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Optimizing Voronoi Diagrams for PolygonalFinite Element Computations

Daniel Sieger, Pierre Alliez, and Mario Botsch

Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.335-350, October 3-6 2010

IMR
PROCEEDINGS

19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

Bielefeld University, Germany.
Email: fdsieger,botschg@techfak.uni-bielefeld.de
INRIA Sophia-Antipolis, France.
Email: pierre.alliez@sophia.inria.fr

Summary
We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal nite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that e ectively 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 e ective optimization achieves a signi cant improvement of the sti ness matrix condition number.

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