VOLUME DISCRETIZATION INTO TETRAHEDRA .2. 3D-TRIANGULATION BY ADVANCING FRONT APPROACH
VOLUME DISCRETIZATION INTO TETRAHEDRA .2. 3D-TRIANGULATION BY ADVANCING FRONT APPROACH
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DOI：
10.1016/0045-7949(91)90059-u
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发表时间：
1991-01-01
影响因子：
4.7
通讯作者：
LO, SH
中科院分区：
文献类型：
--
作者：
LO, SH
对现有的三维实体网格自动剖分方法进行了综述。 虽然三维Delaunay三角剖分最近引起了人们的广泛关注，但它作为有限元网格生成器的适用性受到质疑。 虽然在二维Delaunay三角剖分中，“最大-最小”角准则可以在整个域上得到验证，但没有等价或类似的准则可以将其扩展到三维情况，以确保生成的四面体单元在数值计算中是均匀的。本文提出了一种简单而通用的基于前沿技术的三维三角剖分方法，用于离散任意体积。 为了保证生成的四面体单元尽可能地等边，采用单元体积与无量纲化的边的平方和之比来判断四面体单元的优劣。 因此，如果在网格构建过程中仔细控制每个四面体单元的形状，则可以确保有限元网格的质量。 通过对大量不同特征的算例的研究，发现该算法可以得到高质量的四面体单元网格。
Existing methods of automatic mesh generation for 3D solid objects are reviewed. Although the 3D Delaunay triangulation recently aroused much attention, its suitability as a finite element mesh generator is questioned. Although in 2D Delaunay triangulation, the 'max-min' angle criterion can be verified over the entire domain, no equivalent or similar criterion can be defined for its extension to 3D situations to ensure that tetrahedron elements so generated are well proportioned for numerical calculations.In this paper, a simple but versatile 3D triangulation scheme based on the advancing front technique for the discretization of arbitrary volumes is presented. To ensure that the tetrahedron elements generated are as equilateral as possible, the ratio of volume of the element to the sum of squares of edges put into a dimensionless form is adopted to judge the quality of a tetrahedron element. The quality of the finite element mesh can thus be ensured if the shape of each tetrahedron element is carefully controlled in the mesh construction process. Through the study of numerous examples of various characteristics, it is found that high-quality tetrahedron element meshes are obtained by the proposed algorithm.