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@ARTICLE{Minion:154819,
      author       = {Minion, Michael and Speck, Robert and Bolten, Matthias and
                      Emmett, Matthew and Ruprecht, Daniel},
      title        = {{I}nterweaving {PFASST} and {P}arallel {M}ultigrid},
      reportid     = {FZJ-2014-04087},
      year         = {2014},
      abstract     = {The parallel full approximation scheme in space and time
                      (PFASST) introduced by Emmett and Minion in 2012 is an
                      iterative strategy for the temporal parallelization of ODEs
                      and discretized PDEs. As the name suggests, PFASST is
                      similar in spirit to a space-time FAS multigrid method
                      performed over multiple time-steps in parallel. However,
                      since the original focus of PFASST has been on the
                      performance of the method in terms of time parallelism, the
                      solution of any spatial system arising from the use of
                      implicit or semi-implicit temporal methods within PFASST
                      have simply been assumed to be solved to some desired
                      accuracy completely at each sub-step and each iteration by
                      some unspecified procedure. It hence is natural to
                      investigate how iterative solvers in the spatial dimensions
                      can be interwoven with the PFASST iterations and whether
                      this strategy leads to a more efficient overall approach.
                      This paper presents an initial investigation on the relative
                      performance of different strategies for coupling PFASST
                      iterations with multigrid methods for the implicit treatment
                      of diffusion terms in PDEs. In particular, we compare full
                      accuracy multigrid solves at each sub-step with a small
                      fixed number of multigrid V-cycles. This reduces the cost of
                      each PFASST iteration at the possible expense of a
                      corresponding increase in the number of PFASST iterations
                      needed for convergence. Parallel efficiency of the resulting
                      methods is explored through numerical examples.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411) / DFG project 450829162 - Raum-Zeit-parallele
                      Simulation multimodale Energiesystemen (450829162)},
      pid          = {G:(DE-HGF)POF2-411 / G:(GEPRIS)450829162},
      typ          = {PUB:(DE-HGF)25},
      url          = {https://juser.fz-juelich.de/record/154819},
}