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@PHDTHESIS{Fehling:878206,
      author       = {Fehling, Marc},
      title        = {{A}lgorithms for massively parallel generic hp-adaptive
                      finite element methods},
      volume       = {43},
      school       = {Universität Wuppertal},
      type         = {Dissertation},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {FZJ-2020-02694},
      isbn         = {978-3-95806-486-7},
      series       = {Schriften des Forschungszentrums Jülich. IAS Series},
      pages        = {vii, 78 S.},
      year         = {2020},
      note         = {Universität Wuppertal, 2020},
      abstract     = {Efficient algorithms for the numerical solution of partial
                      differential equations are required to solve problems on an
                      economically viable timescale. In general, this is achieved
                      by adapting the resolution of the discretization to the
                      investigated problem, as well as exploiting hardware
                      specifications. For the latter category, parallelization
                      plays a major role for modern multi-core and multi-node
                      architectures, especially in the context of high-performance
                      computing. Using finite element methods, solutions are
                      approximated by discretizing the function space of the
                      problem with piecewise polynomials. With
                      $\textit{hp}$-adaptive methods, the polynomial degrees of
                      these basis functions may vary on locally refined meshes. We
                      present algorithms and data structures required for generic
                      hp-adaptive finite element software applicable for both
                      continuous and discontinuous Galerkin methods on distributed
                      memory systems. Both function space and mesh may be adapted
                      dynamically during the solution process. We cover details
                      concerning the unique enumeration of degrees of freedom with
                      continuous Galerkin methods, the communication of variable
                      size data, and load balancing. Furthermore, we present
                      strategies to determine the type of adaptation based on
                      error estimation and prediction as well as smoothness
                      estimation via the decay rate of coefficients of Fourier and
                      Legendre series expansions. Both refinement and coarsening
                      are considered. A reference implementation in the
                      open-source library deal. II$^{1}$ is provided and applied
                      to the Laplace problem on a domain with a reentrant corner
                      which invokes a singularity. With this example, we
                      demonstrate the benefits of the $\textit{hp}$-adaptive
                      methods in terms of error convergence and show that our
                      algorithm scales up to 49,152 MPI processes.},
      cin          = {IAS-7},
      cid          = {I:(DE-Juel1)IAS-7-20180321},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / ORPHEUS - Optimierung der Rauchableitung und
                      Personenführung in U-Bahnhöfen: Experimente und
                      Simulationen (BMBF-13N13266) / PhD no Grant - Doktorand ohne
                      besondere Förderung (PHD-NO-GRANT-20170405)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)BMBF-13N13266 /
                      G:(DE-Juel1)PHD-NO-GRANT-20170405},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:0001-2020071402},
      url          = {https://juser.fz-juelich.de/record/878206},
}