用Voronoi图进行新型自然邻居插值的几何学方法与特性  

Geometric method and characteristic of a new natural neighbour interpolation using voronoi diagram

作　　者：周小平[1] 周瑞忠[1] 

机构地区：[1]福州大学土木建筑工程学院,福建福州350002

出　　处：《计算力学学报》2005年第3期355-359,共5页Chinese Journal of Computational Mechanics

基　　金：福建省自然科学基金(E0310011)资助项目.

摘　　要：新的基于Voronoi图的NaturalNeighbour插值是自然单元法的数学基础,也是一种新型的几何插值方法,具有与其他传统常用插值不同的构造方法,并表现出一定的优越性。本文介绍了基于NaturalNeighbour关系的Sibson插值和non-Sibsonian插值,并与有限元法和无单元法所用的插值方法,就离散插值方案和网格总体特性、形函数支撑域、本征边界条件、空间维数扩展与计算工作量等诸问题进行了比较分析。The Natural Neighbour interpolation based on Voronoi Diagram is the mathematical base of Natural Element Method (NEM), it is a new geometric interpolation method and to be constructed by a special procedure differences from traditional method, meanwhile it possesses some advantages. The Sibson interpolation and non-Sibnian interpolation based on Natural Neighbour relation are introduced, then the comparison about discrete scheme and general character of nets, support of shaping function, natural boundary condition, spatial dimensional extension and computing quantity, and etc. with FEM and EFG interpolation are studied.

关 键 词：自然单元法 自然邻居插值 Sibson插值 non—Sibsonian插值 VORONOI图 

分 类 号：O319.56[理学—一般力学与力学基础]