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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
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  17th GAMM-Seminar
February, 1st-3rd, 2001
 
     
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  Abstract Leonardo Traversoni, Thu, 17.15-17.40 Previous Contents Next  
  Grids Based on Circles and Spheres
Leonardo Traversoni (Universidad Autonoma Metropolitana, Mexico)

Based on Voronoi tessellation, Robin Sibson invented in 1980 for geographic sampling the Natural Neighbor Interpolant. Its pointwise definition, which is purely geometric, made it impractical for broader use although it seemed to have very good properties. In 1998 Watson and Sukumar published a method to use Natural Neighbors on Finite Elements that they baptized the Natural Element Method, partially based on an idea I published in 1994 as they cite. However, even when they cite me, they don't use the main idea of that paper and they remain attached to triangles for the partition. The main idea I want to show is that there is a dual of the Voronoi tessellation that I call Covering Spheres, far less known than the Delaunay triangles, that is very useful to be the base of a partition that is, in each of its tiles, the "home" of natural neighbor interpolant and can be used with advantage on finite elements on the plane, the sphere and the space. I also show how this can be used in a multigrid environment or multilevel approximation.
 

 
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