Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important me...Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.展开更多
Compliance motion and footstep adjustment are active balance control strategies from learning human subconscious behaviors.The force estimation without direct end-actuator force measurement and the optimal footsteps b...Compliance motion and footstep adjustment are active balance control strategies from learning human subconscious behaviors.The force estimation without direct end-actuator force measurement and the optimal footsteps based on complex analytical calculation are still challenging tasks for elementary and kid-size position-controlled robots.In this paper,an online compliant controller with Gravity Projection Observer(GPO),which can express the external force condition of perturbations by the estimated Projection of Gravity(PoG)with estimation covariance,is proposed for the realization of disturbance absorption,with which the robustness of the humanoid contact with environments can be maintained.The fuzzy footstep planner based on capturability analysis is proposed,and the Model Predictive Control(MPC)is applied to generate the desired steps.The fuzzification rules are well-designed and give the corresponding control output responding to complex and changeable external disturbances.To validate the presented methods,a series of experiments on a real humanoid robot are conducted.The results verify the effectiveness of the proposed balance control framework.展开更多
This paper is concerned with a control problem of a diffusion process with the help of static mesh sensor networks in a certain region of interest and a team of networked mobile actuators carrying chemical neutralizer...This paper is concerned with a control problem of a diffusion process with the help of static mesh sensor networks in a certain region of interest and a team of networked mobile actuators carrying chemical neutralizers.The major contribution of this paper can be divided into three parts:the first is the construction of a cyber-physical system framework based on centroidal Voronoi tessellations(CVTs),the second is the convergence analysis of the actuators location,and the last is a novel proportional integral(PI)control method for actuator motion planning and neutralizing control(e.g.,spraying)of a diffusion process with a moving or static pollution source,which is more effective than a proportional(P)control method.An optimal spraying control cost function is constructed.Then,the minimization problem of the spraying amount is addressed.Moreover,a new CVT algorithm based on the novel PI control method,henceforth called PI-CVT algorithm,is introduced together with the convergence analysis of the actuators location via a PI control law.Finally,a modified simulation platform called diffusion-mobile-actuators-sensors-2-dimension-proportional integral derivative(Diff-MAS2D-PID)is illustrated.In addition,a numerical simulation example for the diffusion process is presented to verify the effectiveness of our proposed controllers.展开更多
Power图是带权重的Voronoi图,对Power图施加容量限制与质心限制,即可得到基于质心的容量限制Power图(Centroidal Capacity Constrained Power Diagram,CCCPD)。为解决现有CCCPD生成算法交替优化权重和站点位置带来的相互干扰、收敛减慢...Power图是带权重的Voronoi图,对Power图施加容量限制与质心限制,即可得到基于质心的容量限制Power图(Centroidal Capacity Constrained Power Diagram,CCCPD)。为解决现有CCCPD生成算法交替优化权重和站点位置带来的相互干扰、收敛减慢问题,提出对所有变量进行一体化优化的生成算法,采用多目标优化策略,直接优化质心限制和容量限制形成的混合能量。结果表明:所提算法的生成性能比传统方法提高40%。展开更多
In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustnes...In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.展开更多
This research work considers the following inequalities: <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,&l...This research work considers the following inequalities: <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) and <em>C</em>[<i>λ</i><em>a</em> + (1-<i>λ</i>)<em>b</em>, <i>λ</i><em>b</em> + (1-<i>λ</i>)<em>a</em>] ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <em>C</em>[<i>μ</i><em>a</em> + (1-<i>μ</i>)<em>b</em>, <i>μ</i><em>b</em> + (1-<i>μ</i>)<em>a</em>] with <img src="Edit_ce892b1d-c056-44ea-a929-31dbcd1b0e91.bmp" alt="" /> . The researchers attempt to find an answer as to what are the best possible parameters <i>λ</i>, <i>μ</i> that (1.1) and (1.2) can be hold? The main tool is the optimization of some suitable functions that we seek to find out. By searching the best possible parameters such that (1.1) and (1.2) can be held. Firstly, we insert <em>f</em>(<i>t</i>) = <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_efa43881-9a60-44f8-a86f-d4a1057f4378.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become f (<i>t</i>) ≤ 0. Secondly, we insert g(<i>t</i>) = <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_750dddbb-1d71-45d3-be29-6da5c88ba85d.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become <em>g</em>(<i>t</i>) ≥ 0.展开更多
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 Cen...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.展开更多
We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a...We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.展开更多
Most existing applications of centroidal Voronoi tessellations(CVTs) lack consideration of the length of the cluster boundaries.In this paper we propose a new model and algorithms to produce segmentations which would ...Most existing applications of centroidal Voronoi tessellations(CVTs) lack consideration of the length of the cluster boundaries.In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy—a sum of the classic CVT energy and the weighted length of cluster boundaries.To distinguish it with the classic CVTs,we call it an Edge-Weighted CVT(EWCVT).The concept of EWCVT is expected to build a mathematical base for all CVT related data classifications with requirement of smoothness of the cluster boundaries.The EWCVT method is easy in implementation,fast in computation,and natural for any number of clusters.展开更多
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 techn...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.展开更多
High quality mesh plays an important role for finite element methods in science computation and numerical simulation.Whether the mesh quality is good or not,to some extent,it determines the calculation results of the ...High quality mesh plays an important role for finite element methods in science computation and numerical simulation.Whether the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and efficiency.Different from classic Lloyd iteration algorithm which is convergent slowly,a novel accelerated scheme was presented,which consists of two core parts:mesh points replacement and local edges Delaunay swapping.By using it,almost all the equilateral triangular meshes can be generated based on centroidal Voronoi tessellation(CVT).Numerical tests show that it is significantly effective with time consuming decreasing by 40%.Compared with other two types of regular mesh generation methods,CVT mesh demonstrates that higher geometric average quality increases over 0.99.展开更多
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...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.展开更多
3D-power图在图形学和流体仿真等领域应用广泛。为解决已有的3D-power图计算方法时间性能较差的问题,提出了基于GPU的power图构造算法,给出了一种用于计算power图各区域之间的面积估值方法,使基于GPU的构造算法与Lloyd算法、牛顿法相结...3D-power图在图形学和流体仿真等领域应用广泛。为解决已有的3D-power图计算方法时间性能较差的问题,提出了基于GPU的power图构造算法,给出了一种用于计算power图各区域之间的面积估值方法,使基于GPU的构造算法与Lloyd算法、牛顿法相结合,生成满足约束条件的3D质心容量限制power图(3D-centroidal capacity constrained power diagram,3D-CCCPD)。结果表明,本文算法的时间性能较已有的3D-power图构造方法提高了几个数量级。展开更多
This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant sys...This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.展开更多
In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume a...In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.展开更多
Efficient data visualization techniques are critical for many scientific applications. Centroidal Voronoi tessellation(CVT) based algorithms offer a convenient vehicle for performing image analysis,segmentation and co...Efficient data visualization techniques are critical for many scientific applications. Centroidal Voronoi tessellation(CVT) based algorithms offer a convenient vehicle for performing image analysis,segmentation and compression while allowing to optimize retained image quality with respect to a given metric.In experimental science with data counts following Poisson distributions,several CVT-based data tessellation algorithms have been recently developed.Although they surpass their predecessors in robustness and quality of reconstructed data,time consumption remains to be an issue due to heavy utilization of the slowly converging Lloyd iteration.This paper discusses one possible approach to accelerating data visualization algorithms.It relies on a multidimensional generalization of the optimization based multilevel algorithm for the numerical computation of the CVTs introduced in[1],where a rigorous proof of its uniform convergence has been presented in 1-dimensional setting.The multidimensional implementation employs barycentric coordinate based interpolation and maximal independent set coarsening procedures.It is shown that when coupled with bin accretion algorithm accounting for the discrete nature of the data,the algorithm outperforms Lloyd-based schemes and preserves uniform convergence with respect to the problem size.Although numerical demonstrations provided are limited to spectroscopy data analysis,the method has a context-independent setup and can potentially deliver significant speedup to other scientific and engineering applications.展开更多
基金The National Natural Science Foundation of China under contract No.42076214.
文摘Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.
基金supported by the National Natural Science Foundation of China under Grants 62173248,62073245.
文摘Compliance motion and footstep adjustment are active balance control strategies from learning human subconscious behaviors.The force estimation without direct end-actuator force measurement and the optimal footsteps based on complex analytical calculation are still challenging tasks for elementary and kid-size position-controlled robots.In this paper,an online compliant controller with Gravity Projection Observer(GPO),which can express the external force condition of perturbations by the estimated Projection of Gravity(PoG)with estimation covariance,is proposed for the realization of disturbance absorption,with which the robustness of the humanoid contact with environments can be maintained.The fuzzy footstep planner based on capturability analysis is proposed,and the Model Predictive Control(MPC)is applied to generate the desired steps.The fuzzification rules are well-designed and give the corresponding control output responding to complex and changeable external disturbances.To validate the presented methods,a series of experiments on a real humanoid robot are conducted.The results verify the effectiveness of the proposed balance control framework.
基金supported by the National Natural Science Foundation of China(61473136,61807016)the Fundamental Research Funds for the Central Universities(JUSRP51322B)+1 种基金the 111 Project(B12018)Jiangsu Innovation Program for Graduates(KYLX15 1170)
文摘This paper is concerned with a control problem of a diffusion process with the help of static mesh sensor networks in a certain region of interest and a team of networked mobile actuators carrying chemical neutralizers.The major contribution of this paper can be divided into three parts:the first is the construction of a cyber-physical system framework based on centroidal Voronoi tessellations(CVTs),the second is the convergence analysis of the actuators location,and the last is a novel proportional integral(PI)control method for actuator motion planning and neutralizing control(e.g.,spraying)of a diffusion process with a moving or static pollution source,which is more effective than a proportional(P)control method.An optimal spraying control cost function is constructed.Then,the minimization problem of the spraying amount is addressed.Moreover,a new CVT algorithm based on the novel PI control method,henceforth called PI-CVT algorithm,is introduced together with the convergence analysis of the actuators location via a PI control law.Finally,a modified simulation platform called diffusion-mobile-actuators-sensors-2-dimension-proportional integral derivative(Diff-MAS2D-PID)is illustrated.In addition,a numerical simulation example for the diffusion process is presented to verify the effectiveness of our proposed controllers.
文摘Power图是带权重的Voronoi图,对Power图施加容量限制与质心限制,即可得到基于质心的容量限制Power图(Centroidal Capacity Constrained Power Diagram,CCCPD)。为解决现有CCCPD生成算法交替优化权重和站点位置带来的相互干扰、收敛减慢问题,提出对所有变量进行一体化优化的生成算法,采用多目标优化策略,直接优化质心限制和容量限制形成的混合能量。结果表明:所提算法的生成性能比传统方法提高40%。
基金partially supported by Ac RF RG40/12MOE2013-T2-2-011+2 种基金partially supported by National Natural Science Foundation of China (Nos. 61432003 and 61322206)the TNList Cross-discipline Foundationpartially supported by HKSAR Research Grants Council (RGC) General Research Fund (GRF), CUHK/14207414
文摘In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.
文摘This research work considers the following inequalities: <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) and <em>C</em>[<i>λ</i><em>a</em> + (1-<i>λ</i>)<em>b</em>, <i>λ</i><em>b</em> + (1-<i>λ</i>)<em>a</em>] ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <em>C</em>[<i>μ</i><em>a</em> + (1-<i>μ</i>)<em>b</em>, <i>μ</i><em>b</em> + (1-<i>μ</i>)<em>a</em>] with <img src="Edit_ce892b1d-c056-44ea-a929-31dbcd1b0e91.bmp" alt="" /> . The researchers attempt to find an answer as to what are the best possible parameters <i>λ</i>, <i>μ</i> that (1.1) and (1.2) can be hold? The main tool is the optimization of some suitable functions that we seek to find out. By searching the best possible parameters such that (1.1) and (1.2) can be held. Firstly, we insert <em>f</em>(<i>t</i>) = <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_efa43881-9a60-44f8-a86f-d4a1057f4378.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become f (<i>t</i>) ≤ 0. Secondly, we insert g(<i>t</i>) = <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_750dddbb-1d71-45d3-be29-6da5c88ba85d.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become <em>g</em>(<i>t</i>) ≥ 0.
基金supported in part by the NSFC Key Project(11031006)Hunan Provincial NSF Project(10JJ7001)+2 种基金supported in part by Hunan Education Department Key Project 10A117supported in part by NTU star-up grant M58110011,MOE RG 59/08 M52110092 and NRF 2007IDM-IDM 002-010,Singaporesupported partially by NSF DMS-0712744 and NSF DMS-1016073.
文摘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.
基金supported by the National Natural Science Foundation of China (No. 60773179)the National Basic Research Program (973) of China (No. 2004CB318000)
文摘We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.
