基于黎曼度量的复杂参数曲面有限元网格生成方法

Surface Mesh Generation Based on Riemannian Metric

给出了三维空间的黎曼度量和曲面自身的黎曼度量相结合的三维复杂参数曲面自适应网格生成的改进波前推进算法.详细阐述了曲面参数域上任意一点的黎曼度量的计算和插值方法;采用可细化的栅格作为背景网格,在降低了程序实现的难度的同时提高了网格生成的速度;提出按层推进和按最短边推进相结合的方法,在保证边界网格质量的同时,提高曲面内部网格的质量.三维自适应黎曼度量的引入,提高了算法剖分复杂曲面的自适应性.算例表明,该算法对复杂曲面能够生成高质量的网格,而且整个算法具有很好的时间特性和可靠性.

A new mesh generation procedure is suggested for the triangulation of general combined parametric surfaces using an advancing front approach and metric tensor. The calculation and interpolation method of arbitrary points in surface＇s parametric space are detailed. The procedure is simplified and accelerated by using refinable quadrangular cells. Both the layers＇ mesh and the internal mesh of surface are guaranteed by combination of advancing by layer and advancing by edge＇s length. The combination of 3-D adaptive metric and surface＇s metric increases the flexibility of the mesh generation scheme. The examples demonstrate the advantages of the mesh generation scheme based on Riemannian metric which indicating that high quality surface meshes can be generated within a reasonable time limit.