Skip to main content

Hierarchical Delaunay Triangulation for Meshing

  • Conference paper
Experimental Algorithms (SEA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6630))

Included in the following conference series:

  • 2790 Accesses

Abstract

This paper discusses an elliptical pad structure and its polygonal approximation. The elliptical pad is a part of via model structures, which are important and critical components on today’s multilayered Printed Circuit Board (PCB) and electrical packaging. To explore meshing characterization of the elliptical pad helps mesh generation over 3D structures for electromagnetic modeling (EM) and simulation on PCB and electrical packaging. Because elliptical structures are often key PCB features, we introduce a hierarchical mesh construct and show that it has several useful Delaunay quality characteristics. Then we show experimentally that Computational Geometry Algorithm Library’s (CGAL) meshing of an elliptical structure at different resolution levels and with various aspect ratios produces patterns similar to our construct. In particular, our experiment also shows that the result of meshing is not only constrained Delaunay triangulation but also Delaunay triangulation.

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

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. Botsch, M., et al.: ACM SIGGRAPH 2007 course 23: Geometric modeling based on polygonal meshes. Association for Computing Machinery (2007)

    Google Scholar 

  2. CGAL User and Reference Manual, http://www.cgal.org

  3. Edelsbrunner, H.: Geometry and Topology for Mesh Generation. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  4. Frey, P.J., George, P.-L.: Mesh Generation: application to finite elements. Oxford and HERMES Science Publishing, Paris (2000)

    MATH  Google Scholar 

  5. Goodman, J.E., O’Rourke, J. (eds.): Handbook of Discrete and Computational Geometry, 2nd edn. CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  6. Hall, S.H., Hall, G.W., McCall, J.A.: High-Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices. John Wiley & Sons, Inc./A Wiley-Interscience Publication (2000)

    Google Scholar 

  7. Holzbecher, E., Si, H.: Accuracy Tests for COMSOL – and Delaunay Meshes, http://cds.comsol.com/access/dl/papers/5436/Holzbecher.pdf

  8. Hwang, C.-T., et al.: Partially Prism-Gridded FDTD Analysis for Layered Structures of Transversely Curved Boundary. IEEE Transactions of Microwave Theory and Techniques 48(3), 339–346 (2000)

    Article  MathSciNet  Google Scholar 

  9. Lee, S.: Efficient Finite Element Electromagnetic Analysis for High-Frequency/High Speed Circuits and Multiconductor Transmission Lines. Doctoral Dissertation, University of Illinois at Urbana-Champaign, Urbana Illinois (2009)

    Google Scholar 

  10. Ramahi, O.M.: Analysis of Conventional and Novel Delay Lines: A Numerical Study. Journal of Applied Computational Electromagnetic Society 18(3), 181–190 (2003)

    Google Scholar 

  11. Rodger, D., et al.: Finite Element Modelling of Thin Skin Depth Problems using Magnetic Vector Potential. IEEE Transactions on Magnetics 33(2), 1299–1301 (1997)

    Article  Google Scholar 

  12. Thompson, J.F., Soni, B.K., Weatherill, N.P. (eds.): Handbook of Grid Generation. CRC Press, Boca Raton (1999)

    MATH  Google Scholar 

  13. Tsukerman, I.: A General Accuracy Criterion for Finite Element Approximation. IEEE Transactions on Magnetics 34(5), 1–4 (1998)

    Article  Google Scholar 

  14. Tummala, R.R.: SOP: What Is It and Why? A New Microsystem-Integration Technology Paradigm-Moore’s Law for System Integration of Miniaturized Covergent Systems of the New Decade. IEEE Transactions on Advanced Packaging 27(2), 241–249 (2004)

    Article  Google Scholar 

  15. Ye, S., Daniels, K.: Triangle-based Prism Mesh Generation for Electromagnetic Simulations. In: Research Note for the 17th International Meshing Roundtable, Pittsburgh, Pennsylvania, October 12-15 (2008)

    Google Scholar 

  16. Ye, S., Daniels, K.: Triangle-based Prism Mesh Generation on Interconnect Models for Electromagnetic Simulations. In: 19th Annual Fall Workshop on Computational Geometry (sponsored by NSF), Tufts University, Medford, MA, November 13-14 (2009)

    Google Scholar 

  17. Yvinec, M.: Private communication regarding CGAL’s 2D constrained Delaunay algorithm (November 2009)

    Google Scholar 

  18. Miller, G., Phillips, T., Sheehy, D.: Linear-Sized Meshes. In: Canadian Conference on Computational Geometry, Montreal, Quebec, August 13-15 (2008)

    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

Ye, S., Daniels, K. (2011). Hierarchical Delaunay Triangulation for Meshing. In: Pardalos, P.M., Rebennack, S. (eds) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol 6630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20662-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20661-0

  • Online ISBN: 978-3-642-20662-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics