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Biting: Advancing Front Meets Sphere Packing (1999)
| Venue: | INT. JOUR. FOR NUMERICAL METHODS IN ENG |
| Citations: | 26 - 9 self |
BibTeX
@INPROCEEDINGS{Li99biting:advancing,
author = {Xiang-yang Li and Shang-Hua Teng and Alper Üngör},
title = {Biting: Advancing Front Meets Sphere Packing},
booktitle = {INT. JOUR. FOR NUMERICAL METHODS IN ENG},
year = {1999},
publisher = {}
}
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Abstract
A key step in the finite element method is to generate a high quality mesh that is as small as possible for an input domain. Several meshing methods and heuristics have been developed and implemented. Methods based on advancing front, Delaunay triangulations, and quadtrees/octrees are among the most popular ones. Advancing front uses simple data structures and is efficient. Unfortunately, in general, it does not provide any guarantee on the size and quality of the mesh it produces. On the other hand, the circle-packing based Delaunay methods generate a well-shaped mesh whose size is within a constant factor of the optimal. In this paper, we present a new meshing algorithm, the biting method, which combines the strengths of advancing front and circle packing. We prove that it generates a high quality 2D mesh, and the size of the mesh is within a constant factor of the optimal.
