Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm
Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm
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最长边二分算法生成的一系列面对面划分的强规律性
DOI：
10.1134/s0965542508090170
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发表时间：
2008
影响因子：
0.7
通讯作者：
M. Křížek
中科院分区：
文献类型：
--
作者：
S. Korotov;Aleš Kropáč;M. Křížek
我们研究了在给定的有界多边形域的面对面简单划分中选择最长边进行等分的最长边等分算法。在其中点划分这条边，我们定义了围绕这条边的所有简单体的局部精细划分。重复这一过程，我们得到了一个嵌套面对面分区的族(k) = {k h}h→0。对于d = 2，我们证明了这个族是强正则的；也就是说，存在一个常数C >0 0，使得对于所有三角形T∈kh和所有三角形k∈kh， T≥Ch2。特别是，众所周知的最小角度条件是有效的。
We examine the longest-edge bisection algorithm that chooses for bisection the longest edge in a given face-to-face simplicial partition of a bounded polytopic domain in ℝd. Dividing this edge at its midpoint, we define a locally refined partition of all simplices that surround this edge. Repeating this process, we obtain a family ℱ = {ℐh}h → 0 of nested face-to-face partitions ℐh. For d = 2, we prove that this family is strongly regular; i.e., there exists a constant C > 0 such that meas T ≥ Ch2 for all triangles T ∈ ℐh and all triangulations ℐh ∈ ℱ. In particular, the well-known minimum angle condition is valid.