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@PHDTHESIS{Clausnitzer:1043284,
      author       = {Clausnitzer, Julian},
      title        = {{N}umerical solution of {SPDE}s on a class of
                      two-dimensional domains and of random differential equations
                      using {PCE} with exponential time differencing},
      school       = {Brandenburgische Technische Universität
                      Cottbus-Senftenberg},
      type         = {Dissertation},
      reportid     = {FZJ-2025-02810},
      pages        = {129 p.},
      year         = {2025},
      note         = {Dissertation, Brandenburgische Technische Universität
                      Cottbus-Senftenberg, 2024},
      abstract     = {The first part of this thesis deals with the numerical
                      solution of semilinear parabolic stochastic partial
                      differential equations on general two-dimensional
                      C²-bounded domains. The existing exponential Euler time
                      stepping scheme is used on two-dimensional domains, using a
                      spectral approximation in space. Since the base functions
                      are not given analytically, they are numerically
                      approximated using a boundary element method combined with a
                      contour integral method to solve nonlinear eigenvalue
                      problems. An error analysis is given, and numerical
                      experiments conclude the investigation of the method.The
                      second part of the thesis compares the performance of
                      non-intrusive and intrusive polynomial chaos expansion
                      methods based on exponential time differencing schemes for a
                      range of random ordinary and partial differential equations.
                      It is shown in comprehensive numerical experiments that the
                      two approaches are competitive for a range of different
                      equations, but intrusive polynomial chaos becomes less
                      efficient for polynomial nonlinearities of degree greater
                      than two and breaks down for a reaction-diffusion equation
                      exhibiting complex pattern formation behavior.},
      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)11},
      urn          = {urn:nbn:de:kobv:co1-opus4-70206},
      doi          = {10.34734/FZJ-2025-02810},
      url          = {https://juser.fz-juelich.de/record/1043284},
}