Advances in Studies and Applications of Centroidal Voronoi Tessellations  

作　　者：Qiang Du Max Gunzburger Lili Ju 

机构地区：[1]Department of Mathematics, Pennsylvania State University, University Park, PA16802, USA. [2]Department of Scientific Computing, Florida State University, Tallahassee, FL32306, USA. [3]Department of Mathematics, University of South Carolina, Columbia, SC29208,USA.

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2010年第2期119-142,共24页高等学校计算数学学报（英文版）

基　　金：supported by the US Department of Energy Office of Science Climate Change Prediction Program through grant numbers DE-FG02-07ER64431 and DE-FG02-07ER64432;the US National Science Foundation under grant numbers DMS-0609575 and DMS-0913491

摘　　要：Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating.Centroidal Voronoi tessellations （CVTs） have become a useful tool in many applications ranging from geometric modeling, image and data analysis, and numerical partial differential equations, to problems in physics, astrophysics, chemistry, and biology. In this paper, we briefly review the CVT concept and a few of its generalizations and well-known properties. We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs. Whenever possible, we point out some outstanding issues that still need investigating.

关 键 词：Voronoi tessellations CENTROIDS CLUSTERING mesh generation and optimization IMAGEPROCESSING model reduction point sampling. 

分 类 号：TP317[自动化与计算机技术—计算机软件与理论] P208[自动化与计算机技术—计算机科学与技术]