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@ARTICLE{Minion:278997,
      author       = {Minion, M. L. and Speck, R. and Bolten, M. and Emmett, M.
                      and Ruprecht, D.},
      title        = {{I}nterweaving {PFASST} and {P}arallel {M}ultigrid},
      journal      = {SIAM journal on scientific computing},
      volume       = {37},
      number       = {5},
      issn         = {0196-5204},
      address      = {Philadelphia, Pa.},
      publisher    = {SIAM},
      reportid     = {FZJ-2015-07167},
      pages        = {S244 - S263},
      year         = {2015},
      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 full approximation scheme
                      multigrid method performed over multiple time steps in
                      parallel. However, since the original focus of PFASST was 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 substep 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 substep 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 / NIC},
      ddc          = {004},
      cid          = {I:(DE-Juel1)JSC-20090406 / I:(DE-Juel1)NIC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / DFG project 450829162 - Raum-Zeit-parallele
                      Simulation multimodale Energiesystemen (450829162) /
                      Scalable solvers for linear systems and time-dependent
                      problems $(hwu12_20141101)$},
      pid          = {G:(DE-HGF)POF3-511 / G:(GEPRIS)450829162 /
                      $G:(DE-Juel1)hwu12_20141101$},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000364457000031},
      doi          = {10.1137/14097536X},
      url          = {https://juser.fz-juelich.de/record/278997},
}