# Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

Sieger D, Alliez P, Botsch M (2010)
In: Proceedings of the 19th International Meshing Roundtable. Shontz S (Ed); Berlin: Springer: 335-350.

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Conference Paper | Published | English

Author
Editor
Shontz, Suzanne
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.
Publishing Year
Conference
19th International Meshing Roundtable
Location
Chattanooga, TN, USA
Conference Date
2010-10-03 – 2010-10-06
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Sieger D, Alliez P, Botsch M. Optimizing Voronoi Diagrams for Polygonal Finite Element Computations. In: Shontz S, ed. Proceedings of the 19th International Meshing Roundtable. Berlin: Springer; 2010: 335-350.
Sieger, D., Alliez, P., & Botsch, M. (2010). Optimizing Voronoi Diagrams for Polygonal Finite Element Computations. In S. Shontz (Ed.), Proceedings of the 19th International Meshing Roundtable (pp. 335-350). Berlin: Springer. doi:10.1007/978-3-642-15414-0_20
Sieger, D., Alliez, P., and Botsch, M. (2010). “Optimizing Voronoi Diagrams for Polygonal Finite Element Computations” in Proceedings of the 19th International Meshing Roundtable, Shontz, S. ed. (Berlin: Springer), 335-350.
Sieger, D., Alliez, P., & Botsch, M., 2010. Optimizing Voronoi Diagrams for Polygonal Finite Element Computations. In S. Shontz, ed. Proceedings of the 19th International Meshing Roundtable. Berlin: Springer, pp. 335-350.
D. Sieger, P. Alliez, and M. Botsch, “Optimizing Voronoi Diagrams for Polygonal Finite Element Computations”, Proceedings of the 19th International Meshing Roundtable, S. Shontz, ed., Berlin: Springer, 2010, pp.335-350.
Sieger, D., Alliez, P., Botsch, M.: Optimizing Voronoi Diagrams for Polygonal Finite Element Computations. In: Shontz, S. (ed.) Proceedings of the 19th International Meshing Roundtable. p. 335-350. Springer, Berlin (2010).
Sieger, Daniel, Alliez, Pierre, and Botsch, Mario. “Optimizing Voronoi Diagrams for Polygonal Finite Element Computations”. Proceedings of the 19th International Meshing Roundtable. Ed. Suzanne Shontz. Berlin: Springer, 2010. 335-350.
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