%0 Conference Proceedings %T Optimizing Voronoi Diagrams for Polygonal Finite Element Computations %+ Universität Bielefeld = Bielefeld University %+ Geometric computing (GEOMETRICA) %A Sieger, Daniel %A Alliez, Pierre %A Botsch, Mario %< avec comité de lecture %B International Meshing Roundtable %C Chattanooga, United States %Y Suzanne Shontz %I Springer %3 Proceedings of the 19th International Meshing Roundtable %V Part 5 %P 335-350 %8 2010-10-03 %D 2010 %R 10.1007/978-3-642-15414-0_20 %K Voronoi diagram %K optimization %Z Computer Science [cs]/Computational Geometry [cs.CG]Conference papers %X 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. %G English %Z Bielefeld University et GEOMETRICA %Z INRIA %2 https://inria.hal.science/inria-00535602/document %2 https://inria.hal.science/inria-00535602/file/imr19-optimization.pdf %L inria-00535602 %U https://inria.hal.science/inria-00535602 %~ INRIA %~ INRIA-SOPHIA %~ INRIA-SACLAY %~ INRIASO %~ INRIA_TEST %~ TESTALAIN1 %~ INRIA2