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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.

References

  1. Ledoux F, Weill J-C, Bertrand Y (2010) Definition of a generic mesh data structure in the high performance computing context. In: Developments and applications in engineering computational technology, vol 26. Saxe-Coburg Publications, pp 49–80

  2. Blacker TD, Meyers RJ (1993) Seams and wedges in plastering: a 3D hexahedral mesh generation algorithm. Eng Comput 2(9):83–93

    Article  Google Scholar 

  3. Owen S, Sunil S (2000) H-morph: an indirect approach to advancing front hex meshing. Int J Numer Methods Eng 1(49):289–312

    Google Scholar 

  4. Tautges TJ, Blacker TD, Mitchell SA (1996) The whisker weaving algorithm: a connectivity-based method for constructing all-hexahedral finite element meshes. Int J Numer Methods Eng 39:3327–3349

    Article  MathSciNet  MATH  Google Scholar 

  5. Folwell NT, Mitchell SA (1998) Reliable whisker weaving via curve contraction. In: Proceedings of the 7th international meshing roundtable, pp 365–378

  6. Muller-Hannemann M (2001) Shelling hexahedral complexes for mesh generation. J Graph Algorithm Appl 5(5):59–91

    MathSciNet  Google Scholar 

  7. Carbonera CD, Shepherd JF (2006) A constructive approach to constrained hexahedral mesh generation. In: Proceedings of the 15th international meshing roundtable, September 2006, Sandia National Laboratories, pp 435–452

  8. Ledoux F, Weill J-C (2007) An extension of the reliable whisker weaving algorithm. In: Proceedings of the 16th international meshing roundtable. Springer, Berlin, pp 215–232

  9. Kawamura Y, Islamm MS, Sumi Y (2008) A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure. Eng Comput 24:215–219

    Google Scholar 

  10. Schneiders R (1997) An algorithm for the generation of hexahedral element meshes based on a octree technique. In: Proceedings of the 6th international meshing roundtable, pp 183–194

  11. Maréchal L (2009) Advances in octree-based all-hexahedral mesh generation: handling sharp features. In: Clark BW (ed) Proceedings of the 18th international meshing roundtable. Springer, Berlin, pp 65–84

  12. Shepherd JF (2009) Conforming hexahedral mesh generation via geometric capture methods. In: Clark BW (ed) Proceedings of the 18th international meshing roundtable. Springer, Berlin, pp 85–102

  13. Staten ML, Kerr RA, Owen SJ, Blacker TD, Stupazzini M, Shimada K (2010) Unconstrained plastering—hexahedral mesh generation via advancing-front geometry decomposition. Int J Numer Methods Eng 81:135–171

    Google Scholar 

  14. Murdoch P, Benzley SE (1995) The spatial twist continuum: a connectivity-based method for representing all hexahedral finite element meshes. In: Proceedings of the 4th international meshing roundtable, number SAND95-2130, Albuquerque, 1995. Sandia National Laboratories

  15. Cubit, geometry and mesh generation toolkit. http://cuibt.sandia.gov

  16. Blacker TD (1997) The cooper tool. In: Proceedings of the 5th international meshing roundtable, pp 217–228

  17. Shepherd J, Mitchell SA, Knupp P, White DR (2000) Methods for multisweep automation. In: Proceedings of the 9th international meshing roundtable, pp 77–87

  18. Ruiz-Gironés E, Roca X, Sarrate J (2009) A new procedure to compute imprints in multi-sweeping algorithms. In: Clark BW (ed) Proceedings of the 18th international meshing roundtable. Springer, Berlin, pp 281–299

  19. ANSYS, ICEM CFD. http://www.ansys.com/products/icemcfd.asp

  20. Roca X, Sarrate J (2008) Local dual contributions on simplices: a tool for block meshing. In: Proceedings of the 17th international meshing roundtable. Springer, Berlin, pp 513–531

  21. Bern M, Eppstein D, Erickson J (2002) Flipping cubical meshes. Eng Comput 18(3):173–187

    Google Scholar 

  22. Tautges TJ, Knoop SE (2003) Topology modification of hexahedral meshes using atomic dual-based operations. In: Proceedings of the 12th international meshing roundtable, September 2003, Sandia National Laboratories, pp 415–423

  23. Tautges TJ, Knoop SE, Rickmeyer TJ (2008) Local topological modifications of hexahedral meshes. Part I: A set of dual-based operations. In: ESAIM Proceedings CEMRACS 2007, vol 24, pp 14–33

  24. Jurkova K, Ledoux F, Kuate R, Rickmeyer T, Tautges TJ, Zorgati H (2007) Local topological modifications of hexahedral meshes. Part II: Combinatorics and relation to boy surface. In: ESAIM Proceedings CEMRACS 2007, vol 24, pp 34–45

  25. Ledoux F, Shepherd JF (2009) Topological modifications of hexahedral meshes via sheet operations: a theoretical study. Eng Comput. doi:10.1007/s00366-009-0145-2

  26. Mitchell SA (1996) A characterization of the quadrilateral meshes of a surface which admit a compatible hexahedral mesh of the enclosed volume. In: Proceedings of the 13th annual symposium on theoretical aspects of computer science, pp 465–476

  27. Shepherd JF (2007) Topologic and geometric constraint-based hexahedral mesh generation. Published Doctoral Dissertation. University of Utah, Utah

  28. Staten ML, Shepherd JF, Ledoux F, Shimada K (2009) Hexahedral mesh matching: converting non-conforming hexahedral-to-hexahedral interfaces into conforming interfaces. Int J Numer Methods Eng. doi:10.1002/nme.2800

  29. Remacle J-F, Shephard MS (2003) An algorithm oriented mesh database. Int J Numer Methods Eng 58(2)

  30. Ledoux F, Shepherd JF (2009) Topological and geometrical properties of hexahedral meshes. Eng Comput. doi:10.1007/s00366-009-0144-3

  31. Carey GF (2002) Hexing the tet. Commun Numer Methods Eng 18(3):223–227

    Google Scholar 

  32. Mitchell SA, Tautges TJ (1995) Pillowing doublets: refining a mesh to ensure that faces share at most one edge. In: Proceedings of the 4th international meshing roundtable, October 1995, Sandia National Laboratories, pp 231–240

  33. Benzley SE, Borden MJ, Shepherd JF (2002) Hexahedral sheet extraction. In: Proceedings of the 11th international meshing roundtable, pp 147–152

  34. Shepherd JF, Johnson CR (2008) Hexahedral mesh generation constraints. Eng Comput 24(3):195–213

    Google Scholar 

  35. Vyas V, Shimada K (2009) Tensor-guided hex-dominant mesh generation with targeted all-hex regions. In: Clark BW (ed) Proceedings of the 18th international meshing roundtable. Springer, Berlin, pp 377–396

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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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  • DOI: https://doi.org/10.1007/s00366-010-0207-5

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