M. Griebel, B. Metsch, and M. A. Schweitzer.
Coarse grid classification-Part II: Automatic coarse grid
agglomeration for parallel AMG.
Preprint 271, Sonderforschungsbereich 611, Universität Bonn,
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Multigrid methods (MG) are known to be optimal solvers for large sparse linear systems arising from the finite element, finite difference or finite volume discretization of a partial differential equation (PDE). Algebraic multigrid methods (AMG) extend this approach to wide a class of problems, e.g. anisotropic operators or unstructured grids. However, the parallelization of AMG, especially the construction of the coarse grids, is a challenging task. In this paper, we present an extension of the coarse grid classification scheme (CGC) for parallel AMG coarsening. Our new approach allows coarsening rates that are (essentially) independent of the number of processors. This consequently means that the presented scheme can coarsen a grid down to a single point independent of the number of processors, i.e. our scheme can be interpreted as an automatic coarse grid agglomeration scheme. The results of our numerical experiments in two and three space dimensions indicate that the presented scheme gives robust coarsening rates independent of the number of processors and provides small operator and grid complexities.