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1 results

  • Towards Textbook Efficiency for Parallel Multigrid

  • Björn Gmeiner, Ulrich Rüde, Holger Stengel, Christian Waluga, Barbara Wohlmuth
  • Journal:
    Numerical Mathematics: Theory, Methods and Applications / Volume 8 / Issue 1 / February 2015
    Published online by Cambridge University Press:
    03 March 2015, pp. 22-46
    Print publication:
    February 2015

  • In this work, we extend Achi Brandt's notion of textbook multigrid efficiency (TME) to massively parallel algorithms. Using a finite element based geometric multigrid implementation, we recall the classical view on TME with experiments for scalar linear equations with constant and varying coefficients as well as linear systems with saddle-point structure. To extend the idea of TME to the parallel setting, we give a new characterization of a work unit (WU) in an architecture-aware fashion by taking into account performance modeling techniques. We illustrate our newly introduced parallel TME measure by large-scale computations, solving problems with up to 200 billion unknowns on a TOP-10 supercomputer.