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

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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Mineralization and osteoblast response to bioactive glass in vitro

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Journal of Medical engineering and Technology 2010年第4期34卷 285-290页

作者： Zhou, Z.H. Yi, Q.F. Nei, H.D. Ling, Y.L. Zhou, J.N. Liu, L.H. Liu, X.P. Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan China

Bioactive glass, an osteoproductive material, has received considerable attention as a bone graft substitute in the treatment of bony defects. Bioactive CaO-SiO2-P2O5 glass was prepared using the sol-gel method, and mineralization behaviour invitro was investigated by soaking it in simulated body fluid (SBF). Cellular cultivation invitro, MTT (3-(4,5-dimethylthiazol-2-yl)- 2,5-diphenyltetrazolium bromide) and Von Kossa assays were conducted to evaluate the osteoblast response to the bioactive glass. A calcium phosphate carbonate hydroxide (HCA) layer was formed on the bioactive glass after soaking for 3 days in SBF, which indicated that the mineralization on the surface of bioactive glass could progress spontaneously. The osteoblast response results demonstrated that bioactive glass had no cytotoxicity, and it might not be harmful to the morphology of the osteoblast. The growth and proliferation of the osteoblastic cell could not be inhibited. Nodule formation was also observed in conditioned medium containing dissolution bioactive glass and these nodules were shown to be mineralized by Von Kossa staining, which indicates that bioactive glass shows good biocompatibility. © 2010 Informa UK Ltd.

关键词： Biocompatibility

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On the vanishing dissipation limit for the incompressible MHD equations on bounded domains

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science China Mathematics 2022年第1期65卷 31-50页

作者： Qin Duan Yuelong Xiao Zhouping Xin Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China The Institute of Mathematical Sciences The Chinese University of Hong KongHong Kong 999077China

In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded *** the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating *** is shown that the initial boundary value problem has a global weak solution for a general smooth *** importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.

关键词： MHD equations initial boundary value problem vanishing dissipation limit

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Design of Multi-Coupled Laminates with Extension-Twisting Coupling for Application in Adaptive Structures

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Computer Modeling in engineering & sciences 2022年第1期130卷 415-441页

作者： Da Cui Daokui Li Shiming Zhou College of Aerospace Science and Engineering National University of Defense TechnologyChangsha410073China Hunan Key Laboratory of Intelligent Planning and Simulation for AerospaceMissions Changsha410073China

The multiple coupling of composite laminates has a unique advantage in improving the macro mechanical properties of composite structures.A total of three hygro-thermally stablemulti-coupled laminates with extensiontwisting coupling were presented,which were conducive to the formation of passive adaptive ***,the multi-coupled laminates were used to design the bending-twisting coupled box structure,in which the configuration of laminate and box structure could be extended to variable cross-section *** optimal design of stacking sequence was realized,the optimization objectives of which were to maximize bending-twisting coupling of box structure and extension-twisting coupling of laminate,*** effects of multiple coupling on hygro-thermal stability,coupling,failure strength,buckling load,robustness and other comprehensive mechanical properties of laminates and box structures were analyzed by parametric modeling *** results show that the extension-twisting coupling of laminate and the bending-twisting coupling of box structures can be greatly improved by 450%and 260%at maximum,***,it would have a negative impact on the failure strength and buckling load,which,however,can be minimized by a reasonable paving *** laminates have good robustness,and the bending-twisting coupling helps improve ***,the hygro-thermal stability and mechanical properties were verified by numerical simulation with finite element method.

关键词： Multi-coupled laminate passive adaptive structures optimal design mechanical properties numerical simulation

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3D simulation of Flow with Free Surface Based on Adaptive Octree Mesh System

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Transactions of Tianjin University 2015年第1期21卷 32-40页

作者：李绍武庄茜黄筱云王东 State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University Key Laboratory of Water-Sediment Science and Water Disaster Prevention of Hunan Province Changsha University of Science and Technology School of Civil Engineering Tianjin Chengjian University

The technique of adaptive tree mesh is an effective way to reduce computational cost through automatic adjustment of cell size according to necessity. In the present study, the 2D numerical N-S solver based on the adaptive quadtree mesh system was extended to a 3D one, in which a spatially adaptive oetree mesh system and multiple particle level set method were adopted for the convenience to deal with the air-water-structure multiple-medium coexisting domain. The stretching process of a dumbbell was simulated and the results indicate that the meshes are well adaptable to the free surface. The collapsing process of water column impinging a circle cylinder was simulated and from the results, it can be seen that the processes of fluid splitting and merging are properly simulated. The interaction of second-order Stokes waves with a square cylinder was simulated and the obtained drag force is consistent with the result by the Morison＇s wave force formula with the coefficient values of the stable drag component and the inertial force component bein~ set as 2.54.

关键词： adaptive octree mesh 3D numerical flume spatially adaptive multiple particle level set

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Shock wave and bubble characteristics of underwater array explosion of charges

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Defence Technology（防务技术） 2022年第8期18卷 1445-1453页

作者： Hong-Wei Hu Pu Song Shuang-feng Guo Hai-yun Feng Dao-kui Li College of Aerospace Science and Engineering National University of Defense TechnologyChangsha410073HunanChina Xi'an Modern Chemistry Research Institute Xi'an710065ShaanxiChina Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073HunanChina

In this study, we focused on the effect of the underwater explosion parameters of multi-point array explosion. The shock wave and bubble parameters of aggregate charge, two charges, and four charges were measured through an underwater explosion test, and their influence on the explosion power field of charge quantity and array distance was analyzed. Results show that the multi-shock wave collision of array explosion can be approximated to a linear superposition, and the interaction of delayed shock wave can be deemed as the increase of the shock wave baseline. Shock wave focusing and delayed superposition increase the shock wave peak pressure. Compared with the aggregate charge, the greater the number of array explosion points is, the higher the impulse and the gain of the bubble peak pressure are. At the same array distance, the smaller the charge quantity is, the higher the bubble impulse will be. At the same charge quantity, the smaller the array distance is, the higher the bubble impulse will be. The bubble period decreases gradually with the increase of the charge quantity, but the test orientation has little effect on the bubble period.

关键词： Explosion mechanics Underwater explosion Array explosion Shock waveBubble

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Enthalpies Estimation of Formation of Monosubstituted Alkanes by Interaction Potential Index

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Chinese Journal of Chemical Physics 2012年第2期25卷 153-160,I0003页

作者： Ya-xin Wu Chen-zhong Cao Hua Yuan School of Chemistry and Chemical Engineering Central South UniversityChangsha 410083China School of Chemistry and Chemical Engineering Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of EducationHunan University of Science and Technologyand Hunan Provincial University Key Laboratory of QSAR/QSPRXiangtan 411201China

The interaction potential index IPI（X） of 16 Br, C1, I, NO2, CN, CHO, COOH, CH3, CH： kinds of substituents X （X---OH, SH, NH2, ：CH2, C-CH, Ph, COCH3, COOCH3） were proposed, which are derived from the experimental enthalpies of formation △fHФ （g） values of monosubstituted straight-chain alkanes. Based on the IPI（X） and polarizability effect index, a simple and effective model was constructed to estimate the △fHФ （g） values of monosubstituted alkanes RX （including the branched derivatives）. The present model takes into account not only the contributions of the alkyl R and the substituent X, but also the contribution of the interaction between R and X. Its stability and prediction ability was confirmed by the results of leave-one-out method. Compared with previous reported studies, the obtained equation can be used to estimate enthalpies of formation for much more kinds of monosubstituted alkanes with less parameters. Thus, it is recommended for the calculation of the △fHФ（g） for the RX.

关键词： Interaction potential index Substituent Monosubstituted alkane Enthalpy offormation Polarizability effect index

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A review of space-object collision probability computation methods

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Astrodynamics 2022年第2期6卷 95-120页

作者： Jia-Sheng Li Zhen Yang Ya-Zhong Luo College of Aerospace Science and Engineering National University of Defense TechnologyChangsha 410073China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha 410073China

The collision probability computation of space objects plays an important role in space situational awareness,particularly for conjunction assessment and collision *** works mainly relied on Monte Carlo simulations to predict collision *** such simulations are accurate when a large number of samples are used,these methods are perceived as computationally intensive,which limits their application in *** overcome this limitation,many approximation methods have been developed over the past three *** paper presents a comprehensive review of existing space-object collision probability computation *** advantages and limitations of different methods are analyzed and a systematic comparison is *** regarding how to select a suitable method for different short-term encounter scenarios is then ***,potential future research avenues are discussed.

关键词： collision probability space situational awareness collision avoidance astrodynamics

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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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Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

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Advances in Applied Mathematics and Mechanics 2010年第1期2卷 56-75页

作者： Yanping Chen Li Dai Zuliang Lu School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdongChina Mathematics Teaching and Research Group Xiguan Foreign Language SchoolGuangzhouGuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtanHunanChina

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element *** use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control *** obtain the superconvergence of O(h^(1+s))(0

关键词： Constrained optimal control problem linear elliptic equation mixed finite element methods rectangular partition superconvergence properties

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