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

  author = {Michael Griebel and Bram Metsch and Daniel Oeltz and Marc
		  Alexander Schweitzer},
  title = {Coarse Grid Classification: A Parallel Coarsening Scheme
		  For Algebraic Multigrid Methods},
  journal = {Numerical Linear Algebra with Applications},
  volume = {13},
  number = {2--3},
  pages = {193--214},
  year = {2006},
  note = {Also available as SFB 611 preprint No. 225, Universit\"at
		  Bonn, 2005},
  ps = { 1},
  pdf = { 1},
  abstract = {In this paper we present a new approach to the
		  parallelization of algebraic multigrid (AMG), i.e., to the
		  parallel coarse grid selection in AMG. Our approach does
		  not involve any special treatment of processor subdomain
		  boundaries and hence avoids a number of drawbacks of other
		  AMG parallelization techniques. The key idea is to select
		  an appropriate (local) coarse grid on each processor from
		  all admissible grids such that the composed coarse grid
		  forms a suitable coarse grid for the whole domain, i.e.
		  there is no need for any boundary treatment. To this end,
		  we first construct multiple equivalent coarse grids on each
		  processor subdomain. In a second step we then select
		  exactly one grid per processor by a graph clustering
		  technique. The results of our numerical experiments clearly
		  indicate that this approach results in coarse grids of high
		  quality which are very close to those obtained with
		  sequential AMG. Furthermore, the operator and grid
		  complexities of our parallel AMG are mostly smaller than
		  those obtained by other parallel AMG methods, whereas the
		  scale-up behavior of the proposed algorithm is similar to
		  that of other parallel AMG techniques. However a
		  significant improvement with respect to the speed-up
		  performance is achieved.},
  annote = {article,C2,paramg}