Biting: Advancing Front Meets Sphere Packing
نویسندگان
چکیده
A key step in the nite 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 eecient. 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.
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Biting Spheres in 3D
We present an eecient 3D meshing algorithm which combines the merits of two popular meshing methods, advancing front and sphere packing methods. In particular , it inherits the practicality and simplicity of advancing front and the size-and-quality guarantee of the sphere packing method. We prove that it generates a well-shaped mesh whose size is within a constant factor of the optimal possible...
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