deployment of virtual network topology on the underlying real network through traffic control mechanisms. Finally, through experimental analysis, the VNTDD deception defense mechanism proposed in this paper can effectively prolong the scanning process of the intranet by internal attackers. © 2023 SPIE. All rights reserved.

关键词： Topology

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RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-state Problems on Triangular Meshes

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Communications on Applied Mathematics and Computation 2024年第3期6卷 1575-1599页

作者： Jun Zhu Chi-Wang Shu Jianxian Qiu State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005FujianChina

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

关键词： RKDG method Steady-state problem Multi-resolution WENO limiter Triangular mesh Machine zero

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LF-PGVIO: A Visual-Inertial-Odometry Framework for Large Field-of-View Cameras using Points and Geodesic Segments

IEEE Transactions on Intelligent Vehicles

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IEEE Transactions on Intelligent Vehicles 2024年 1-13页

作者： Wang, Ze Yang, Kailun Shi, Hao Zhang, Yufan Xu, Zhijie Gao, Fei Wang, Kaiwei State Key Laboratory of Extreme Photonics and Instrumentation School of Robotics and the National Engineering Research Center of Robot Visual Perception and Control Technology Hunan University Changsha China School of Computing and Engineering University of Huddersfield Huddersfield U.K State Key Laboratory of Industrial Control Technology Zhejiang University Hangzhou China

In this paper, we propose LF-PGVIO, a Visual-Inertial-Odometry (VIO) framework for large Field-of-View (FoV) cameras with a negative plane using points and geodesic segments. The purpose of our research is to unleash the potential of point-line odometry with large-FoV omnidirectional cameras, even for cameras with negative-plane FoV. To achieve this, we propose an Omnidirectional Curve Segment Detection (OCSD) method combined with a camera model which is applicable to images with large distortions, such as panoramic annular images, fisheye images, and various panoramic images. The geodesic segment is sliced into multiple straight-line segments based on the radian and descriptors are extracted and recombined. Descriptor matching establishes the constraint relationship between 3D line segments in multiple frames. In our VIO system, line feature residual is also extended to support large-FoV cameras. Extensive evaluations on public datasets demonstrate the superior accuracy and robustness of LF-PGVIO compared to state-of-the-art methods. The source code will be made publicly available at https://***/flysoaryun/LF-PGVIO. IEEE

关键词： Feature extraction

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Theoretical analysis of the elastic Kelvin-Helmholtz instability in explosive weldings

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Defence Technology（防务技术） 2024年第2期32卷 521-528页

作者： Yuanbo Sun Jianning Gou Cheng Wang Qiang Zhou Rui Liu Pengwan Chen Tonghui Yang Xiang Zhao State Key Laboratory of Explosion Science and Technology Beijing Institute of TechnologyBeijing100081China Beijing HIWING Scientific and Technological Information Institute Beijing100084China School of Aerospace Engineering Tsinghua UniversityBeijing100084China

By considering the joint effects of the Kelvin-Helmholtz(KH) and Rayleigh-Taylor(RT) instabilities, this paper presents an interpretation of the wavy patterns that occur in explosive welding. It is assumed that the elasticity of the material at the interface effectively determines the wavelength, because explosive welding is basically a solid-state welding process. To this end, an analytical model of elastic hydrodynamic instabilities is proposed, and the most unstable mode is selected in the solid phase. Similar approaches have been widely used to study the interfacial behavior of solid metals in high-energy-density physics. By comparing the experimental and theoretical results, it is concluded that thermal softening,which significantly reduces the shear modulus, is necessary and sufficient for successful welding. The thermal softening is verified by theoretical analysis of the increase in temperature due to the impacting and sliding of the flyer and base plates, and some experimental observations are qualitatively *** summary, the combined effect of the KH and RT instabilities in solids determines the wavy morphology, and our theoretical results are in good qualitative agreement with experimental and numerical observations.

关键词： Explosive welding Hydrodynamic instabilities Elasticity

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Research on performance optimization of virtual data space across WAN

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Frontiers of Computer Science 2024年第6期18卷 167-187页

作者： Jiantong HUO Zhisheng HUO Limin XIAO Zhenxue HE State Key Laboratory of Software Development Environment Beihang UniversityBeijing 100191China School of Computer Science and Engineering Beihang UniversityBeijing 100191China High Performance Computing Center Beihang UniversityBeijing 100191China Hebei Key Laboratory of Agricultural Big Data Hebei Agricultural UniversityBaoding 071001China

