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Variational Delaunay approach to the generation of tetrahedral finite element meshes

Krysl, Petr and Ortiz, Michael (2001) Variational Delaunay approach to the generation of tetrahedral finite element meshes. International Journal for Numerical Methods in Engineering, 50 (7). pp. 1681-1700. ISSN 0029-5981. https://resolver.caltech.edu/CaltechAUTHORS:20170408-162713466

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Abstract

We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set àpriori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a constraining facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1002/nme.91DOIArticle
Additional Information:© 2001 John Wiley & Sons, Ltd. Received 1 February 1999. Revised 9 April 1999. Contract=grant sponsor: Department of Energy We are grateful for support from the Department of Energy through Caltech’s ASCI Center of Excellencefor Simulating Dynamic Response of Materials.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:ite element method; tetrahedral mesh; boundary constraints; variational Delaunay
Issue or Number:7
Record Number:CaltechAUTHORS:20170408-162713466
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-162713466
Official Citation:Krysl, P. and Ortiz, M. (2001), Variational Delaunay approach to the generation of tetrahedral finite element meshes. Int. J. Numer. Meth. Engng., 50: 1681–1700. doi:10.1002/nme.91
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76186
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:09 Aug 2017 23:07
Last Modified:03 Oct 2019 16:58

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