Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Daniel Sieger, Pierre Alliez, Mario Botsch
International Meshing Roundtable, 2010
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Abstract

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.

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