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图论在有限元节点标号优化问题上的应用

刘贞荣   

  1. 中国科学院工程力学研究所
  • 出版日期:1981-03-20 发布日期:1981-03-20

刘贞荣. 图论在有限元节点标号优化问题上的应用[J]. 数值计算与计算机应用, 1981, 2(3): 129-137.

APPLICATION OF GRAPH THEORY TO OPTIMIZATION OF NODAL NUMBERING FOR A FINITE ELEMENT SYSTEM

  1. Liu Zhen-rong The Institute of Engineering Mechanics, Academia Sinica
  • Online:1981-03-20 Published:1981-03-20
一、问题的由来与发展 本文讨论在二维有限元设计中,压缩机器存贮要求(主要是刚度矩阵)的计算技术. 有限元网格实际是点、线组成的集合.因此,过去的研究工作者,大多是从离散数学的角度来考虑这个问题的.1961年,Parter在处理高斯消去法中的优化问题时,就已经引用了图的概念.但他的优化目标不是存贮量,而是消去过程中可能出现的新生非零元素.重要的是通过图的概念,他把数据结构形式与高斯消去法的优化问题联系起来了.
In this paper, the least degree principle in ordering vertices of a graph is used. Inthe first part, it introduces the general procedure for application of the reversedCuthill-Mckee (RCM) algorithm to minimize the storage requirement of data duringcomputer implementation for finite element technique. It is emphasized that re-numbering the set of nodal points is but a process to construct a special kind of datastructure the, so called the spanning tree. In the second part computing experiment is carried out to study the effect ofdifferent types of element meshes on the result of RCM scheme. The superiority of thesystem of right triangular elements with guadratic variation of shape function and thestorage reguirement are presented in the conclusions.
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