Mesh Insertion of Hybrid Meshes

  • Mohamed S. Ebeida
  • Eric Mestreau
  • Yongjie Zhang
  • Saikat Dey

Abstract

A mesh insertion method is presented to merge a tool mesh into a target mesh. All the entities of the tool mesh are preserved in the output mesh while some of the entities of the target mesh are modified or eliminated in order to obtain a topologically conforming mesh. The algorithm can handle non-manifold surfaces formed of quadrilaterals and/or triangles as well as volumetric meshes based on hexahedra, prisms, pyramids and/or tetrahedra. Lower order elements such as beams can also be taken into consideration. A robust 2-steps advancing front algorithm is introduced to fill the narrow gap between the two mesh objects to obtain a complete crack-free connection. An efficient mesh data structure is developed to optimize the search operations and the intersection tests needed by the algorithm. Several application examples are provided to show the strength of the presented algorithm.

Keywords

Hybrid meshes mesh data structure advancing front methods mesh insertion 

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References

  1. 1.
    Lohner, R., Parikh, P.: Generation of three-dimensional unstructured grids by the advancing front method. Int. J. Numer. Meth. Fluids 8, 1135–1149 (1998)CrossRefGoogle Scholar
  2. 2.
    George, P.L., Seveno, E.: The advancing front mesh generation method revisited. Int. J. Numer. Meth. Engng. 37, 3605–3619 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Jin, H., Tanner, R.I.: Generation of unstructured tetrahedral meshes by the advancing front technique. Int. J. Numer. Meth. Engng. 36, 1805–1823 (1993)MATHCrossRefGoogle Scholar
  4. 4.
    Ito, Y., Shih, A., Soni, B.: Reliable isotropic tetrahedral mesh generation based on an advancing front method. In: 13th International Meshing Roundtable, pp. 95–105 (2004)Google Scholar
  5. 5.
    Chew, L.P.: Constrained Delaunay triangulations. Algorithmica 4, 97–108 (1989)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Shewchuk, J.R.: Constrained Delaunay tetrahedralizations and provably good boundary recovery. In: 11th International Meshing Roundtable, pp. 193–204 (2002)Google Scholar
  7. 7.
    Cohen-Steiner, D., Colin, E., Yvinec, M.: Conforming Delaunay triangulations in 3D. In: 18th Annual Symposium on Computational Geometry, pp. 199–208 (2002)Google Scholar
  8. 8.
    Dey, T.K., Bajaj, C.L., Sugihara, K.: On good triangulations in three dimensions. Int. J. Comput. Geom. & App. 2, 75–95 (1992)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Miller, G.L., Talmor, D., Teng, S.-H., Walkington, N.: A Delaunay based numerical method for three dimensions: generation, formulation, and partition. In: 27th Annual ACM Symposium on the Theory of Computing, Las Vegas, Nevada, pp. 683–692 (1995)Google Scholar
  10. 10.
    Shewchuk, J.R.: Tetrahedral mesh generation by Delaunay refinement. In: 14th Annual Symposium on Computational Geometry, Minneapolis, Minnesota, pp. 86–95 (1998)Google Scholar
  11. 11.
    Shewchuk, J.R.: Mesh generation for domains with small angles. In: 16th Annual Symposium on Computational Geometry, Hong Kong, pp. 1–10 (2000)Google Scholar
  12. 12.
    Edelsbrunner, H., Li, X.-Y., Miller, G., Stathopoulos, A., Talmor, D., Teng, S.-H., Ungor, A., Walkington, N.: Smoothing and cleaning up slivers. In: 32nd Annual Symposium on the Theory of Computing, Portland, Oregon, pp. 273–278 (2000)Google Scholar
  13. 13.
    Mavriplis, D.J.: An advancing front Delaunay triangulation algorithm designed for robustness. J. of Comput. Phys. 117, 90–101 (1995)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Marcum, D.L., Weatherill, N.P.: Unstructured grid generation using iterative point insertion and local reconnection. AIAA J. 33, 1619–1625 (1995)MATHCrossRefGoogle Scholar
  15. 15.
    Owen, S.J., Saigal, S.: H-Morph: an indirect approach to advancing front hex meshing. Int. J. Numer. Meth. Engng. 49, 289–312 (2000)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Staten, M.L., Owen, S.J., Blacker, T.D.: Unconstrained paving & plastering: a new idea for all hexahedral mesh generation. In: 14th International Meshing Roundtable, pp. 399–416 (2005)Google Scholar
  17. 17.
    Ito, Y., Murayama, M., Yamamoto, K., Shih, A.M., Soni, B.K.: Efficient computational fluid dynamics evaluation of small device locations with automatic local remeshing. AIAA Journal 47, 1270–1276 (2009)CrossRefGoogle Scholar
  18. 18.
    Zhang, Y., Bajaj, C., Sohn, B.-S.: 3D finite element meshing from imaging data. Comput. Meth. in Appl. Mech. Engng. 194, 5083–5106 (2005)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mohamed S. Ebeida
    • 1
  • Eric Mestreau
    • 2
  • Yongjie Zhang
    • 1
  • Saikat Dey
    • 2
  1. 1.Department of Mechanical EngineeringCarnegie Mellon UniversityPittsburghUSA
  2. 2.Code 7130, Physical Acoustics BranchNaval Research LabWashingtonUSA

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