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Compact Array-Based Mesh Data Structures

  • Conference paper
Proceedings of the 14th International Meshing Roundtable

Summary

In this paper, we present simple and efficient array-based mesh data structures, including a compact representation of the half-edge data structure for surface meshes, and its generalization—a half-face data structure—for volume meshes. These array-based structures provide comprehensive and efficient support for querying incidence, adjacency, and boundary classification, but require substantially less memory than pointer-based mesh representations. In addition, they are easy to implement in traditional programming languages (such as in C or Fortran 90) and convenient to exchange across different software packages or different storage media. In a parallel setting, they also support partitioned meshes and hence are particularly appealing for large-scale scientific and engineering applications. We demonstrate the construction and usage of these data structures for various operations, and compare their space and time complexities with alternative structures.

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References

  1. B. Baumgart. Winged-edge polyhedron representation. Technical report, Stanford Artificial Intelligence Report No. CS-320, October 1972.

    Google Scholar 

  2. B. G. Baumgart. A polyhedron representation for computer vision. In National Computer Conference, pages 589–596, 1975.

    Google Scholar 

  3. Daniel K. Blandford, Guy E. Blelloch, David E. Cardoze, and Clemens Kadow. Compact representations of simplicial meshes in two and three dimensions. In Proceedings of 12th International Meshing Roundtable, pages 135–146, 2003.

    Google Scholar 

  4. E. B. Becker, G. F. Carey, and J. Tinsley Oden. Finite Elements: An Introduction, volume 1. Prentice-Hall, 1981.

    Google Scholar 

  5. J. Blazek. Comparison of two conservative coupling algorithms for structured-unstructured grid interfaces, 2003. AIAA Paper 2003-3536.

    Google Scholar 

  6. J. Bonet and J. Peraire. An alternated digital tree (adt) algorithm for 3d geometric searching and intersection problems. Int. J. Numer. Meth. Engrg., 31:1–17, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  7. Mark W. Beall and Mark S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meth. Engrg., 40:1573–1596, 1997.

    Article  MathSciNet  Google Scholar 

  8. R. Biswas and R.C. Strawn. Tetrahedral and hexahedral mesh adaptation for cfd problems. Applied Numerical Mathematics, 21:135–151, 1998.

    Article  MathSciNet  Google Scholar 

  9. S. D. Connell and D. G. Holmes. 3-dimensional unstructured adaptive multigrid scheme for the Euler equations. AIAA J., 32:1626–1632, 1994.

    MATH  Google Scholar 

  10. W. Celes, G.H. Paulino, and R. Espinha. A compact adjacency-based topological data structure for finite element mesh representation. Int. J. Numer. Meth. Engrg., 2005. in press.

    Google Scholar 

  11. G. F. Carey, M. Sharma, and K.C. Wang. A class of data structures for 2-d and 3-d adaptive mesh refinement. Int. J. Numer. Meth. Engrg., 26:2607–2622, 1988.

    Article  MATH  Google Scholar 

  12. W. A. Dick and M.T. Heath. Whole system simulation of solid propellant rockets. In 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 2002. 2002–4345.

    Google Scholar 

  13. H. Dannelongue and P. Tanguy. Efficient data structure for adaptive remeshing with fem. J. Comput. Phys., 91:94–109, 1990.

    Article  MATH  Google Scholar 

  14. Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer, 2nd edition, 2000.

    Google Scholar 

  15. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag Berlin Heidelberg, Germany, 1987.

    MATH  Google Scholar 

  16. Pascal Jean Frey and Paul-Louis George. Mesh Generation: Application to Finite Elements. Hermes, 2002.

    Google Scholar 

  17. [FGK+00]_A. Fabri, G.-J. Giezeman, L. Kettner, S. Schirra, and S. Schönherr. On the design of CGAL, a computational geometry algorithms library. Softw. — Pract. Exp., 30:1167–1202, 2000. Special Issue on Discrete Algorithm Engineering.

    Article  MATH  Google Scholar 

  18. A. S. Glassner. Maintaining winged-edge models. In J. Arvo, editor, Graphics Gems II, pages 191–201. Academic Press, 1991.

    Google Scholar 

  19. John. R. Gilbert, Gary L. Miller, and Shang-Hua Teng. Geometric mesh partitioning: Implementation and experiments. SIAM J. Sci. Comp., 19:2091–2110, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  20. L. J. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graphics, 4:74–123, 1985.

