Development of a system for adaptive mesh generation

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，并在前处理级别发展成正确的网格。据说，这一过程既耗时又昂贵。因此，开发一种既能立即得到可接受解，又能减少迭代次数以获得更好结果的网格生成方法是非常重要的。本文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三角剖分方法构造三维四面体网格，保证了区域的边界面被包含在三角剖分中，网格密度分布的预测是通过求解粗网格有限差分方程组来实现的。通过数值算例说明了该方法的有效性，并讨论了一种提高三维推进阵面技术稳健性的方法。在该方法中，给出一组节点作为输入数据，通过检查是否可以产生未来的四面体单元，通过将选定的前沿连接到现有节点而不是连接到新节点来产生新单元。文中给出了一个简单的算例，并与传统的前沿推进技术进行了比较。

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.