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Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation

Radovitzky, R. and Ortiz, M. (2000) Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering, 187 (3-4). pp. 543-569. ISSN 0045-7825. http://resolver.caltech.edu/CaltechAUTHORS:20171213-084912550

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Abstract

A method of unstructured technical mesh generation for general three-dimensional domains is presented. A conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology. The geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation. A preliminary surface mesh is generated by an advancing-front method, with the nodes inserted by hard-sphere packing in physical space in accordance with a prescribed mesh density. Interior nodes are inserted in a face-centered-cubic (FCC) crystal lattice arrangements coupled to octree spatial subdivision, with the local lattice parameter determined by a prespecified nodal density function. Prior to triangulation of the volume, the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume Delaunay triangulation. A joint Delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing-front approach. The resulting mesh is finally improved upon by the application of local transformations. The overall time complexity of the mesher is O(N log N). The robustness and versatility of the approach, as well as the good quality of the resulting meshes, is demostrated with the aid of selected examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/S0045-7825(99)00339-4DOIArticle
https://www.sciencedirect.com/science/article/pii/S0045782599003394PublisherArticle
Additional Information:© 2000 Elsevier. Available online 17 July 2000. The support of the Army Research Office through contract DAAH04-96-1-0056, and of the Sandia National Laboratories through contract DE-AC04-76DP00789, is gratefully acknowledged. We are grateful to Joe Jung, of the Sandia National Laboratories for helpful discussions and for providing the surface triangulations of the examples shown in Figs. 22 and 23.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)DAAH04-96-1-0056
Department of Energy (DOE)DE-AC04-76DP00789
Record Number:CaltechAUTHORS:20171213-084912550
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171213-084912550
Official Citation:R. Radovitzky, M. Ortiz, Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation, In Computer Methods in Applied Mechanics and Engineering, Volume 187, Issues 3–4, 2000, Pages 543-569, ISSN 0045-7825, https://doi.org/10.1016/S0045-7825(99)00339-4. (http://www.sciencedirect.com/science/article/pii/S0045782599003394)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83852
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:13 Dec 2017 16:58
Last Modified:13 Dec 2017 16:58

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