For the high-performance computing in a WAN environment,the geographical locations of national supercomputing centers are scattered and the network topology is complex,so it is difficult to form a unified view of *** aggregate the widely dispersed storage resources of national supercomputing centers in China,we have previously proposed a global virtual data space named GVDS in the project of“High Performance computing Virtual Data Space”,a part of the National key Research and Development Program of *** GVDS enables large-scale applications of the high-performance computing to run efficiently across ***,the applications running on the GVDS are often data-intensive,requiring large amounts of data from multiple supercomputing centers across *** this regard,the GVDS suffers from performance bottlenecks in data migration and access across *** solve the above-mentioned problem,this paper proposes a performance optimization framework of GVDS including the multitask-oriented data migration method and the request access-aware IO proxy resource allocation *** a WAN environment,the framework proposed in this paper can make an efficient migration decision based on the amount of migrated data and the number of multiple data sources,guaranteeing lower average migration latency when multiple data migration tasks are running in *** addition,it can ensure that the thread resource of the IO proxy node is fairly allocated among different types of requests(the IO proxy is a module of GVDS),so as to improve the application’s performance across *** experimental results show that the framework can effectively reduce the average data access delay of GVDS while improving the performance of the application greatly.

关键词： storage aggregation across WANs large-scale applications GVDS data migration allocation of IO proxy resource

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The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation

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Science China Mathematics 2024年第5期67卷 975-1010页

作者： Qi Qiao Xiang Zhang School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Scientific and Engineering Computing(Ministry of Education) and Shanghai Frontier Science Center of Modern Analysis(CMA-Shanghai)Shanghai Jiao Tong UniversityShanghai 200240China

For a coupled slow-fast FitzHugh-Nagumo(FHN)equation derived from a reaction-diffusionmechanics(RDM)model,Holzer et al.(2013)studied the existence and stability of the travelling pulse,which consists of two fast orbit arcs and two slow ones,where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve *** and Zhang(2021)obtained the existence of the travelling pulse,whose two fast orbit arcs both exponentially decrease,and one of the slow orbit arcs could be normally hyperbolic or not at the ***,we characterize both the nonlinear and spectral stability of this travelling pulse.

关键词： coupled FitzHugh-Nagumo equation singular perturbation travelling pulse spectrum nonlinear stability spectral stability

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SHARP POINTWISE-IN-TIME ERROR ESTIMATE OF L1 SCHEME FOR NONLINEAR SUBDIFFUSION EQUATIONS

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Journal of Computational Mathematics 2024年第3期42卷 662-678页

作者： Dongfang Li Hongyu Qin Jiwei Zhang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial *** weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1)∪(1,2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion *** present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

关键词： Sharp pointwise-in-time error estimate Ll scheme Nonlinear subdiffusion equations Non-smooth solutions

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MC-Nonlocal-PINNs:Handling Nonlocal Operators in PINNs Via Monte Carlo Sampling

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Numerical Mathematics(Theory,Methods and Applications) 2023年第3期16卷 769-791页

作者： Xiaodong Feng Yue Qian Wanfang Shen Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina Shandong Key Laboratory of Blockchain Finance Shandong University of Finance and EconomicsJinan 250014China

We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral equations and nonlocal *** to MC-fPINNs,our MC-Nonlocal-PINNs handle nonlocal operators in a Monte Carlo way,resulting in a very stable approach for high dimensional *** present a variety of test problems,including high dimensional Volterra type integral equations,hypersingular integral equations and nonlocal PDEs,to demonstrate the effectiveness of our approach.

关键词： Nonlocal models PINNs Monte Carlo sampling deep neural networks

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Recent advances in hybrid water electrolysis for energy-saving hydrogen production

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Green Chemical engineering 2023年第1期4卷 17-29页

作者： Di Li Jibing Tu Yingying Lu Bing Zhang State Key Laboratory of Chemical Engineering Institute of Pharmaceutical EngineeringCollege of Chemical and Biological EngineeringZhejiang UniversityHangzhou310027China ZJU-Hangzhou Global Scientific and Technological Innovation Center Hangzhou311215China

Electricity-driven water splitting to convert water into hydrogen(H_(2)has been widely regarded as an efficient approach for H_(2)***,the energy conversion efficiency of it is greatly limited due to the disadvantage of the sluggish kinetic of oxidation evolution reaction(OER).To effectively address the issue,a novel concept of hybrid water electrolysis has been developed for energy–saving H_(2)*** strategy aims to replace the sluggish kinetics of OER by utilizing thermodynamically favorable organics oxidation reaction to replace ***,recent advances in such water splitting system for boosting H_(2)evolution under low cell voltage are systematically *** notable progress of different organics oxidation reactions coupled with hydrogen evolution reaction(HER)are discussed in *** facilitate the development of hybrid water electrolysis,the major challenges and perspectives are also proposed.

关键词： Hydrogen evolution reaction Hybrid water electrolysis Electrocatalytic oxidation Organic electro-oxidation High-value products

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