Bobach, T., Constantiniu, A., Steinmann, P. and Umlauf, G. (2008) Geometric Properties of the Adaptive Delaunay Tessellation. 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, Tonsberg, Norway, 26 Jun- 1 Jul 2008. ISBN 9783642116193 (doi: 10.1007/978-3-642-11620-9_4)
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Abstract
Recently, the Adaptive Delaunay Tessellation (Adt) was introduced in the context of computational mechanics as a tool to support Voronoi-based nodal integration schemes in the finite element method. While focusing on applications in mechanical engineering, the former presentation lacked rigorous proofs for the claimed geometric properties of the Adt necessary for the computation of the nodal integration scheme. This paper gives pending proofs for the three main claims which are uniqueness of the Adt, connectedness of the Adt, and coverage of the Voronoi tiles by adjacent Adt tiles. Furthermore, this paper provides a critical assessment of the Adt for arbitrary point sets.
| Item Type: | Conference or Workshop Item |
|---|---|
| Additional Information: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)., volume 5862 LNCS, 2010, pages 41-54. Online ISBN: 9783642116209. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Steinmann, Professor Paul |
| Authors: | Bobach, T., Constantiniu, A., Steinmann, P., and Umlauf, G. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| ISBN: | 9783642116193 |
| Related URLs: |
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