Meshing highly regular structures: the case of super carbon nanotubes of arbitrary order
Meshing highly regular structures: the case of super carbon nanotubes of arbitrary order
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DOI：
10.1155/2015/736943
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发表时间：
2015
影响因子：
--
通讯作者：
Christian Schröppel;J. Wackerfuß
中科院分区：
文献类型：
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作者：
Christian Schröppel;J. Wackerfuß
网格剖分是许多数值方法中的重要步骤。我们提出了“层次图网格”（HGM）方法作为一种新的方法来生成网格，代数图论的基础上。HGM方法可用于系统地构造具有多层次和复杂对称特性的构型。由HGM方法提供的结构的分层描述可以被利用来提高多尺度和多重网格方法的效率。在本文中，HGM方法是用于系统的任意顺序的超级碳纳米管的建设，提出了一个结构和几何复杂的，但高度规则的结构的相关例子。HGM算法计算效率高，具有良好的缩放特性。特别是，它对超级碳纳米管结构线性缩放，并且比采用邻域搜索算法的基于几何的方法快得多。它的模块化特点使其有利于自动化。为了生成网格，以将几何对称性与结构对称性相关联的方式添加关于给定配置中的结构的几何形状的信息。所得网格的内在层次描述大大减少了确定网格层次结构的多重网格和多尺度应用程序的努力，并有助于利用复杂结构的力学分析中的相关方法。
Mesh generation is an important step in many numerical methods. We present the "Hierarchical Graph Meshing" (HGM) method as a novel approach to mesh generation, based on algebraic graph theory. The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGM method is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGM algorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.