% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@MASTERSTHESIS{Abele:872687,
      author       = {Abele, Daniel},
      title        = {{E}igenvalue optimization for acoustic scattering problems},
      school       = {Fachhochschule Aachen},
      type         = {Masterarbeit},
      reportid     = {FZJ-2020-00178},
      pages        = {XI, 72},
      year         = {2019},
      note         = {Masterarbeit, Fachhochschule Aachen, 2019},
      abstract     = {This master thesis is concerned with the optimization of
                      eigenvalues of the Laplace differential operator,
                      specifically interior Neumann eigenvalues, with respect to
                      the shapeof the domain. Such eigenvalue problems arise in
                      the study of acoustic scattering, whichhas applications in
                      sonar or radar detection and medical imaging. The shape of
                      the spacesignificantly affects the eigenvalues. Improved
                      optimal values for some of them are reported.The main focus
                      of the thesis is finding a description of the shape that is
                      well suited foroptimization. The number of parameters should
                      be low to keep the optimization spacesimple. At the same
                      time, the range of representable shapes should be large
                      enough toimprove upon previous results. Inspired by physics,
                      equipotentials are used to modelthe knobbly objects found by
                      previous researchers in a simple way.The work discusses a
                      method of solving the eigenvalue problem. The
                      BoundaryElement Method for boundary value problems is
                      combined with Beyn’s method fornonlinear eigenvalue
                      problems. The implementation of these methods is another
                      centralissue. As the optimizer requires many evaluations,
                      high speed is desired. The code isparallelized for efficient
                      computation on a large cluster.The implemented solvers are
                      tested for convergence. The parameter space is thoroughly
                      numerically explored to facilitate optimization. Finally the
                      results of the optimization are presented. The shape
                      description shows a lot of promise but is not yetgeneral
                      enough to optimize every eigenvalue.},
      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)19},
      url          = {https://juser.fz-juelich.de/record/872687},
}