基金supported in part by the U.S.National Science Foundation under grant number DMS-0913491.
文摘Most existing applications of centroidal Voronoi tessellations(CVTs) lack consideration of the length of the cluster boundaries.In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy—a sum of the classic CVT energy and the weighted length of cluster boundaries.To distinguish it with the classic CVTs,we call it an Edge-Weighted CVT(EWCVT).The concept of EWCVT is expected to build a mathematical base for all CVT related data classifications with requirement of smoothness of the cluster boundaries.The EWCVT method is easy in implementation,fast in computation,and natural for any number of clusters.
基金This work was supported by National Natural Science Foundation of China(No.61772243)Jiangsu Provincial Key Research and Development Program(BE2018108)Six talent peak high level talent plan projects of Jiangsu Province(XYDXX-115).
文摘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.
基金Project(11002121) supported by the National Natural Science Foundation of ChinaProject(09QDZ09) supported by Doctor Foundation of Xiangtan University, China+2 种基金Project(2009LCSSE11) supported by Hunan Key Laboratory for CSSE, ChinaProject(2011FJ3231) supported by Planned Science and Technology Project of Hunan Province,ChinaProject(12JJ3054) supported by the Provincial Natural Science Foundation of Hunan,China
文摘High quality mesh plays an important role for finite element methods in science computation and numerical simulation.Whether the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and efficiency.Different from classic Lloyd iteration algorithm which is convergent slowly,a novel accelerated scheme was presented,which consists of two core parts:mesh points replacement and local edges Delaunay swapping.By using it,almost all the equilateral triangular meshes can be generated based on centroidal Voronoi tessellation(CVT).Numerical tests show that it is significantly effective with time consuming decreasing by 40%.Compared with other two types of regular mesh generation methods,CVT mesh demonstrates that higher geometric average quality increases over 0.99.
基金supported by the U.S.Department of Energy under Award DE-SC-0001691support from the ORAU Ralph E.Powe Junior Faculty Enhancement Award and from the National Science Foundation under the grants DMS-1056821 and DMS-0915013.
文摘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.
文摘3D-power图在图形学和流体仿真等领域应用广泛。为解决已有的3D-power图计算方法时间性能较差的问题,提出了基于GPU的power图构造算法,给出了一种用于计算power图各区域之间的面积估值方法,使基于GPU的构造算法与Lloyd算法、牛顿法相结合,生成满足约束条件的3D质心容量限制power图(3D-centroidal capacity constrained power diagram,3D-CCCPD)。结果表明,本文算法的时间性能较已有的3D-power图构造方法提高了几个数量级。
基金supported in part by NSF grants #0552758,#0851709, and #0540179.
文摘This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.
基金supported by Singapore AcRF RG59/08 (M52110092)Singapore NRF 2007 IDM-IDM002-010.
文摘In this paper, we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh, the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho＇s conjecture. We show that the linear finite element solution uh and the linear interpolation uI have superclose gradient on Par6 meshes. Consequently, the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to Vu. A numerical example is presented to verify the theoretical result.
基金supported by the grants DMS 0405343 and DMR 0520425.
文摘Efficient data visualization techniques are critical for many scientific applications. Centroidal Voronoi tessellation(CVT) based algorithms offer a convenient vehicle for performing image analysis,segmentation and compression while allowing to optimize retained image quality with respect to a given metric.In experimental science with data counts following Poisson distributions,several CVT-based data tessellation algorithms have been recently developed.Although they surpass their predecessors in robustness and quality of reconstructed data,time consumption remains to be an issue due to heavy utilization of the slowly converging Lloyd iteration.This paper discusses one possible approach to accelerating data visualization algorithms.It relies on a multidimensional generalization of the optimization based multilevel algorithm for the numerical computation of the CVTs introduced in[1],where a rigorous proof of its uniform convergence has been presented in 1-dimensional setting.The multidimensional implementation employs barycentric coordinate based interpolation and maximal independent set coarsening procedures.It is shown that when coupled with bin accretion algorithm accounting for the discrete nature of the data,the algorithm outperforms Lloyd-based schemes and preserves uniform convergence with respect to the problem size.Although numerical demonstrations provided are limited to spectroscopy data analysis,the method has a context-independent setup and can potentially deliver significant speedup to other scientific and engineering applications.
