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 Volker Reichelt, Fri, 11.30-11.55 Previous Contents Next  
  On a Parallel Tetrahedral Grid Refinement Technique
Volker Reichelt (RWTH Aachen)

The refinement algorithm of Bey [1,2] can be used to construct, in an adaptive way, a stable and consistent hierarchical family of locally refined tetrahedral grids. The green closure used in this algorithm is based on an incomplete set of rules: A complicated green refinement pattern may be replaced by a regular (red) pattern. This, however, changes the refinement pattern of the neighbors, which can result in a nonlocal domino effect on a fixed level in the grid hierarchy. Clearly, this is undesirable if one wants to parallelize this method. In this talk we present a full set of rules that allows to use a green refinement of a tetrahedron without having to consider its neighbors. As a consequence this modified method is much better suited for a parallel implementation. We will present the modified algorithm and results obtained from a serial implementation. We plan to combine this local grid refinement technique with a finite element discretization method and a parallel multigrid solver for problems from the CFD field.

[1] Bey, J., Tetrahedral grid refinement, Computing 55, 355-378 (1995)

[2] Bey, J., Simplicial grid refinement: on Freudenthal's algorithm and the optimal number of congruence classes, Numer. Math. 85, 1-29 (2000)

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