Quality Local Refinement of Tetrahedral Meshes Based on Bisection
Quality Local Refinement of Tetrahedral Meshes Based on Bisection
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DOI：
10.1137/0916074
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发表时间：
1995-11
期刊：
影响因子：
--
通讯作者：
Anwei Liu;B. Joe
中科院分区：
文献类型：
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作者：
Anwei Liu;B. Joe
我们提出了一种基于二分过程的四面体网格三维 (3-D) 局部细化算法。细化网格的质量通过四面体形状度量 $\eta $ 来保证。具体来说，证明该算法创建了有限数量的所有细化四面体中相似四面体的类，该数量仅取决于初始网格中四面体的数量。此外，如果 ${\bf T}$ 是原始网格中的四面体，并且 ${\bf T}_i^n $ 是 ${\bf T}$ 的任何细化四面体，则 $\eta ({\bf T}_i^n ) \geq c\eta ({\bf T})$，其中 c 是独立于 ${\bf T}$ 和细化次数的正常数。还证明，对于最终网格中的任何内部面，入射到该面上的两个相邻四面体的平分水平之差的绝对值为$\leq 2$，这表明四面体上的局部细化可以平滑地扩展到它们的邻居。该算法的预期时间复杂度为$O(N)$，wh...
We present a three-dimensional (3-D) local refinement algorithm for tetrahedral meshes based on a bisection procedure. The quality of refined meshes is guaranteed in terms of a tetrahedron shape measure $\eta $. Specifically, it is proved that the algorithm creates a finite number, which only depends on the number of tetrahedra in the initial mesh, of classes of similar tetrahedra in all refined tetrahedra. Furthermore, if ${\bf T}$ is a tetrahedron in the original mesh, and ${\bf T}_i^n $ is any refined tetrahedron of ${\bf T}$, then $\eta ({\bf T}_i^n ) \geq c\eta ({\bf T})$, where c is a positive constant independent of ${\bf T}$ and the number of refinements. It is also proved that for any interior face in the final mesh, the absolute value of the difference of the bisection levels of the two adjacent tetrahedra incident on the face is $ \leq 2$, which indicates that local refinements on tetrahedra can be smoothly extended to their neighbors. The expected time complexity of the algorithm is $O(N)$, wh...