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Journal of Nanomaterials
Volume 2015 (2015), Article ID 736943, 26 pages
Research Article

Meshing Highly Regular Structures: The Case of Super Carbon Nanotubes of Arbitrary Order

Emmy Noether Research Group MISMO (Mechanical Instabilities in Self-Similar Molecular Structures of Higher Order), Institute of Structural Analysis, University of Kassel, Mönchebergstraße 7, 34125 Kassel, Germany

Received 16 January 2015; Accepted 12 July 2015

Academic Editor: Xiao-Yu Yang

Copyright © 2015 Christian Schröppel and Jens Wackerfuß. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.