一种四边形网格的并行边定向算法
A parallel edge orientation algorithm for quadrilateral meshes
摘要：
实现正确有限元组装的一种方法是确保小平面相对于网格中每个单元的局部取向与该小平面的全局取向一致。Rognes等人已经展示了如何对任何由单纯形元素组成的网格实现这一点，并且Deal.II包含了一个串行算法来构造可定向流形的任何四边形网格的一致定向。本文的核心贡献是将该算法扩展到分布式内存并行计算机，这有利于其作为并行仿真系统的一部分的无缝应用。此外，我们的分析建立了著名的联合查找算法和建设一个一致的方向的四边形网格之间的联系。其结果是，现有的工作的并行化的联合查找算法可以很容易地适应构建进一步的并行算法的网格方向。
英文摘要：
One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve this for any mesh composed of simplex elements, and deal.II contains a serial algorithm to construct a consistent orientation of any quadrilateral mesh of an orientable manifold. The core contribution of this paper is the extension of this algorithm for distributed memory parallel computers, which facilitates its seamless application as part of a parallel simulation system. Furthermore, our analysis establishes a link between the well-known Union-Find algorithm and the construction of a consistent orientation of a quadrilateral mesh. As a result, existing work on the parallelisation of the Union-Find algorithm can be easily adapted to construct further parallel algorithms for mesh orientations.
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