Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {Michael Griebel and Bram Metsch and Marc Alexander
  title = {Coarse grid classification--{P}art {II}: Automatic coarse
		  grid agglomeration for parallel {AMG}},
  institution = {Sonderforschungsbereich 611, {U}niversit\"at {B}onn},
  type = {Preprint},
  number = {271},
  year = {2006},
  ps = { 1},
  pdf = { 1},
  abstract = {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.},
  annote = {report,C2,paramg}