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@MASTERSTHESIS{Mller:1005457,
      author       = {Müller, Björn},
      title        = {{I}nvestigation of {E}xponential {T}ime {D}ifferencing
                      {S}chemes for {A}dvection-{D}iffusion-{R}eaction {P}roblems
                      in the {P}resence of {S}ignificant {A}dvection},
      school       = {University of Louisiana at Lafayette},
      type         = {Masterarbeit},
      reportid     = {FZJ-2023-01486},
      pages        = {x, 121 p.},
      year         = {2022},
      note         = {Defense at FH Aachen Campus Jülich March 9th, 2023;
                      Masterarbeit, University of Louisiana at Lafayette, 2022},
      abstract     = {Advection-diffusion-reaction equations are partial
                      differential equations (PDEs)with various applications
                      across the sciences. Exponential time differencing
                      schemesare efficient methods of numerically solving PDEs of
                      this type. We consider anexponential time differencing
                      scheme called ETD-RDP-IF that approximates thearising matrix
                      exponentials using a rational approximation with real
                      distinct poles andemploys a dimensional splitting technique
                      to improve computational performance.The scheme has
                      originally been derived for systems without advection. We
                      show thatthe derivation still holds in the presence of
                      advection and prove new results on thesecond-order temporal
                      accuracy of the scheme. In numerical experiments,
                      weinvestigate the real-world performance of the scheme
                      depending on the strength ofadvection as quantified by the
                      Péclet and Courant numbers. We confirmsecond-order
                      convergence in space and time for linear problems with
                      smooth initialcondition and observe order reduction for
                      non-smooth initial conditions. We furtherfind that
                      upwind-biased discretizations of advection improve
                      computational efficiency.A comparison with an ETD scheme
                      that uses Krylov-subspace approximations of thematrix
                      exponentials shows that the Krylov-subspace technique has a
                      bettercomputational performance in low-advection regimes.
                      Outside of these regimes,ETD-RDP-IF is more robust and
                      therefore more widely applicable.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)19},
      url          = {https://juser.fz-juelich.de/record/1005457},
}