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@ARTICLE{Ruprecht:820610,
      author       = {Ruprecht, Daniel and Speck, Robert},
      title        = {{S}pectral {D}eferred {C}orrections with {F}ast-wave
                      {S}low-wave {S}plitting},
      journal      = {SIAM journal on scientific computing},
      volume       = {38},
      number       = {4},
      issn         = {0196-5204},
      address      = {Philadelphia, Pa.},
      publisher    = {SIAM},
      reportid     = {FZJ-2016-05882},
      pages        = {A2535 - A2557},
      year         = {2016},
      abstract     = {The paper investigates a variant of semi-implicit spectral
                      deferred corrections (SISDC) in which the stiff, fast
                      dynamics correspond to fast propagating waves (``fast-wave
                      slow-wave problem''). We show that for a scalar test problem
                      with two imaginary eigenvalues $i \lambda_{\text{f}}$, $i
                      \lambda_{\text{s}}$, having $\Delta t ( | \lambda_{\text{f}}
                      | + | \lambda_{\text{s}} | ) < 1$ is sufficient for the
                      fast-wave slow-wave SDC (fwsw-SDC) iteration to converge and
                      that in the limit of infinitely fast waves the convergence
                      rate of the nonsplit version is retained. Stability function
                      and discrete dispersion relation are derived and show that
                      the method is stable for essentially arbitrary fast-wave CFL
                      numbers as long as the slow dynamics are resolved. The
                      method causes little numerical diffusion and its
                      semidiscrete phase speed is accurate also for large wave
                      number modes. Performance is studied for an
                      acoustic-advection problem and for the linearised Boussinesq
                      equations, describing compressible, stratified flow.
                      fwsw-SDC is compared to diagonally implicit Runge-Kutta
                      (DIRK) and implicit-explicit (IMEX) Runge-Kutta methods and
                      found to be competitive in terms of both accuracy and cost.},
      cin          = {JSC},
      ddc          = {004},
      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:000385283400026},
      doi          = {10.1137/16M1060078},
      url          = {https://juser.fz-juelich.de/record/820610},
}