Multigrid in energy preconditioner for Krylov solvers

  • Authors:

  • R. N. Slaybaugh;T. M. Evans;G. G. Davidson;P. P. H. Wilson

  • Affiliations:

  • Department of Mechanical Engineering and Material Science, University of Pittsburgh, 605 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261, USA;Radiation Transport Group, Oak Ridge National Laboratory, P.O. BOX 2008 MS6170, Oak Ridge TN 37831, USA;Radiation Transport Group, Oak Ridge National Laboratory, P.O. BOX 2008 MS6170, Oak Ridge TN 37831, USA;Department of Nuclear Engineering and Engineering Physics, University of Wisconsin - Madison, 419 ERB, 1500 Engineering Drive, Madison, WI 52706, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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Abstract

We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.