基于波前法的参数曲面有限元网格生成算法

Parametric Surface Mesh Generation Based on Advancing Front Technique

为克服参数曲面有限元网格生成中的单元形状映射畸变问题,提出一种曲面有限元网格自动生成算法.该算法由弹性矢量确定曲面上新节点的生成方向和空间位置,利用相应的参数域网格进行新单元拓扑相容性判断.在生成闭曲面网格时,通过添加参/虚边界棱边对闭曲面边界进行调整,确保闭曲面边界信息相对其参数域的完整性;在给出闭曲面极点初始化方法和适当设置单元边线段相等条件的基础上,该算法适用于各种不同形式闭曲面的网格自动生成.实验算例表明,文中算法可生成质量良好的参数曲面和组合面有限元网格.

To solve the problem of shape distortion when generating the finite element mesh of parametric surfaces with mapping method,a new algorithm for parametric surface mesh generation based on advancing front technique is proposed.The algorithm selects the direction along which a new node is located according to an elastic vector.The topological compatibility of the new element is then checked against the surrounding mesh in the parameter domain.Moreover,a method for adjusting the boundary of closed surface is suggested by introducing new edges related to its real boundary and the virtual boundary in the parametric domain.We also present a method for initializing the poles of closed surface and set appropriate conditions to check if one element edge being equal to another,enabling our algorithm applicable to the mesh generation of various closed surfaces.Experimental examples demonstrate that the proposed method is suitable for the high quality finite element mesh generation of the parametric surface and the combo surface.