Optimizing Voronoi Diagrams for Polygonal Finite Element Computations
Résumé
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.
Domaines
Géométrie algorithmique [cs.CG]
Origine : Fichiers produits par l'(les) auteur(s)
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