On Orienting Edges of Unstructured Two- and Three-Dimensional Meshes
On Orienting Edges of Unstructured Two- and Three-Dimensional Meshes
复制标题
关于非结构化二维和三维网格的边定向
DOI：
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发表时间：
2015
影响因子：
2.7
通讯作者：
W. Barth
中科院分区：
文献类型：
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作者：
Rainer Agelek;Michael L. Anderson;W. Bangerth;W. Barth
有限元代码通常使用将非结构化网格表示为单元、面和边的集合的数据结构，其中每一个都需要关联的坐标系。然后需要存储每个边缘的坐标系如何与相邻单元的坐标系相关。然而，如果我们能够先验地确定坐标系的方向，使得边缘上的坐标系按照规则唯一地遵循单元上的坐标系，则可以简化数据结构和算法。这样的规则要求每个非结构化网格允许分配方向的边缘，满足公约在相邻的细胞。我们表明，约定选择的非结构化四边形网格在处理。II库总是允许定向网格。因此，它可以用来使代码更简单，更快，更少的bug。我们提出了一个算法，定向网格在O（N）的操作。然后，我们表明，一致的方向并不总是可能的三维六面体网格。因此，细胞通常需要存储相邻边缘的方向，但我们的方法也允许表征的情况下，这是不必要的。我们的算法的3D扩展或者一致地定向边缘，或者中止，都在O（N）步内。
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each edge relates to that of neighboring cells. However, we can simplify data structures and algorithms if we can a priori orient coordinate systems in such a way that the coordinate systems on the edges follow uniquely from those on the cells by rule. Such rules require that every unstructured mesh allow the assignment of directions to edges that satisfy the convention in adjacent cells. We show that the convention chosen for unstructured quadrilateral meshes in the deal.II library always allows to orient meshes. It can therefore be used to make codes simpler, faster, and less bug prone. We present an algorithm that orients meshes in O(N) operations. We then show that consistent orientations are not always possible for 3D hexahedral meshes. Thus, cells generally need to store the direction of adjacent edges, but our approach also allows the characterization of cases where this is not necessary. The 3D extension of our algorithm either orients edges consistently, or aborts, both within O(N) steps.
影响因子：
3.1
作者：
Homolya M
通讯作者：
Homolya M