Research Article

Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations

  1. Qiang Du1,2,*,
  2. Desheng Wang2

Article first published online: 3 JAN 2003

DOI: 10.1002/nme.616

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 56, Issue 9, pages 1355–1373, 7 March 2003

Additional Information

How to Cite

Du, Q. and Wang, D. (2003), Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Int. J. Numer. Meth. Engng., 56: 1355–1373. doi: 10.1002/nme.616

Author Information

  1. 1

    Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.

  2. 2

    Lab for Scientific and Engineering Computing, Academy of Sciences, Beijing, China

*Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.

Publication History

  1. Issue published online: 3 JAN 2003
  2. Article first published online: 3 JAN 2003
  3. Manuscript Accepted: 16 MAY 2002
  4. Manuscript Revised: 21 JAN 2002
  5. Manuscript Received: 26 NOV 2001

Funded by

  • China State Major Basic Research Project and US NSF. Grant Numbers: G199903280, CCR9988303

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Keywords:

  • centroidal Voronoi Delaunay triangulation;
  • tetrahedral mesh generation;
  • optimization;
  • mesh quality

Abstract

The centroidal Voronoi tessellation based Delaunay triangulation (CVDT) provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high-quality mesh. In this paper, we discuss algorithms for the construction of the constrained CVDT from an initial Delaunay tetrahedral mesh of a three-dimensional domain. By establishing an appropriate relationship between the density function and the specified sizing field and applying the Lloyd's iteration, the constrained CVDT mesh is obtained as a natural global optimization of the initial mesh. Simple local operations such as edges/faces flippings are also used to further improve the CVDT mesh. Several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method. Copyright © 2003 John Wiley & Sons, Ltd.

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