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Development of a system for adaptive mesh generation

自适应网格生成系统的开发

基本信息

批准号：
09650076
负责人：
ISHIKAWA Takeo
金额：
$ 1.28万
依托单位：
GUNMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650076/
关键词：
mesh generation adaptive mesh finite element method

项目摘要

Several methods of adaptive mesh generation have been proposed for finite element analysis. The procedure of adaptive mesh generation starts with a coarse mesh and develops a correct mesh at the preprocessing level. It is said that the procedure is time consuming and costly. Thus, it is very important to develop a method for mesh generation that either immediately leads to an acceptable solution or would require less iteration to achieve better results.This research has proposed a method to generate three-dimensional finite element meshes taking into account mesh density. The three-dimensional tetrahedral mesh is constructed by using the Delaunay triangulation method which ensures that the boundary surface of the domain is contained in the triangulation, Prediction of mesh density distribution is accomplished by solving a finite difference equation with a coarse grid. Several numerical examples are provided to illustrate the usefulness of the proposed method.Moreover, this research has discussed a method to improve robustness of the three-dimensional advancing front technique. in this method, a set of nodes is given as input data, and a new element is produced by connecting a selected front to an existing node not to a new node by checking if future tetrahedron elements can be produced. A simple example is shown for comparing with the conventional advancing front technique.

针对有限元分析，提出了几种自适应网格生成方法。自适应网格生成过程从粗网格开始，在预处理阶段生成正确的网格。据说这个过程既耗时又费钱。因此，开发一种网格生成方法是非常重要的，这种方法要么立即产生可接受的解决方案，要么需要更少的迭代来获得更好的结果。本研究提出了一种考虑网格密度的三维有限元网格生成方法。采用Delaunay三角剖分法构建三维四面体网格，保证了区域的边界面包含在三角剖分中，通过求解粗糙网格的有限差分方程来预测网格密度分布。给出了几个数值算例来说明所提方法的有效性。此外，本研究还探讨了一种提高三维推进前沿技术鲁棒性的方法。在该方法中，给定一组节点作为输入数据，并通过将选定的前端连接到现有节点而不是通过检查是否可以产生未来的四面体元素来连接到新节点来产生新元素。并给出了一个简单的算例，与传统的前推进技术进行了比较。