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

Max-Planck-Institute for Mathematics in the Sciences
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  17th GAMM-Seminar
February, 1st-3rd, 2001
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  Hierarchical Meshes and Local Multigrid Methods
C. Wieners (Uni Heidelberg)

We present a specification for hierarchically structured meshes which allows the realization parallel local multigrid methods for general finite element discretizations. For an efficient implementation of parallel multiplicative multigrid methods it is required that the local defect evaluation and a local smoothing procedure can be performed without data transfer between the mesh levels. This is realized by additional copy elements on every levels in a neighborhood of the refined elements.

We use the concept of vector classes for a precise definition of copy elements which are required for a consistent defect computation on a mesh hierarchy and a consistent defect restriction; furthermore, the smoothing is required on the copy elements as well. Note that the definition of the vector classes rely on the matrix graph and therefore on the discretization.

Moreover, we give a specification of the required geometry information for the refinement process and for the implementation of higher order elements.

Local multigrid methods following these specifications are implemented in the software system UG. We present examples for conforming, nonconforming and mixed finite elements on hierarchically structured meshes.

This presentation is a joint work with the UG-group and it generalizes the results in [1].

[1] P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neu\ss, H. Rentz-Reichert, C. Wieners:
UG -- a flexible software toolbox for solving partial differential equations.
Computing and Visualization in Science 1, (1997) 27-40

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30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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