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Optimizing Voronoi Diagrams for Polygonal Finite Element Computations
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.
keyword :
Voronoi diagram
optimization
Cited literature [43 references]
https://hal.inria.fr/inria-00535602
Contributor : Pierre Alliez Connect in order to contact the contributor
Submitted on : Friday, November 12, 2010 - 9:20:28 AM
Last modification on : Thursday, January 20, 2022 - 4:13:42 PM
Long-term archiving on: : Friday, October 26, 2012 - 3:30:19 PM
Contributor : Pierre Alliez Connect in order to contact the contributor
Submitted on : Friday, November 12, 2010 - 9:20:28 AM
Last modification on : Thursday, January 20, 2022 - 4:13:42 PM
Long-term archiving on: : Friday, October 26, 2012 - 3:30:19 PM
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imr19-optimization.pdf
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