Biting: advancing front meets sphere packing

International Journal for Numerical Methods in Engineering, John Wiley, Vol 49, Num 1, pp.61-81, September 10-20 2000

MESHING
RESEARCH
CORNER

Special Edition on Unstructured Mesh Generation
International Journal for Numerical Methods in Engineering, Vol 49 Number 1-2, 10-20 September 2000

Correspondence to: Xiang-Yang Li, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana. IL 61801, U.S.A.
E-mail: xli2@cs.uiuc.edu
E-mail: steng@cs.uiuc.edu
E-mail: ungor@uiuc.edu

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 quadtreesjoctrees 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.