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@INPROCEEDINGS{Kleefeld:875440,
      author       = {Kleefeld, Andreas and Abele, Daniel},
      title        = {{N}ew {N}umerical {R}esults for the {O}ptimization of
                      {N}eumann {E}igenvalues},
      address      = {Basel},
      publisher    = {Birkhäuser},
      reportid     = {FZJ-2020-02035},
      pages        = {1-19},
      year         = {2020},
      comment      = {Computational and Analytic Methods in Science and
                      Engineering},
      booktitle     = {Computational and Analytic Methods in
                       Science and Engineering},
      abstract     = {We present new numerical results for shape optimization
                      problems ofinterior Neumann eigenvalues. This field is not
                      well understood from a theoreticalstandpoint. The existence
                      of shape maximizers is not proven beyond the firsttwo
                      eigenvalues, so we study the problem numerically. We
                      describe a method tocompute the eigenvalues for a given
                      shape that combines the boundary elementmethod with an
                      algorithm for nonlinear eigenvalues. As numerical
                      optimizationrequires many such evaluations, we put a focus
                      on the efficiency of the methodand the implemented routine.
                      The method is well suited for parallelization. Usingthe
                      resulting fast routines and a specialized parametrization of
                      the shapes, we foundimproved maxima for several
                      eigenvalues.},
      month         = {Jun},
      date          = {2019-06-30},
      organization  = {Computational and Mathematical Methods
                       in Science and Engineering, Cadiz
                       (Spain), 30 Jun 2019 - 6 Jul 2019},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      url          = {https://juser.fz-juelich.de/record/875440},
}