自然单元法原理与三维算法实现  

The Natural Element Method and Its Computational Algorithms in Three Dimensions

作　　者：戴斌[1] 王建华[1] 

机构地区：[1]上海交通大学土木工程系,上海200030

出　　处：《上海交通大学学报》2004年第7期1222-1224,1228,共4页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金资助项目 ( 5 98790 12 )

摘　　要：自然单元法是一种新兴的无网格数值计算方法 ,其实质是基于自然相邻插值 ( C∞ )的伽辽金法 .文中推导了基于 Lasserre凸多面体体积公式的三维自然邻结点坐标及其导数的算法 ,给出了三维自然单元法算法的流程图 .该算法实际上可以用于任意维数的自然单元法计算 .对于Lasserre算法带来的多余约束问题 ,提出了 2种可行的解决算法 .经验证算例 。Natural element method(NEM) is a recently developed meshless method and is essentially the Galerkin method based on natural neighbour interpolation. The algorithm for calculating natural neighbour co-ordinates and their derivatives based on Lasserre's algorithm for the volume of a convex polyhedron was derived and the generalized flowchart for NEM in 3D case was presented. The algorithm can be applied to NEM in any dimensions case in fact. Two algorithms to solve the redundant constraint problem lying in Lasserre's algorithm were also presented. The example's numerical results are equal to the results of hexahedral finite element method.

关 键 词：自然单元法 自然相邻插值 DELAUNAY三角化 伽辽金法 

分 类 号：O242.21[理学—计算数学]