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@ARTICLE{Gander:1020591,
      author       = {Gander, Martin J. and Lunet, Thibaut and Ruprecht, Daniel
                      and Speck, Robert},
      title        = {{A} {U}nified {A}nalysis {F}ramework for {I}terative
                      {P}arallel-in-{T}ime {A}lgorithms},
      journal      = {SIAM journal on scientific computing},
      volume       = {45},
      number       = {5},
      issn         = {1064-8275},
      address      = {Philadelphia, Pa.},
      publisher    = {SIAM},
      reportid     = {FZJ-2024-00286},
      pages        = {A2275 - A2303},
      year         = {2023},
      abstract     = {Parallel-in-time integration has been the focus of
                      intensive research efforts over the past two decades due to
                      the advent of massively parallel computer architectures and
                      the scaling limits of purely spatial parallelization.
                      Various iterative parallel-in-time algorithms have been
                      proposed, like Parareal, PFASST, MGRIT, and Space-Time
                      Multi-Grid (STMG). These methods have been described using
                      different notation, and the convergence estimates that are
                      available are difficult to compare. We describe Parareal,
                      PFASST, MGRIT, and STMG for the Dahlquist model problem
                      using a common notation and give precise convergence
                      estimates using generating functions. This allows us, for
                      the first time, to directly compare their convergence. We
                      prove that all four methods eventually converge
                      superlinearly, and we also compare them numerically. The
                      generating function framework provides further opportunities
                      to explore and analyze existing and new methods.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511) / TIME-X - TIME
                      parallelisation: for eXascale computing and beyond (955701)
                      / Verbundprojekt: TIME-X - Parallelisierung zeitabhängiger
                      Simulationen für das zukünftige Supercomputing (16HPC047)},
      pid          = {G:(DE-HGF)POF4-5112 / G:(EU-Grant)955701 /
                      G:(BMBF)16HPC047},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001108755600010},
      doi          = {10.1137/22M1487163},
      url          = {https://juser.fz-juelich.de/record/1020591},
}