Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

A Comparison of Mesh Morphing Methods for 3D Shape Optimization

  • Conference paper
Proceedings of the 20th International Meshing Roundtable

Summary

The ability to automatically morph an existing mesh to conform to geometry modifications is a necessary capability to enable rapid prototyping of design variations. This paper compares six methods for morphing hexahedral and tetrahedral meshes, including the previously published FEMWARP and LBWARP methods as well as four new methods. Element quality and performance results show that different methods are superior on different models. We recommend that designers of applications that use mesh morphing consider both the FEMWARP and a linear simplex based method.

The work of the third author is supported in part by NSF grant CNS-0720749 and NSF CAREER Award OCI-1054459.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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.

Similar content being viewed by others

References

  1. Baker, T.J.: Mesh movement and metamorphosis. In: Proc. 10th Int. Meshing Roundtable, pp. 387–396 (2001)

    Google Scholar 

  2. Branets, L., Carey, G.F.: A local cell quality metric and variational grid smoothing algorithm. Eng. Comput. 21, 19–28 (2005)

    Article  Google Scholar 

  3. Brewer, M., Diachin, L., Knupp, P., Leurent, T., Melander, D.: The Mesquite mesh quality improvement toolkit. In: Proc. 12th Int. Meshing Roundtable, pp. 239–250 (2003)

    Google Scholar 

  4. Cardoze, D., Miller, G., Olah, M., Phillips, T.: A Bézier-based moving mesh framework for simulation with elastic membranes. In: Proc. 13th Int. Meshing Roundtable, 71-80 (2004)

    Google Scholar 

  5. Dai, M., Schmidt, D.P.: Adaptive tetrahedral meshing in free-surface flow. J. Comp. Phys. 208, 228–252 (2005)

    Article  MATH  Google Scholar 

  6. Davis, T.A., Natarajan, E.P.: Algorithm 8xx:KLU, a direct sparse solver for circuit simulation problems. ACM Transactions on Mathematical Software, 1-17 (2011)

    Google Scholar 

  7. Floater, M.S.: One-to-one piecewise linear mappings over triangulations. Math. Comp. 72, 685–696 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. GSH3D, INRIA, http://www-roc.inria.fr/gamma/gamma/ghs3d/ghs.php

  9. Helenbrook, B.T.: Mesh deformation using the biharmonic operator. Int. J. Num. Meth. Engr. 56, 1007–1021 (2003)

    Article  MATH  Google Scholar 

  10. Jacobson, A., Baran, I., Popović, J., Sorkine, O.: Bounded Biharmonic Weights for Real-Time Deformation. To Appear In ACM Transactions On Graphics (Proc. Of ACM SIGGRAPH) 30(4) (2011), http://igl.ethz.ch/projects/bbw/

  11. Knupp, P.: Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities, part I. Int. J. Num. Meth. Engr. 48, 401–420 (2000)

    Article  MATH  Google Scholar 

  12. Knupp, P.: Next-generation sweep tool: a method for generating all-hex meshes on two-and-one-half dimensional geomtries. In: Proc. 7th Int. Meshing Roundtable, pp. 505–513 (1998)

    Google Scholar 

  13. Knupp, P.: Updating meshes on deforming domains: An application of the target-matrix paradigm. Commun. Num. Meth. Engr. 24(6), 467–476 (2007)

    Article  MathSciNet  Google Scholar 

  14. Li, R., Tang, T., Zhang, P.: Moving mesh methods in multiple dimensions based on harmonic maps. J. Comput. Phys. 170, 562–588 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Michler, A.K.: Aircraft control surface deflection using RBF-based mesh deformation. Int. J. Num. Meth. Engr. (2011), doi: 10.1002/nme.3208

    Google Scholar 

  16. Nocedal, J., Wright, S.J.: Numerical optimization, 2nd edn. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  17. Shontz, S.M., Vavasis, S.A.: Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes. BIT, Numerical Mathematics 50, 863–884 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  18. Shontz, S.M., Vavasis, S.A.: A mesh warping algorithm based on weighted Laplacian smoothing. In: Proc. 12th Int. Meshing Roundtable, pp. 147–158 (2003)

    Google Scholar 

  19. Shontz, S.M., Vavasis, S.A.: A robust solution procedure for hyperelastic solids with large boundary deformation. Eng. Comput. (2011), doi: 10.1007/s00366-011-0225-y

    Google Scholar 

  20. Sibson, R.: A brief description of natural neighbor interpolation. In: Interpretting Multivariate Data, pp. 21–36. John Wiley and Sons, New York (1981)

    Google Scholar 

  21. Sigal, I.A., Hardisty, M.R., Whyne, C.M.: Mesh-morphing algorithms for specimen-specific finite element modeling. J. Biomech. 41(7), 1381–1389 (2008)

    Article  Google Scholar 

  22. Stein, K., Tezduyar, T., Benney, R.: Mesh moving techniques for fluid-structure interactions with large displacements. Trans. ASME 2003 70, 58–63 (2003)

    MATH  Google Scholar 

  23. Stein, K., Tezduyar, T., Benney, R.: Automatic mesh update with the solid-extension mesh moving technique. Comput. Meth. Appl. M. 193, 2019–2032 (2004)

    Article  MATH  Google Scholar 

  24. Staten, M.L., Canann, S.A., Owen, S.J.: BMSWEEP: locating interior nodes during sweeping. Eng. Comput. 15(3), 212–218 (1999)

    Article  MATH  Google Scholar 

  25. Tezduyar, T., Behr, M., Mittal, S., Johnson, A.A.: Computation of unsteady incompressible flows with the finite element methods – Space-time formulations, iterative strategies and massively parallel implementations. New Methods in Transient Analysis, PVP-vol. 246/AMD-vol. 143, ASME, New York, 7-24 (1992)

    Google Scholar 

  26. The Trilinos Project, Sandia Nat. Lab., http://trilinos.sandia.gov/

  27. Vavasis, S.: QMG: mesh generation and related software (2010), http://www.cs.cornell.edu/home/vavasis/qmg-home.html

  28. Vurputoor, R., Mukherjee, N., Cabello, J., Hancock, M.: A mesh morphing technique for geometrically dissimilar tesselated surfaces. In: Proc. 16th Int. Meshing Roundtable, pp. 315–334 (2007)

    Google Scholar 

  29. Watson, D.F.: nngridr: an implementation of natural neighbor interpolation. University of Western Australia (1994)

    Google Scholar 

  30. Wright, S.J.: Primal-dual interior-point methods. SIAM (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Staten, M.L., Owen, S.J., Shontz, S.M., Salinger, A.G., Coffey, T.S. (2011). A Comparison of Mesh Morphing Methods for 3D Shape Optimization. In: Quadros, W.R. (eds) Proceedings of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24734-7_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24734-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24733-0

  • Online ISBN: 978-3-642-24734-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics