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The receding front method applied to hexahedral mesh generation of exterior domains

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Abstract

Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.

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References

  1. Owen SJ (1998) A survey for unstructured mesh generation technology. In: 7th International Meshing Roundtable, pp 239–267

  2. Blacker TD (2001) Automated conformal hexahedral meshing constraints, challenges and opportunities. Eng Comput 17(3):201–210

    Article  MATH  Google Scholar 

  3. Tautges TJ (2001) The generation of hexahedral meshes for assembly geometry: survey and progress. Int J Numer Methods Eng 50(12):2617–2642

    Article  MATH  Google Scholar 

  4. Baker TJ (2005) Mesh generation: art or science? Prog Aerosp Sci 41(1):29–63

    Article  Google Scholar 

  5. Shepherd JF (2007) Topologic and geometric constraint-based hexahedral mesh generation. PhD thesis, The University of Utah

  6. Roca X (2009) Paving the path towards automatic hexahedral mesh generation. PhD thesis, Universitat Politècnica de Catalunya

  7. Schneiders R, Bünten R (1995) Automatic generation of hexahedral finite element meshes. Comput Aided Geom Des 12(7):693–707

    Article  MathSciNet  MATH  Google Scholar 

  8. Schneiders R (1996) A grid-based algorithm for the generation of hexahedral element meshes. Eng Comput 12(3):168–177

    Article  Google Scholar 

  9. Zhang Y, Bajaj C, Sohn BS (2005) 3D finite element meshing from imaging data. Comput Methods Appl Mech Eng 194(48-49):5083–5106

    Article  MATH  Google Scholar 

  10. Zhang Y, Bajaj C (2006) Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Comput Methods Appl Mech Eng 195(9–12):942–960

    Article  MathSciNet  MATH  Google Scholar 

  11. Qian J, Zhang Y (2010) Sharp feature preservation in octree-based hexahedral mesh generation for CAD assembly models. In: Proceedings of the 19th International Meshing Roundtable, pp 243–262

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

    Article  Google Scholar 

  13. Staten ML, Owen SJ, Blacker TD (2005) Unconstrained paving and plastering: a new idea for all hexahedral mesh generation. In: 14th International Meshing Roundtable

  14. Staten ML, Kerr RA, Owen SJ, Blacker TD (2006) Unconstrained paving and plastering: Progress update. In: Proceedings, 15th International Meshing Roundtable, Springer, Berlin, pp 469–486

  15. 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(2):135–171

    MATH  Google Scholar 

  16. Meshkat S, Talmor D (2000) Generating a mixed mesh of hexahedra, pentahedra and tetrahedra from an underlying tetrahedral mesh. Int J Numer Methods Eng 49(1–2):17–30

    Article  MATH  Google Scholar 

  17. Owen SJ, Saigal S (2000) H-Morph: an indirect approach to advancing front hex meshing. Int J Numer Methods Eng 49(1–2):289–312

    Article  MATH  Google Scholar 

  18. Roca X, Sarrate J (2008) Local dual contributions on simplices: a tool for block meshing. In: Proceedings of the 17th International Meshing Roundtable

  19. Roca X, Sarrate J (2010) Local dual contributions: representing dual surfaces for block meshing. Int J Numer Methods Eng 83(6):709–740

    MathSciNet  MATH  Google Scholar 

  20. Kowalski N, Ledoux F, Staten ML, Owen SJ (2009) Fun sheet matching—automatic generation of block-structured hexahedral mesh using fundamental sheets. In: 10th USNCCM

  21. Roca X, Ruiz-Gironés E, Sarrate J (2010) Receding front method: a new approach applied to generate hexahedral meshes of outer domains. In: Proceedings of the 19th International Meshing Roundtable

  22. Ruiz-Gironés E (2011) Automatic hexahedral meshing algorithms: from structured to unstructured meshes. PhD thesis, Universitat Politècnica de Catalunya

  23. Sethian JA (1994) Curvature flow and entropy conditions applied to grid generation. J Comp Phys 115(2):440–454

    Google Scholar 

  24. Wang Y, Guibault F, Camarero R (2007) Eikonal equation-based front propagation for arbitrary complex configurations. Int J Numer Methods Eng 73(2):226–247

    Article  MathSciNet  Google Scholar 

  25. Xia H, Tucker PG (2009) Finite volume distance field and its application to medial axis transforms. Int J Numer Methods Eng 82(1):114–134

    MathSciNet  Google Scholar 

  26. Xia H, Tucker PG (2009) Distance solutions for medial axis transform. In: Proceedings of the 18th International Meshing Roundtable, pp 247–265

  27. Tam TKH, Armstrong CG (1991) 2D finite element mesh generation by medical axis subdivision. Adv Eng Softw Workstn 13(5–6):313–324

    Article  MATH  Google Scholar 

  28. Price MA, Armstrong CG (1997) Hexahedral mesh generation by medial surface subdivision: Part II. Solids with flat and concave edges. Int J Numer Methods Eng 40(1):111–136

    Article  Google Scholar 

  29. Price MA, Armstrong CG, Sabin MA (1995) Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges. Int J Numer Methods Eng 38(19):3335–3359

    Article  MATH  Google Scholar 

  30. Sheffer A, Etzion M, Rappoport A, Bercovier M (1999) Hexahedral mesh generation using the embedded Voronoi graph. Eng Comput 15(3):248–262

    Article  MATH  Google Scholar 

  31. Sheffer A, Bercovier M (2000) Hexahedral meshing of non-linear volumes using Voronoi faces and edges. Int J Numer Methods Eng 49:329–351

    Article  MathSciNet  MATH  Google Scholar 

  32. Quadros WR, Ramaswami K, Prinz FB, Gurumoorthy B (2004) Laytracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform. Int J Numer Methods Eng 61(2):209–237

    Article  MATH  Google Scholar 

  33. Yamakawa S, Shimada K (2003) Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cells. Int J Numer Methods Eng 57(15):2099–2129

    Article  MathSciNet  MATH  Google Scholar 

  34. Vyas V, Shimada K (2009) Tensor-guided hex-dominant mesh generation with targeted all-hex regions. In: Proceedings of the 18th International Meshing Roundtable, pp 377–396

  35. Maréchal L (2009) Advances in octree-based all-hexahedral mesh generation: handling sharp features. In: Proceedings of the 18th International Meshing Roundtable

  36. Shepherd JF (2009) Conforming hexahedral mesh generation via geometric capture methods. In: Proceedings of the 18th International Meshing Roundtable

  37. Owen SJ, Shepherd JF (2009) Embedding features in a cartesian grid. In: Proceedings of the 18th International Meshing Roundtable

  38. Ito Y, Shih AM, Soni BK (2009) Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates. Int J Numer Methods Eng 77(13):1809–1833

    Article  MathSciNet  MATH  Google Scholar 

  39. 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(19):3327–3350

    Article  MathSciNet  MATH  Google Scholar 

  40. Ledoux F, Weill JC (2007) An Extension of the Reliable Whisker Weaving Algorithm. In: 16th International Meshing Roundtable, Springer, Berlin, pp 215–232

  41. Mitchell SA, Tautges TJ (1995) Pillowing doublets: refining a mesh to ensure that faces share at most one edge. In: 4th International Meshing Roundtable

  42. Shepherd JF, Dewey MW, Woodbury AC, Benzley SE, Staten ML, Owen SJ (2010) Adaptive mesh coarsening for quadrilateral and hexahedral meshes. Finite Elements Anal Des 46(1–2):17–32

    Article  MathSciNet  Google Scholar 

  43. Staten ML, Shepherd JF, Ledoux F, Shimada K (2010) Hexahedral mesh matching: Converting non-conforming hexahedral-to-hexahedral interfaces into conforming interfaces. Int J Numer Methods Eng 82(12):1475–1509

    MATH  Google Scholar 

  44. Sethian JA (1999) Level set methods and fast marching methods. Cambridge university press, Cambridge

    MATH  Google Scholar 

  45. Sarrate J, Huerta A (2000) Efficient unstructured quadrilateral mesh generation. Int J Numer Methods Eng 49(10):1327–1350

    Article  MATH  Google Scholar 

  46. Sarrate J, Huerta A (2000) Automatic mesh generation of nonstructured quadrilateral meshes over curved surfaces in r3. In: 3th ECCOMAS conference

  47. Knupp PM (2003) A method for hexahedral mesh shape optimization. Int J Numer Methods Eng 58(2):319–332

    Article  MATH  Google Scholar 

  48. Knupp PM (2001) Hexahedral and tetrahedral mesh untangling. Eng Comput 17(3):261–268

    Article  MATH  Google Scholar 

  49. Carreras J (2008) Refinament conforme per malles de quadrilàters i hexàedres. Master’s thesis, Facultat de Matemàtiques i Estadística. Universitat Politècnica de Catalunya

  50. Thompson JF (1999) Handbook of grid generation. CRC Press, Boca Raton

    MATH  Google Scholar 

  51. Roca X, Sarrate J, Ruiz-Gironés E (2007) A graphical modeling and mesh generation environment for simulations based on boundary representation data. In Congresso de Métodos Numéricos em Engenharia

  52. Roca X, Ruiz-Gironés E, Sarrate J (2010) ez4u. mesh generation environment. http://www-lacan.upc.edu/ez4u.htm

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Authors and Affiliations

  1. Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034, Barcelona, Spain

    Eloi Ruiz-Gironés, Xevi Roca & Josep Sarrate

Authors
  1. Eloi Ruiz-Gironés
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  2. Xevi Roca
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  3. Josep Sarrate
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Correspondence to Josep Sarrate.

Additional information

This work was partially sponsored by the Spanish Ministerio de Ciencia e Innovación under grants DPI2007-62395, BIA2007-66965 and CGL2008-06003-C03-02/CLI and by Universitat Politècnica de Catalunya (UPC).

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Ruiz-Gironés, E., Roca, X. & Sarrate, J. The receding front method applied to hexahedral mesh generation of exterior domains. Engineering with Computers 28, 391–408 (2012). https://doi.org/10.1007/s00366-011-0233-y

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