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Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Daniel Sieger 1, * Pierre Alliez 2 Mario Botsch 1
* Corresponding author
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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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Submitted on : Friday, November 12, 2010 - 9:20:28 AM
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Daniel Sieger, Pierre Alliez, Mario Botsch. Optimizing Voronoi Diagrams for Polygonal Finite Element Computations. International Meshing Roundtable, Sandia Labs, Oct 2010, Chattanooga, United States. pp.335-350, ⟨10.1007/978-3-642-15414-0_20⟩. ⟨inria-00535602⟩

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