Mesh Refinement Based on the 8-Tetrahedra Longest- Edge Partition
Mesh Refinement Based on the 8-Tetrahedra Longest- Edge Partition
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发表时间：
2003
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通讯作者：
Ángel Plaza;M. Rivara
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作者：
Ángel Plaza;M. Rivara
任何四面体的8-四面体最长边（8 T-LE）划分是根据三个连续的边二等分来定义的，第一个由最长边执行。相关的局部细化算法可以描述的多面体骨架的概念，使用一组预先计算的分区模式，或通过一个简单的edgemidpoint四面体平分过程。一个有效的3D去细化算法也可以简单地说。本文讨论了8-四面体的剖分、加细算法及其性质，包括一个非退化分形性质。经验实验表明，3D分区具有类似于2D情况下的行为，在这个意义上，在第一个细化级别之后，一个明确的单调改善行为。对于一些四面体，由于引入了反映与四面体厚度相关的局部特征尺寸的新面，在第一分区中可以观察到四面体质量的有限降低。
The 8-tetrahedra longest-edge (8T-LE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longest-edge. The associated local refinement algorithm can be described in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint tetrahedron bisection procedure. An effective 3D derefinement algorithm can be also simply stated. In this paper we discuss the 8-tetrahedra partition, the refinement algorithm and its properties, including a non-degeneracy fractal property. Empirical experiments show that the 3D partition has analogous behavior to the 2D case in the sense that after the first refinement level, a clear monotonic improvement behavior holds. For some tetrahedra a limited decreasing of the tetrahedron quality can be observed in the first partition due to the introduction of a new face which reflects a local feature size related with the tetrahedron thickness.