DARSS: a hybrid mesh smoother for all hexahedral meshes | Engineering with Computers
Skip to main content
Springer Nature Link
Log in

DARSS: a hybrid mesh smoother for all hexahedral meshes

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

Abstract

A method for smoothing hexahedral meshes has been developed. The method consists of two phases. In the first phase, the nodes are moved based on an explicit formulation. A constraint has also been implemented to prevent the deterioration of elements associated with the node being moved. The second phase of the method is optismoothing based on the Nelder–Mead simplex method. The summation of the Jacobian of all the elements sharing a node has been taken as the function to be maximized. The method has been tested on meshes up to 18,305 hexahedral elements and was found to be stable and improved the mesh in about 112.6 s on an Intel Centrino® 1.6 GHz, 1 GB RAM machine. The method thus has the advantage of being effective as well as being computationally efficient.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. White DR, Mingu L, Benzley SE, Sjaardema GD (1995) Automated hexahedral mesh generation by virtual decomposition. In: Proceedings of 4th international meshing roundtable. Sandia National Laboratories, California, pp 165–176

  2. Knupp PM (1998) Next generation Sweep Tool: a method for generating all hex meshes on a two and one half dimensional geometries. In: Proceedings of 7th international meshing roundtable. Sandia National Laboratory, California, pp 505–513

  3. Folwell NT, Mitchell SA (1999) Reliable whisker weaving via curve contraction. Eng Comput 15:292–302

    Article  MATH  Google Scholar 

  4. Jankovich SR, Benzley SE, Shepherd JF, Mitchell SA (1999) The Graft Tool: an all-hexahedral transition algorithm for creating a multi-directional swept volume mesh. In: 8th international meshing roundtable. S. Lake Tahoe, CA, pp 387–392

  5. Owen SJ, Saigal S (2000) H-Morph: an indirect approach to advancing from hex meshing. Int J Numer Methods Eng 49:289–312

    Article  MATH  Google Scholar 

  6. White D, Rodrigue G (1997) Improved vector FEM solutions of Maxwell’s equations using grid pre-conditioning. Int J Numer Meth Eng 40:3815–3837

    Article  MathSciNet  MATH  Google Scholar 

  7. Shontz SM, Vavasis SA (2004) A linear weighted laplacian smoothing framework for warping tetrahedral meshes. CS.NA/0410045. October 2004

  8. Persson P-O, Strang G (2004) A simple mesh generator in MATLAB. SIAM Rev 46(2):329–345

    Article  MathSciNet  MATH  Google Scholar 

  9. Canann SA, Stephenson MB, Blacker T (1993) Optismoothing: an optimization-driven approach to mesh smoothing. Finite Elem Anal Des 13:185–190

    Article  MathSciNet  MATH  Google Scholar 

  10. Cannan SA, Tristano JR, Staten ML (1998) An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes 7th international meshing roundtable, October 26–28, 1998, Dearborn, Michigan, USA

  11. Hansbo P (1995) Generalized Laplacian smoothing of unstructured grids. Commun Numer Methods Eng 11:455–464

    Article  MATH  Google Scholar 

  12. Amenta N, Bern M, Eppstein D (1997) Optimal point placement for mesh smoothing. In 8th ACM–SIAM symposium on discrete algorithms. New Orleans, pp 528–537

  13. Freitag L (1997) On combining Laplacian and optimization-based mesh smoothing techniques. Trends in unstructured mesh generation, July 1997, ASME, pp 37–43

  14. Xu H, Newman TS (2006) An angle-based optimization approach for 2D finite element mesh smoothing. Finite Elem Anal Des 42:1150–1164

    Article  MathSciNet  Google Scholar 

  15. Khattri S (2006) A new smoothing algorithm for quadrilateral and hexahedral meshes, LNCS, ICCS 2006, pp 239–246

  16. Lee CK, Lo SH (1994) A new scheme for the generation of a graded quadrilateral mesh. Comput Struct 52(5):847–857

    Article  MathSciNet  MATH  Google Scholar 

  17. Herrmann LR (1976) Laplacian–isoparametric grid generation scheme. J Eng Mech Div 102(5):749–756

    Google Scholar 

  18. Knupp PM (1999) Winslow smoothing on two-dimensional unstructured meshes. Eng Comput 15:263–268

    Article  MATH  Google Scholar 

  19. Vartziotis D, Wipper J (2009) The geometric element transformation method for mixed mesh smoothing. Eng Comput 25:287–301

    Article  Google Scholar 

  20. Semonova I, Kozhekin N, Savchenko V, Hagiwara I (2005) A general framework for analysis and comparison of surface mesh optimization techniques. Eng Comput 21:91–100

    Article  Google Scholar 

  21. Knupp PM (2001) Hexahedral and tetrahedral mesh untangling. Eng Comput 17:261–268

    Article  MATH  Google Scholar 

  22. Parthasarathy V, Kodiyalam S (1991) A constrained optimization approach to finite element mesh smoothing. Finite Elem Anal Des 9:309–320

    Article  MATH  Google Scholar 

  23. Calvo NA, Ideslohn SR (2001) All hexahedral mesh smoothing with a node based measure of mesh quality. Int J Numer Methods Eng 50:1957–1967

    Article  MATH  Google Scholar 

  24. Knupp PM (2003) A method for hexahedral mesh shape optimization. Int J Numer Methods Eng 58:319–332

    Article  MATH  Google Scholar 

  25. Shimada K, Gossard DC (1995) Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing. Solid modelling ‘95 (conference proceedings), pp 409–419

  26. Shimada K, Yamada A, Itoh T (2000) Anisotropic triangular meshing of parametric surfaces via close packing of ellipsoidal bubbles. Int J Comput Geom Appl 10(4):400–424

    Article  MathSciNet  Google Scholar 

  27. Zhou T, Shimada K (2000) An angle based approach to two dimensional mesh smoothing. In: Proceedings of the 9th international meshing roundtable, pp 373–384

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

    Article  Google Scholar 

  29. Kober C, Muller-Hannemann M (2001) A case study in hexahedral mesh generation: simulation of the human mandible. Eng Comput 17:249–260

    Article  MATH  Google Scholar 

  30. Vartziotis D, Athanasiadis T, Goudas I, Wipper J (2008) Mesh smoothing using the geometric element transformation method. Comput Methods Appl Mech Eng 197(45–48):3760–3767

    Google Scholar 

  31. Vartziotis D, Wipper J (2009) The geometric element transformation method for mixed mesh smoothing. Eng Comput 25(3):287–301

    Article  Google Scholar 

  32. Vartziotis D, Wipper J (2009) Classification of symmetry generating polygon transformations and geometric prime algorithms. Math Pannon 20(2):167–187

    MathSciNet  MATH  Google Scholar 

  33. Vartziotis D, Wipper J (2010) Characteristic parameter sets and limits of circulant Hermitian polygon transformations. Linear Algebra Appl 433(5):945–955

    Article  MathSciNet  MATH  Google Scholar 

  34. Vartziotis D, Wipper J, Schwald B (2009) The geometric element transformation method for tetrahedral mesh smoothing. Comput Methods Appl Mech Eng 199(1–4):169–182

    Article  MathSciNet  MATH  Google Scholar 

  35. Vartziotis D, Wipper J (2011) A dual element based geometric element transformation method for all-hexahedral mesh smoothing. Comput Methods Appl Mech Eng 200:1186–1203

    Article  MathSciNet  MATH  Google Scholar 

  36. Savchenko M, Egorova O, Hagiwara I, Savchenko V (2005) Hexahedral mesh improvement algorithm. JSME Int J Ser C 48(2):130–136

    Article  Google Scholar 

  37. Savchenko V, Savchenko M, Egorova O, Hagiwara I (2008) Mesh quality improvement radial basis functions approach. Int J Comput Math 85(10):1589–1607

    Article  MathSciNet  MATH  Google Scholar 

  38. Taubin G (1995) A signal processing approach to fair surface design. Proc SIGGRPH’95 29:351–358

    Google Scholar 

  39. Riccius J, Schweizerhof K, Baumann M (1997) Combination of adaptivity and mesh smoothing for the finite element analysis of shells with intersections. Int J Numer Meth Eng 40:2459–2474

    Article  MATH  Google Scholar 

  40. Bank RE, Smith RK (997) 1997. Mesh smoothing using a posteriori error estimates SIAM J Numer Anal(34):3–979

    MathSciNet  Google Scholar 

  41. Jacquotte OP, Coussement G (1992) Structured mesh adaption: space accuracy and interpolation methods. Comput Methods Appl Mech Eng 101:397–432

    Article  MathSciNet  MATH  Google Scholar 

  42. Yin J, Teodosiu C (2008) Constrained mesh optimization on boundary. Eng Comput 24:231–240

    Article  Google Scholar 

  43. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J Optim 9(1):112–147

    Article  MathSciNet  MATH  Google Scholar 

  44. Mathews J, Fink KK (2004) Numerical methods using Matlab, 4th edn. Prentice Hall Inc., New Jersey, pp 430–433

    Google Scholar 

  45. Knupp PM (2000) Hexahedral mesh untangling and algebraic mesh quality metrics. In: Proceedings of 9th international meshing roundtable, pp 173–183

  46. Deng B (2007) Human model for real-world vehicle–pedestrian impact simulations. Human modeling and simulation in automotive safety. Technical Report, ENSAM de Paris, Paris

  47. Untaroiu CD (2005) Development and validation of a finite element model of human lower limb. PhD thesis, UVA

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Dhaval Jani, Anoop Chawla & Sudipto Mukherjee

  2. Department of Computer Science, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Raman Khattri

Authors
  1. Dhaval Jani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anoop Chawla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sudipto Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Raman Khattri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anoop Chawla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jani, D., Chawla, A., Mukherjee, S. et al. DARSS: a hybrid mesh smoother for all hexahedral meshes. Engineering with Computers 28, 179–188 (2012). https://doi.org/10.1007/s00366-011-0235-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-011-0235-9

Keywords

Search

Navigation