自然单元法研究进展

FSI

http://www.wanfangdata.com.cn/qi ... 004/0404/040402.htm

力学进展
ADVANCES IN MECHANICS
2004 Vol.34 No.4 P.437-445


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自然单元法研究进展


ADVANCES IN NATURAL ELEMENT METHOD

王兆清　 冯伟　

摘　要：自然单元法是一种基于Voronoi图和Delaunay三角化几何结构,以自然邻点插值为试函数的一种新型数值方法.其既具有无网格方法和经典有限元方法的优点,又克服了两者的一些缺陷,是一种发展前景广阔的求解微分方程的数值方法.自然单元法的形函数满足插值性质,可以像有限元法一样直接施加本质边界条件,不存在基于移动最小二乘拟合的无网格方法不能直接施加本质边界条件的难题.由于自然单元法是无网格方法,可以方便处理有限元方法较难处理的一些问题,例如移动边界和大变形等问题.自然单元法与其他数值方法的最根本区别于其插值格式的不同.将自然邻点插值用于Galerkin过程,就得到基于Voronoi结构的自然单元Galerkin法.自然邻点插值有自然邻点Sibson插值和Laplace插值(非Sibson插值)两种.Laplace插值比Sibson插值在计算上要简单的多,并且不论对凸的或非凸的区域都能精确施加本质边界条件.以Laplace插值为试函数的自然单元法在数值实施上比以Sibson插值为试函数的自然单元法简单.本文对基于Voronoi结构的自然邻点插值和自然单元法的基本思想作了介绍,综述了国内外关于自然单元法的研究成果,总结了自然单元法的优点和尚需解决的问题.
关键词：Voronoi图,Delaunay三角化,自然邻点插值,自然单元法




作者单位：王兆清（上海大学上海市应用数学与力学研究所,上海,200072）　
　　　　　冯伟（上海大学上海市应用数学与力学研究所,上海,200072）　

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收稿日期：2003年9月22日

修稿日期：2004年6月2日

出版日期：2004年11月25日

[ 本帖最后由 yejet 于 2006-11-3 21:23 编辑 ]

风花雪月

不错，找篇全文看看

sdjzu

本文作者可以提供pdf文件:lol

896092887

有熟悉自然单元法具体算法的没？:loveliness:

896092887

我用fortran编了一个搜索自然邻接点的小程序，感觉不太好
不知道那位高手能帮忙