一种新的曲面有限元三角网格划分方法

A New Method for Surface Finite Element Triangulation

新方法在参数域内按修改的Delaunay准则生成网格 ,然后将此二维网格映射到曲面 .由于映射变形的存在 ,曲面上的三角形外接圆对应到参数域上会变形为椭圆 ,插点位置也随之改变为外接椭圆圆心 ,对此提出了一种插点定位算法和椭圆近似构造算法 ;针对边界附近的插点而提出了一种边界段外接椭圆构造算法 ;采用了多个指标对曲面边界离散和参数域网格加密进行控制 ,有效保证了网格质量 .

An algorithm constructing the diameter circle for segments on border is proposed. Some criteria are employed to control the surface boundary discretion and mesh refinement in parametric space, and consequently, the mesh quality is well guaranteed. The experiments show that the method presented in this paper is quite applicable.