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@ARTICLE{Rittich:877487,
      author       = {Rittich, Hannah and Speck, Robert},
      title        = {{T}ime-parallel simulation of the {S}chrödinger
                      {E}quation},
      journal      = {Computer physics communications},
      volume       = {255},
      issn         = {0010-4655},
      publisher    = {Elsevier},
      reportid     = {FZJ-2020-02239},
      pages        = {107363 -},
      year         = {2020},
      abstract     = {The numerical simulation of the time-dependent Schrödinger
                      equation for quantum systems is a very active research
                      topic. Yet, resolving the solution sufficiently in space and
                      time is challenging and mandates the use of modern
                      high-performance computing systems. While classical
                      parallelization techniques in space can reduce the runtime
                      per time step, novel parallel-in-time integrators expose
                      parallelism in the temporal domain. They work, however, not
                      very well for wave-type problems such as the Schrödinger
                      equation. One notable exception is the rational
                      approximation of exponential integrators. In this paper we
                      derive an efficient variant of this approach suitable for
                      the complex-valued Schrödinger equation. Using the
                      Faber–Carathéodory–Fejér approximation, this variant
                      is already a fast serial and in particular an efficient
                      time-parallel integrator. It can be used to augment
                      classical parallelization in space and we show the
                      efficiency and effectiveness of our method along the lines
                      of two challenging, realistic examples.},
      cin          = {JSC},
      ddc          = {530},
      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:000541251400012},
      doi          = {10.1016/j.cpc.2020.107363},
      url          = {https://juser.fz-juelich.de/record/877487},
}