调和分析法在有限元网格自动生成中的应用

Applicaton of Harmonic Analysis in Automatic Mesh Generation for FEM

本文先以调和函数建立起参考域和物理域之间的映射,并把这种映射拓广到了三角形域间的变换。然后通过有限单元法求解两个Dirichlet问题的数值解来给出物理域中各节点的坐标值。最后详述了如何根据各子域间的拓扑关系,将这些子域拼装成一个可含有节理或空洞的真实域。文中给出了程序框图和若个算例。

In this paper, the mapping between reference region and physical region is built in advance by harmonic function, and which is extended to the transformation between triangular regions. Then all of the nodal coordinates in physical region are obtained by the numerical solutions of two Dirichlet's problems through F.E.A. Finally, it is detailed that some subregions are combined a real region with joints or holes, according to their toplogic relationships. The flow-chart of program and calculating examples are given in this paper.