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Multithread Lepp-Bisection Algorithm for Tetrahedral Meshes

  • Conference paper
Proceedings of the 22nd International Meshing Roundtable

Summary

We discuss a multithread Lepp-bisection algorithm for the refinement of quality tetrahedral meshes over multicore architectures. We include an empirical study that show that an efficient and robust serial implementation was obtained, and that an scalable and efficient multithread implementation was obtained. Furthermore, the algorithms tend to improve the refined meshes.

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References

  1. Antonopoulos, C., Blagojevic, F., Chernikov, A., Chrisochoides, N., Nikolopoulos, D.: Algorithm, software, and hardware optimizations for delaunay mesh generation on simultaneous multithreaded architectures. Journal on Parallel and Distributed Computing 69(7) (2009)

    Google Scholar 

  2. Antonopoulos, C., Blagojevic, F., Chernikov, A., Chrisochoides, N., Nikolopoulos, D.: A multigrain delaunay mesh generation method for multicore smt-based architectures. Journal on Parallel and Distributed Computing 69(7) (2009)

    Google Scholar 

  3. Bedregal, C., Rivara, M.-C.: A study on size-optimal longest edge refinement algorithms. In: Jiao, X., Weill, J.-C. (eds.) Proceedings of the 21st International Meshing Roundtable, vol. 123, pp. 121–136. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Balman, M.: Tetrahedral mesh refinement in distributed environments. In: ICPP Workshops, pp. 497–504. IEEE Computer Society (2006)

    Google Scholar 

  5. Boissonnat, J.-D., Devillers, O., Pion, S., Teillaud, M., Yvinec, M.: Triangulations in CGAL. Computational Geometry 22, 5–19 (2002); Special issue SoCG00

    Article  MathSciNet  MATH  Google Scholar 

  6. Breshears, C.: The Art of Concurrency: A Thread Monkey’s Guide to Writing Parallel Applications. O’Reilly Media Inc. (2009)

    Google Scholar 

  7. Castaños, J., Savage, J.: Pared: A framework for the adaptive solution of pdes. In: HPDC (1999)

    Google Scholar 

  8. Castaños, J., Savage, J.: Repartitioning unstructured adaptive meshes. In: IPDPS, pp. 823–832. IEEE Computer Society (2000)

    Google Scholar 

  9. Castaños, J., Savage, J.: Parallel refinement of unstructured meshes. Technical report cs-99-10, Department of Computer Science, Brown University

    Google Scholar 

  10. Chernikov, A., Chrisochoides, N.: Algorithm 872: Parallel 2d constrained delaunay mesh generation. ACM Transactions on Mathematical Software 34(1) (2008)

    Google Scholar 

  11. Chernikov, A., Chrisochoides, N.: Generalized two-dimensional delaunay mesh refinement. SIAM Journal on Scientific Computing 31, 3387–3403 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Grama, A., Karypis, G., Kumar, V., Gupta, A.: Introduction to Parallel Computing, 2nd edn. Addison Wesley (2003)

    Google Scholar 

  13. Jones, M., Plassmann, P.: Computational results for parallel unstructured mesh computations. Computing Systems in Engineering 5(4-6), 297–309 (1994); 3rd National Symposium on Large-Scale Structural Analysis for High-Performance Computers and Workstations

    Article  Google Scholar 

  14. Jones, M., Plassmann, P.: Adaptive refinement of unstructured finite-element meshes. Finite Elem. Anal. Des. 25(1-2), 41–60 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Jones, M., Plassmann, P.: Parallel algorithms for the adaptive refinement and partitioning of unstructured meshes. In: Proceedings of the Scalable High-Performance Computing Conference, pp. 478–485. IEEE (1997)

    Google Scholar 

  16. Plaza, A., Rivara, M.C.: Mesh refinement based on the 8-tetrahedra longest-edge partition. In: 12th International Meshing Roundtable, pp. 67–78 (2003)

    Google Scholar 

  17. Rauber, T., Rünger, G.: Parallel Programming for multicore and cluster systems. Springer (2010)

    Google Scholar 

  18. Rivara, M.C.: Lepp-bisection algorithms, applications and mathematical properties. Appl. Numer. Math. 59(9), 2218–2235 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rivara, M.C., Calderon, C., Fedorov, A., Chrisochoides, N.: Parallel decoupled terminal-edge bisection method for 3d mesh generation. Eng. Comput. 22(2), 111–119 (2006)

    Article  Google Scholar 

  20. Rivara, M.C., Rodriguez, P., Montenegro, R., Jorquera, J.: Multithread parallelization of lepp-bisection algorithms. Appl. Numer. Math. 62(4), 473–488 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Rivara, M.C.: New longest-edge algorithms for the refinement and/or improvement of unstructured triangulations. International Journal for Numerical Methods in Engineering 40(18), 3313–3324 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Shephard, M., Flaherty, J., Bottasso, C., de Cougny, H., Ozturan, C., Simone, M.: Parallel automatic adaptive analysis. Parallel Comput. 23(9), 1327–1347 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  23. Shephard, M.S., Guerinoni, F., Flaherty, J., Ludwig, R., Baehmann, P.: Finite octree mesh generation for automated adaptive three-dimensional flow analysis. In: Proc. 2nd Int. Conf. Numer. Grid Generation in Computational Fluid Mechanics, pp. 709–718 (1988)

    Google Scholar 

  24. Teillaud, M.: Three dimensional triangulations in cgal. Abstracts 15th European Workshop Computational Geometry, pp. 175–178. INRIA Sophia-Antipolis (1999)

    Google Scholar 

  25. Williams, R.: Adaptive parallel meshes with complex geometry. In: Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, pp. 201–213. Elsevier Science Publishers (1991)

    Google Scholar 

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Correspondence to Pedro A. Rodriguez .

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Rodriguez, P.A., Rivara, MC. (2014). Multithread Lepp-Bisection Algorithm for Tetrahedral Meshes. In: Sarrate, J., Staten, M. (eds) Proceedings of the 22nd International Meshing Roundtable. Springer, Cham. https://doi.org/10.1007/978-3-319-02335-9_29

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  • DOI: https://doi.org/10.1007/978-3-319-02335-9_29

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02334-2

  • Online ISBN: 978-3-319-02335-9

  • eBook Packages: EngineeringEngineering (R0)

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