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Fun sheet matching: towards automatic block decomposition for hexahedral meshes

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Abstract

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay’s algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3- and 4-valent vertices.

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Notes

  1. Under the acceptable conditions of having a volume isomorphic to a ball and an even number of quadrilaterals on the boundary [26].

  2. In a hexahedral mesh discretizing a 3D bounded domain, this set is reduced to one or two faces.

  3. In topology-based modeling this notion is called embedding.

  4. We adopt the same naming for second and third levels of fundamental primal sheets.

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Acknowledgments

The authors wish to acknowledge the work of Jason Shephard in providing some of the foundational concepts in this work and for his insightful comments over the years in the area of dual-based hexahedral mesh generation. We also wish to acknowledge sponsorship from the high performance computing international collaboration between the US Department of Energy, National Nuclear Security Administration and the French Commissariat à l’Energie Atomique under the direction of Robert Meisner (NNSA) and Jean Gonnard (CEA/DAM).

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Authors and Affiliations

  1. CEA, DAM, DIF, 91297, Arpajon, France

    Nicolas Kowalski & Franck Ledoux

  2. Sandia National Laboratories, Albuquerque, USA

    Matthew L. Staten & Steve J. Owen

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  1. Nicolas Kowalski
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  2. Franck Ledoux
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  3. Matthew L. Staten
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  4. Steve J. Owen
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Correspondence to Franck Ledoux.

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Kowalski, N., Ledoux, F., Staten, M.L. et al. Fun sheet matching: towards automatic block decomposition for hexahedral meshes. Engineering with Computers 28, 241–253 (2012). https://doi.org/10.1007/s00366-010-0207-5

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