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Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

  • Daniel Sieger
  • Pierre Alliez
  • Mario Botsch

Summary

We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities—short edges in the Voronoi diagram. We evaluate our method on a 2D Poisson problem and demonstrate that our simple but effective optimization achieves a significant improvement of the stiffness matrix condition number.

Keywords

Voronoi Diagram Delaunay Triangulation Voronoi Cell Short Edge Mesh Optimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniel Sieger
    • 1
  • Pierre Alliez
    • 2
  • Mario Botsch
    • 1
  1. 1.Bielefeld UniversityGermany
  2. 2.INRIA Sophia-AntipolisFrance

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