Skip to main content
SpringerLink
Log in

Parallel Curved Mesh Adaptation for Large Scale High-Order Finite Element Simulations

  • Conference paper
Proceedings of the 21st International Meshing Roundtable

Summary

This paper presents the development of a parallel adaptive mesh control procedure designed to operate with high-order finite element analysis packages to enable large scale automated simulations on massively parallel computers. The curved mesh adaptation procedure uses curved entity mesh modification operations. Applications of the curved mesh adaptation procedure have been developed to support the parallel automated adaptive accelerator simulations at SLAC National Accelerator Laboratory.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alauzet, F., Li, X., Seol, E.S., Shephard, M.S.: Parallel anisotropic 3d mesh adaptation by mesh modification. Engineering with Computers 21, 247–258 (2006)

    Article  Google Scholar 

  2. de Cougny, H.L., Shephard, M.S.: Parallel refinement and coarsening of tetrahedral meshes. International Journal for Numerical Methods in Engineering 46(7), 1101–1125 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. de Cougny, H.L., Shephard, M.S., Georges, M.K.: Explicit node point mesh smoothing within the octree mesh generator. Technical report, Scientfic Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY (1990)

    Google Scholar 

  4. Dey, S., O’Bara, R.M., Shephard, M.S.: Curvilinear mesh generation in 3d. Computer-Aided Design 33, 199–209 (2001)

    Article  Google Scholar 

  5. Farin, G.E.: Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide, 3rd edn. Academic Press, Waltham (1992)

    Google Scholar 

  6. Freitag, L.A., Knupp, P.M.: Tetrahedral element shape optimization via the jacobian determinant and condition number. In: Proceeding of the 8th International Meshing Roundtable, South Lake Tahoe, CA, pp. 247–258 (1999)

    Google Scholar 

  7. George, P.L., Borouchaki, H.: Construction of tetrahedral meshes of degree two. International Journal for Numerical Methods in Engineering 90, 1156–1182 (2012)

    Article  MATH  Google Scholar 

  8. Johnen, A., Remacle, J.-F., Geuzaine, C.: Geometrical Validity of Curvilinear Finite Elements. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, vol. 90, pp. 255–271. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Knupp, P.M.: Introducing the target-matrix paradigm for mesh optimization via node-movement. In: Proceedings of the 19th International Meshing Roundtable, Chattanooga, TN, pp. 67–84 (2010)

    Google Scholar 

  10. Li, X., Shephard, M.S., Beall, M.W.: Accounting for curved domains in mesh adaptation. International Journal for Numerical Methods in Engineering 58(2), 247–276 (2003)

    Article  MATH  Google Scholar 

  11. Li, X., Shephard, M.S., Beall, M.W.: 3d anisotropic mesh adaptation by mesh modification. Computer Methods in Applied Mechanics and Engineering 194, 4915–4950 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, A., Joe, B.: Relationship between tetrahedron shape measures. BIT Numerical Mathematics 34(2), 268–287 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lu, Q.: Developments of parallel curved meshing for high-order finite element simulations. Master’s thesis, Rensselaer Polytechnic Institute., Troy, NY (December 2011)

    Google Scholar 

  14. Luo, X., Shephard, M.S., Lee, L.-Q., Ge, L., Ng, C.: Moving curved mesh adaptation for higher-order finite element simulations. Engineering with Computers 27(1), 41–50 (2010)

    Article  MATH  Google Scholar 

  15. Luo, X., Shephard, M.S., Yin, L.-Z., O’Bara, R.M., Nastasi, R., Beall, M.W.: Construction of near optimal meshes for 3d curved domains with thin sections and singularities for p-version method. Engineering with Computers 22(1), 41–50 (2010)

    Google Scholar 

  16. Morin, G., Goldman, R.: On the smooth convergence of subdivision and degree elevation for bezier curves. Computer Aided Geometric Design 18, 657–666 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mubarak, M., Seol, S., Lu, Q., Shephard, M.S.: A parallel ghosting algorithm for the flexible distributed mesh database. Submitted to Scientific Programming (2012)

    Google Scholar 

  18. Persson, P.-O., Peraire, J.: Curved mesh generation and mesh refinement using lagrangian solid mechanics. In: Proceedings of the 47th AIAA Aerospace Sciences Meeting and Exhibit (January 2009)

    Google Scholar 

  19. Prautzsch, H., Kobbelt, L.: Convergence of subdivision and degree elevation. Advances in Computational Mathematics 2, 143–154 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sederberg, T.W.: Computer Aided Geometric Design (2011), http://tom.cs.byu.edu/~557/text/cagd.pdf (accessed May 31, 2012)

  21. Szabo, B.A., Babuska, I.: Finite Element Analysis. John Wiley & Sons Inc., New York (1991)

    MATH  Google Scholar 

  22. Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. part 1. the recovery technique. International Journal for Numerical Methods in Engineering 33, 1331–1361 (1992)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY, USA

    Qiukai Lu & Mark S. Shephard

  2. Simmetrix Inc., Clifton Park, NY, USA

    Saurabh Tendulkar & Mark W. Beall

Authors
  1. Qiukai Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark S. Shephard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saurabh Tendulkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mark W. Beall
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiukai Lu .

Editor information

Editors and Affiliations

  1. , Department of Applied Mathematics &, Stony Brook University, Stony Brook, 11794-3600, New York, USA

    Xiangmin Jiao

  2. , Bruyeres le Chatel, CEA, Arpajon Cedex, 91297, France

    Jean-Christophe Weill

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lu, Q., Shephard, M.S., Tendulkar, S., Beall, M.W. (2013). Parallel Curved Mesh Adaptation for Large Scale High-Order Finite Element Simulations. In: Jiao, X., Weill, JC. (eds) Proceedings of the 21st International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33573-0_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33573-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33572-3

  • Online ISBN: 978-3-642-33573-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation