Skip to main content

High Quality Bi-Linear Transfinite Meshing with Interior Point Constraints

  • Conference paper
Book cover Proceedings of the 15th International Meshing Roundtable

Abstract

For a variety of structural finite element analyses on automotive body panels, aerospace wings and space satellite panels, high-quality, structured quadrilateral meshing is imperative. Transfinite meshing, the technique to produce such meshes is severely infringed by the presence of surface-interior point constraints. The present paper attempts to solve the inverse problem of transfinite meshing with interior point cointraints. A modified Newton Raphson based solution is proposed to inverse solve Coons bi-linear blending equation. The Coons parametric coordinates are thus determined for a set of face-interior points from their global coordinates. The boundary of the surface is next seeded with “soft-apoints” at reflected locations and smart-discretized to result in high fidelity, high-quality transfinite meshes.

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

Access this chapter

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. 1. O.C., Zienkiewicz and D. V. Phillips, “An Automatic Mesh Generation Scheme For Plane and Curved Surfaces By Isoparametric Co-ordinates” International J. Numerical Meth. Engg. Vol 3 pp. 519–528 (1971).

    Article  MATH  Google Scholar 

  2. 2. W.J., Gordon and C.A. Hall, “Construction of curvilinear co-ordinate systems and applications to mesh generation” International J. Numerical Meth. Engg. Vol 7 pp. 461–477 (1973).

    Article  MATH  Google Scholar 

  3. 3. W.A., Cook, “Body oriented (natural) co-ordinates for generating three-dimensional meshes” International J. Numerical Meth. Engg. Vol 8 pp. 27–43 (1974).

    Article  MATH  Google Scholar 

  4. 4. Robert, Haber, Mark, S. Shepherd, John, F. Abel, Richard, H. Gallagher and Donald, P. Greenberg “A General Two-Dimensional, Graphical Finite Element Preprocessor Utilizing Discrete Transfinite Mappings” International J. Numerical Meth. Engg. Vol 17 pp. 1015–1044 (1981).

    Article  MATH  Google Scholar 

  5. 5. R. Pierrot, J. Vazeilles and A. Perronnet, “Une methode de generation d'un maillage 2d ou 3d a' partir d'un maillage grossier” Annales de l'I.T.B.T.P. Nol 372 (May 1979).

    Google Scholar 

  6. 6. A. Perronnet, “Logical and physical representation of an object, modularity for the programming of f.e.m.” PDE Software, Interface and Systems, Elsevier Publishers North-Holland IFIP. Soderkoping, Sweden (1984).

    Google Scholar 

  7. 7. Alain, Perronnet, “Triangle, tetrahedron, pentahedron transfinite interpolations. Application to the generation of C0 or G1-continuous algebraic meshes” Proc. Int. Conf. Numerical Grid Generation in Computational Field Simulations. Greenwich, England. Vol 7 pp. 467–476 (July6-9,1998).

    Google Scholar 

  8. 8. Scott, A. Mitchell, “Choosing Corners of Rectangles for Mapped Meshing” Proc. 13th Annual Symposium on Computational Geometry, ACM Press, pp. 87–93, (June 1997).

    Google Scholar 

  9. 9. Scott, A. Mitchell, “High Fidelity Interval Assignment” Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp. 33–44, (October 1997).

    Google Scholar 

  10. 10. T.K.H.Tam and Cecil, G. Armstrong, “Finite Element mesh control by integer programming” International J. Numerical Meth. Engg. Vol 36, pp. 2581–2605 (1993).

    Article  MATH  Google Scholar 

  11. 11. G. Farin, Curves and Surfaces for computer aided geometric design. Academic Press Inc., San Diego, 1990.

    MATH  Google Scholar 

  12. 12. I.D. Faux and M.J. Pratt, Computational geometry for design and manufacture. Ellis Horwood, Chichester, 1979.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this paper

Cite this paper

Mukherjee, N. (2006). High Quality Bi-Linear Transfinite Meshing with Interior Point Constraints. In: Pébay, P.P. (eds) Proceedings of the 15th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34958-7_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-34958-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34957-0

  • Online ISBN: 978-3-540-34958-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics