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Convergent Adaptive Finite Element Method Based on centroidal voronoi tessellations and Superconvergence

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 recovery.The constructions of CVT and its dual centroidal voronoi Delaunay Triangulation(CVDT)are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes.Working 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 obtained.Through a seamless integration of these techniques,a convergent adaptive procedure is developed.As 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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Truncated Newton-Based Multigrid Algorithm for centroidal voronoi Diagram Calculation

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Numerical Mathematics(Theory,Methods and Applications) 2012年第2期5卷 242-259页

作者： Zichao Di Maria Emelianenko Stephen Nash Department of Mathematical Sciences George Mason UniversityFairfaxVA 22030USA. Systems Engineering and Operations Research Department George Mason UniversityFairfaxVA 22030USA

In a variety of modern applications there arises a need to tessellate the domain into representative regions,called voronoi cells.A particular type of such tessellations,called centroidal voronoi tessellations or CVTs,are in big demand due to their optimality properties important for many applications.The availability of fast and reliable algorithms for their construction is crucial for their successful use in practical settings.This paper introduces a new multigrid algorithm for constructing CVTs that is based on the MG/Opt algorithm that was originally designed to solve large nonlinear optimization problems.Uniform convergence of the new method and its speedup comparing to existing techniques are demonstrated for linear and nonlinear densities for several 1d and 2d problems,and O(k)complexity estimation is provided for a problem with k generators.

关键词： centroidal voronoi tessellation optimal quantization truncated Newton method Lloyd’s algorithm multilevel method uniform convergence

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LED Adaptive Deployment Optimization in Indoor VLC Networks

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China Communications 2021年第6期18卷 201-213页

作者： Jiangtao Li Xu Bao Wence Zhang School of Computer Science and Communication Engineering Jiangsu UniversityZhenjiang 212013China

Driven by the continuous penetration of high data rate services and applications,a large amount of unregulated visible light spectrum is used for communication to fully meet the needs of 6th generation(6G)mobile technologies.Visible light communication(VLC)faces many challenges as a solution that complements existing radio frequency(RF)networks.This paper studies the optimal configuration of LEDs in indoor environments under the constraints of illumination and quality of experience(QoE).Based on the voronoi tessellation(VT)and centroidal voronoi tessellation(CVT)theory,combined with the Lloyd’s algorithm,we propose two approaches for optimizing LED deployments to meet the illumination and QoE requirements of all users.Focusing on(i)the minimization of the number of LEDs to be installed in order to meet illumination and average QoE constraints,and(ii)the maximization of the average QoE of users to be served with a fixed number of LEDs.Monte Carlo simulations are carried out for different user distribution compared with hexagonal,square and VT deployment.The simulation results illustrate that under the same conditions,the proposed deployment approach can provide less LEDs and achieve better QoE performance.

关键词： visible light communication lightemitting diodes centroidal voronoi tessellation quality of experience optimal deployment

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A RBNN BASED RESPONSE SURFACE CONSTRUCTION METHOD FOR MECHANICAL SYSTEMS

A RBNN BASED RESPONSE SURFACE CONSTRUCTION METHOD FOR MECHAN...

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2007中国宁波国际计算机科学与技术学术大会

作者： Ren Yuan Bai Guangchen School of Jet Propulsion Beijing University of Aeronautics ＆ Astronautics

ISBN: (纸本)9780972147903

Response surface functions are often used as simple replacements for computationally expensive computer models of mechanical systems over some parameter space.A response surface construction method based on radial basis neural networks（RBNN） was developed.Two kinds of RBNN were investigated.They are the exact design network（EDN） and the generalized regression network（GRN）.The developed method was compared with the polynomial regression model（PRM） in two example problems.The centroidal voronoi tessellation（CVT）experimental design was used.It was found that both of the two RBNN methods produced smaller errors for a given set of sample points than the PRM method.The EDN method was the most accurate method for the example problems studied.The GRN method,while better than the PRM,still did not perform as well as the EDN method.Compared with the commonly used PRM method,the suggested approach is a better choice to construct a response surface for a mechanical system.

关键词： Response surface Radial basis neural networks Mechanical systems Polynomial regression centroidal voronoi tessellation

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