任意平面区域的高质量有限元网格自动剖分

Quality Mesh Generation of Arbitrary Planar Domain for FEM

实现了任意平面区域的高质量三角形有限元网格自动剖分。初始化时利用广度优先搜索查找孔及凹槽中需删除的三角形 ,不需定义有向边界 ,可十分方便地定出实际剖分区域 ;给出了一种方便、快捷的点定位法 ,可大大提高程序运行速度 ;利用Delaunay网格优化算法实现了对三角形形状的控制 ,可使三角形最小角达到 35° ;分割坏三角形时 ,按最小角由小到大的顺序处理 。

Quality triangulation is desirable for FEM analysis. In this paper, the Delaunay refinement algorithm is utilized to control the shape of triangles. The data structure of linked list is used to store the bad triangles indexed by their smallest angle, so that we can always split the worst existing triangle firstly. The triangles in holes and concavities to be removed are found by width-first search, which eliminates the need of oriented boundaries. An efficient point location algorithm is presented to improve the speed of triangulation. The program is used to triangulate several PSLGs(planar straight line graph). The results indicate that the program is capable of triangulating arbitrary complex planar domain and ultimately halts for an angle constraint of up to 350 degrees.