Mesh Refinement Processes Based on the Generalized Bisection of Simplices
Mesh Refinement Processes Based on the Generalized Bisection of Simplices
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DOI：
10.1137/0721042
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发表时间：
1984-06
影响因子：
2.9
通讯作者：
M. Rivara
中科院分区：
文献类型：
--
作者：
M. Rivara
在 Rheinboldt 的一般理论 [SIAM J. Numer.分析，17 (1980)，第 766–778 页]。然后证明，这样的过程允许构建自然平滑、一致和嵌套的非均匀网格序列。事实上，它表明存在一个广义的网格细化算子，对于任何一致的三角剖分 $\Delta $ 和任何 $V \subset \Delta $，都会产生一个嵌套的、平滑的、一致的三角剖分 $\Delta ^ * $ ，其中包含 V 的所有元素的后继，并且 $\Delta ^ * $ 的最小单元大小从下面以 $\Delta $ 的最小单元大小的一半为界。明确给出了两种允许选择性细化计算三角剖分的一致网格细化算法。
Mesh-refinement processes based on the generalized bisection of simplices are discussed and characterized in the context of the general theory of Rheinboldt [SIAM J. Numer. Anal., 17 (1980), pp. 766–778]. Then it is proved that such processes allow the construction of sequences of naturally smooth, conforming and nested nonuniform meshes. In fact it is shown that there exists a generalized mesh-refinement operator that for any conforming triangulation $\Delta $ and for any $V \subset \Delta $, produces a nested, smooth, conforming triangulation $\Delta ^ * $ containing successors of all elements of V and such that the minimum cell-size of $\Delta ^ * $ is bounded from below by half the minimum cell-size of $\Delta $. Two conforming mesh-refinement algorithms that allow the selective refinement of computational triangulations are explicitly given.