OPTIMAL DELAUNAY TRIANGULATIONS

作     者：LongChen Jin-chaoXu 

作者机构：MathematicsDepartmentThePennsylvaniaStateUniversityUniversityParkPA16802USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2004年第22卷第2期

页      面：299-308页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：美国国家科学基金 

主　　题：Delaunay triangulation Anisotropic mesh generation N term approximation Interpolation error Mesh quality Finite element 

摘      要：The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous *** an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring *** the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.