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@ARTICLE{Ruprecht:151267,
      author       = {Ruprecht, Daniel and Speck, Robert and Krause, Rolf},
      title        = {{P}arareal for diffusion problems with space- and
                      time-dependent coefficients},
      reportid     = {FZJ-2014-01258},
      year         = {2014},
      abstract     = {For the time-parallel Parareal method, there exists both
                      numerical and analytical proof that it converges very well
                      for diffusive problems like the heat equation. Many
                      applications, however, do not lead to simple homogeneous
                      diffusive scenarios but feature strongly inhomogeneous and
                      possibly anisotropic coefficients. The paper presents
                      results from a numerical study of how space- and
                      time-dependent coefficients in a diffusion setup affect
                      Parareal's convergence behaviour. It is shown that, for the
                      presented examples, non-constant diffusion coefficients have
                      only marginal influence on how fast Parareal converges.
                      Furthermore, an example is shown that illustrates how for
                      linear problems the maximum singular value of the Parareal
                      iteration matrix can be used to estimate convergence rates.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411) / DFG project 450829162 - Raum-Zeit-parallele
                      Simulation multimodale Energiesystemen (450829162)},
      pid          = {G:(DE-HGF)POF2-411 / G:(GEPRIS)450829162},
      typ          = {PUB:(DE-HGF)25},
      url          = {https://juser.fz-juelich.de/record/151267},
}