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@INBOOK{Kleefeld:863988,
      author       = {Kleefeld, Andreas},
      title        = {{S}hape {O}ptimization for {I}nterior {N}eumann and
                      {T}ransmission {E}igenvalues},
      address      = {Cham},
      publisher    = {Springer International Publishing},
      reportid     = {FZJ-2019-03904},
      isbn         = {978-3-030-16076-0},
      pages        = {185-196},
      year         = {2019},
      comment      = {Integral Methods in Science and Engineering},
      booktitle     = {Integral Methods in Science and
                       Engineering},
      abstract     = {Shape optimization problems for interior eigenvalues is a
                      very challenging task since already the computation of
                      interior eigenvalues for a given shape is far from trivial.
                      For example, a concrete maximizer with respect to shapes of
                      fixed area is theoretically established only for the first
                      two non-trivial Neumann eigenvalues. The existence of such a
                      maximizer for higher Neumann eigenvalues is still unknown.
                      Hence, the problem should be addressed numerically. Better
                      numerical results are achieved for the maximization of some
                      Neumann eigenvalues using boundary integral equations for a
                      simplified parametrization of the boundary in combination
                      with a non-linear eigenvalue solver. Shape optimization for
                      interior transmission eigenvalues is even more complicated
                      since the corresponding transmission problem is
                      non-self-adjoint and non-elliptic. For the first time
                      numerical results are presented for the minimization of
                      interior transmission eigenvalues for which no single
                      theoretical result is yet available.},
      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)7},
      doi          = {10.1007/978-3-030-16077-7_15},
      url          = {https://juser.fz-juelich.de/record/863988},
}