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@ARTICLE{Speck:151266,
      author       = {Speck, Robert and Ruprecht, Daniel and Minion, Michael and
                      Emmett, Matthew and Krause, Rolf},
      title        = {{I}nexact spectral deferred corrections using single-cycle
                      multigrid},
      reportid     = {FZJ-2014-01257},
      year         = {2014},
      abstract     = {Spectral deferred correction (SDC) methods are an
                      attractive approach to iteratively computing collocation
                      solutions to an ODE by performing so-called sweeps with a
                      low-order time stepping method. SDC allows to easily
                      construct high order split methods where e.g. stiff terms of
                      the ODE are treated implicitly. This requires the solution
                      to full accuracy of multiple linear systems of equations
                      during each sweep, e.g. with a multigrid method. In this
                      paper, we present an inexact variant of SDC, where each
                      solve of a linear system is replaced by a single multigrid
                      V-cycle and thus significantly reduces the cost for each
                      sweep. For the investigated examples, this strategy results
                      only in a small increase of the number of required sweeps
                      and we demonstrate that 'inexact spectral deferred
                      corrections' can provide a dramatic reduction of the overall
                      number of multigrid V-cycles required to complete an SDC
                      time step.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411)},
      pid          = {G:(DE-HGF)POF2-411},
      typ          = {PUB:(DE-HGF)25},
      url          = {https://juser.fz-juelich.de/record/151266},
}