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@ARTICLE{Bolten:857114,
      author       = {Bolten, Matthias and Moser, Dieter and Speck, Robert},
      title        = {{A}symptotic convergence of the parallel full approximation
                      scheme in space and time for linear problems},
      journal      = {Numerical linear algebra with applications},
      volume       = {25},
      number       = {6},
      issn         = {1070-5325},
      address      = {New York, NY [u.a.]},
      publisher    = {Wiley},
      reportid     = {FZJ-2018-06359},
      pages        = {e2208 -},
      year         = {2018},
      abstract     = {For time‐dependent partial differential equations,
                      parallel‐in‐time integration using the “parallel full
                      approximation scheme in space and time” (PFASST) is a
                      promising way to accelerate existing space‐parallel
                      approaches beyond their scaling limits. Inspired by the
                      classical Parareal method and multigrid ideas, PFASST allows
                      to integrate multiple time steps simultaneously using a
                      space–time hierarchy of spectral deferred correction
                      sweeps. While many use cases and benchmarks exist, a solid
                      and reliable mathematical foundation is still missing. Very
                      recently, however, PFASST for linear problems has been
                      identified as a multigrid method. In this paper, we will use
                      this multigrid formulation and, in particular, PFASST's
                      iteration matrix to show that, in the nonstiff and stiff
                      limit, PFASST indeed is a convergent iterative method. We
                      will provide upper bounds for the spectral radius of the
                      iteration matrix and investigate how PFASST performs for
                      increasing numbers of parallel time steps. Finally, we will
                      demonstrate that the results obtained here indeed relate to
                      actual PFASST runs.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / DFG project 450829162 - Raum-Zeit-parallele
                      Simulation multimodale Energiesystemen (450829162)},
      pid          = {G:(DE-HGF)POF3-511 / G:(GEPRIS)450829162},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000449497500001},
      doi          = {10.1002/nla.2208},
      url          = {https://juser.fz-juelich.de/record/857114},
}