17th GAMM-Seminar Leipzig on
Construction of Grid Generation Algorithms

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  17th GAMM-Seminar
February, 1st-3rd, 2001
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  Abstract N. Walkington, Thu, 16.45-17.10 Previous Contents Next  
  Algorithms for 3D Unstructured Mesh Generation
N. Walkington (Carnegie Mellon, Pittsburgh)

The design of an unstructured meshing program requires algorithms that will (1) guarantee that the mesh conforms to any specified bounding data and (2a) guarantee that mesh quality is maintained in the sense that the mesh elements must have bounds on their aspect ratios. Often this is accomplished by adding ``Steiner'' points into the mesh and we then have the requirement that (2b) the final mesh must suitably graded and not be overly refined. Finally, we require that (3) the algorithms must be efficient enough to be practical. These three requirements can lead to very complicated algorithms; so much that it can be difficult to verify correctness. In this talk we introduce an elementary algorithm that provides both an implementation and extension of the ideas of Ruppert and Shewchuk for the generation of two and three dimensional meshes. As with most Delaunay based meshing algorithms the aspect ratio controlled by our algorithm is the ratio of circumradius to shortest edge of each simplex.

This work is joint with Umut A. Acar, Guy Blelloch, Gary L. Miller, and Steven Pav.

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