Skip to main content
SpringerLink
Log in

On control of adaptation in parallel mesh generation

  • Original article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

A black-box methodology of a parallel generation of adaptive anisotropic meshes is described. A control of mesh adaptation, important for robustness and flexibility, may effect parallel properties of the methodology. This is demonstrated with a 3D example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. D’Azevedo E (1991) Optimal triangular mesh generation by coordinate transformation. SIAM J Sci Stat Comput 12:755–786

    Google Scholar 

  2. Rippa S (1992) Long and thin triangles can be good for linear interpolation. SIAM J Numer Anal 29:257–270

    MathSciNet  MATH  Google Scholar 

  3. Agouzal A, Lipnikov K, Vassilevski Y (1999) Adaptive generation of quasi-optimal tetrahedral meshes. East-West J Numer Math 7:223–244

    Google Scholar 

  4. Vassilevski Y, Lipnikov K (1999) Adaptive algorithm for generation of quasi-optimal meshes. Comp Math Math Phys 39:1532–1551

    Google Scholar 

  5. Buscaglia G, Dari E (1997) Anisotropic mesh optimization and its application in adaptivity. Inter J Numer Methods Eng 40:4119–4136

    Article  MATH  Google Scholar 

  6. Vassilevski Y, Lipnikov K (2003) Optimal triangulations: existence, approximation and double differentiation of P1 finite element functions. Comp Math Math Phys 43:827–835

    Google Scholar 

  7. Lipnikov K, Vassilevski Y (2003) Parallel adaptive solution of 3D boundary value problems by Hessian recovery. Comput Methods Appl Mech Eng 192:1495–1513

    Article  MATH  Google Scholar 

  8. Zienkiewicz O, Wu J (1994) Automatic directional refinement in adaptive analysis of compressible flows. Int J Numer Meth Eng 37:2189–2210

    MathSciNet  MATH  Google Scholar 

  9. Ait-Ali-Yahia D, Habashi W, Tam A, Vallet M-G, Fortin M (1996) A directionally adaptive methodology using an edge-based error estimate on quadrilateral grids. Int J Numer Methods Fluids 23:673–690

    Article  MathSciNet  MATH  Google Scholar 

  10. Agouzal A, Vassilevski Y (2002) On a discrete Hessian recovery for P1 finite elements. J Numer Math 10:1–12

    MathSciNet  MATH  Google Scholar 

  11. Buscaglia G, Agouzal A, Ramirez P, Dari E (1998) On Hessian recovery and anisotropic adaptivity. In: Proceedings of the 4th ECCOMAS computational fluid dynamics conference, Athens, Greece, September 1998, pp 403–407

  12. Apel T, Randrianarivony H (2003) Stability of discretizations of the Stokes problem on anisotropic meshes. Math Comput Simulat 61:437–447

    Article  MATH  Google Scholar 

  13. Farhat C, Lesoinne M (1993) Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics. Int J Numer Methods Eng 36:745–764

    MATH  Google Scholar 

  14. D’Azevedo E, Simpson R (1991) On optimal triangular meshes for minimizing the gradient error. Numerische Mathematik 59:321–348

    Google Scholar 

  15. Zavattieri P, Dari E, Buscaglia G (1996) Optimization strategies in unstructured mesh generation. Inter J Numer Meth Eng 39:2055–2071

    Article  MATH  Google Scholar 

  16. Foster I (1995) Designing and building parallel programs. Addison-Wesley, New York

  17. Pothen A, Simon H, Liou K (1990) Partitioning sparse matrices with eigenvectors of graphs. SIAM J Math Anal Appl 11:430–452

    MATH  Google Scholar 

  18. Williams R (1992) Performance of dynamic load balancing algorithms for unstructured mesh calculations. Concurrency–Pract Experience 3:457–481

  19. Prudhomme S, Oden J (1999) On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Comput Methods Appl Mech Eng 176:313–331

    Article  MathSciNet  MATH  Google Scholar 

  20. Apel T (1999) Anisotropic finite elements: local estimates and applications. Teubner, Stuttgart

    Google Scholar 

Download references

Acknowledgements

The authors are grateful to D. Tromeur-Dervoux for his assistance in performing the numerical experiments. The work of the second author has been supported by grant #04-07-90336 of the Russian Foundation for Basic Research of Russian Academy of Sciences.

Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, MS B284, Los Alamos, NM, 87545, USA

    Konstantin Lipnikov

  2. Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, 119991, Moscow, Russia

    Yuri Vassilevski

Authors
  1. Konstantin Lipnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuri Vassilevski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Konstantin Lipnikov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lipnikov, K., Vassilevski, Y. On control of adaptation in parallel mesh generation. Engineering with Computers 20, 193–201 (2004). https://doi.org/10.1007/s00366-004-0287-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-004-0287-1

Keywords

Search

Navigation