    Article  MATH  Google Scholar 

  21. M. T. Heath and W. A. Dick. Virtual prototyping of solid propellant rockets. Computing in Science & Engineering, 2:21–32, 2000.

    Article  Google Scholar 

  22. D. Hawken, P. Townsend, and M. Webster. The use of dynamic data structures in finite element applications. Int. J. Numer. Meth. Engrg., 33:1795–1811, 1992.

    Article  Google Scholar 

  23. X. Jiao and M.T. Heath. Accurate, conservative data transfer between nonmatching meshes in multiphysics simulations. In 7th US National Congress on Computational Mechanics, July 2003.

    Google Scholar 

  24. Lutz Kettner. Designing a data structure for polyhedral surfaces. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 146–154, 1998.

    Google Scholar 

  25. Lutz Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Comput. Geom. Theo. Appl., 13:65–90, 1999.

    MATH  Google Scholar 

  26. Y. Kallinderis and P. Vijayan. Adaptive refinement-coarsening schemes for three-dimensional unstructured meshes. AIAA J., 31:1440–1447, 1993.

    Article  Google Scholar 

  27. R. Löhner. Some useful data structures for the generation of unstructured grids. Comm. Appl. Numer. Methods, 4:123–135, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  28. M. Mäntylä. An Introduction to Solid Modeling. Computer Science Press, Rockville, MD, 1988.

    Google Scholar 

  29. D. J. Mavriplis. Adaptive meshing techniques for viscous flow calculations on mixed element unstructured meshes. Int. J. Numer. Meth. Fluids, 34:93–111, 2000.

    Article  MATH  Google Scholar 

  30. F. Noel, J.J.C. Leon, and P. Trompette. Data structures dedicated to an integrated free-form surface meshing environment. Computers and Structures, 57:345–355, 1991.

    Article  Google Scholar 

  31. Mark H. Overmars. Designing the computational geometry algorithms library cgal. In ACM Workshop on Applied Computational Geometry, May 1996.

    Google Scholar 

  32. [PAM+98]_D. Poirier, S. R. Allmaras, D. R. McCarthy, M. F. Smith, and F. Y. Enomoto. The CGNS system, 1998. AIAA Paper 98-3007.

    Google Scholar 

  33. M. C. Rivara. Design and data structure of fully adaptive, multigrid, finite-element software. ACM Trns. Math. Soft., 10:242–264, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  34. J.-F. Remacle, O. Klaas, J. E. Flaherty, and M. S. Shephard. Parallel algorithm oriented mesh database. Engineering with Computers, 18:274–284, 2002.

    Article  Google Scholar 

  35. Jean-Francois. Remacle, B.K. Karamete, and M. Shephard. Algorithm oriented mesh database. In 9th International Meshing Roundtable, 2000.

    Google Scholar 

  36. Jean-François Remacle and Mark S. Shephard. An algorithm oriented mesh database. Int. J. Numer. Meth. Engrg., 58:349–374, 2003.

    Article  MATH  Google Scholar 

  37. The CGNS Steering Sub-committee. The CFD General Notation System Standard Interface Data Structures. AIAA, 2002.

    Google Scholar 

  38. K. Weiler. Edge-based data structures for solid modeling in curvedsurface environments. IEEE Computer Graphics and Applications, 5:21–44, 1985.

    Article  Google Scholar 

  39. K. Weiler. The radial-edge structure: a topological representation for non-manifold geometric boundary representations. In M. Wosny, H. McLaughlin, and J. Encarnacao, editors, Geometric Modeling for CAD Applications, pages 3–36. 1988.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Simulation of Advanced Rockets Computational Science and Engineering, University of Illinois at Urbana-Champaign, USA

    Tyler J. Alumbaugh & Xiangmin Jiao

Authors
  1. Tyler J. Alumbaugh
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  2. Xiangmin Jiao
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Editor information

Editors and Affiliations

  1. Computer Modeling and Sciences Dept., Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM, 87185, USA

    Byron W. Hanks

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© 2005 Springer-Verlag Berlin Heidelberg

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Alumbaugh, T.J., Jiao, X. (2005). Compact Array-Based Mesh Data Structures. In: Hanks, B.W. (eds) Proceedings of the 14th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29090-7_29

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  • DOI: https://doi.org/10.1007/3-540-29090-7_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25137-8

  • Online ISBN: 978-3-540-29090-2

  • eBook Packages: EngineeringEngineering (R0)

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