@incollection{PieronekKleefeld2019,
  author    = {Pieronek, Lukas and Kleefeld, Andreas},
  title     = {The Method of Fundamental Solutions for Computing Interior Transmission Eigenvalues of Inhomogeneous Media},
  series = {Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations},
  booktitle = {Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations},
  editor    = {Constanda, Christian and Harris, Paul},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-16077-7},
  doi       = {10.1007/978-3-030-16077-7_28},
  pages     = {353 -- 365},
  year      = {2019},
  abstract  = {The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach.},
  language  = {en}
}
@incollection{AbeleKleefeld2020,
  author    = {Abele, Daniel and Kleefeld, Andreas},
  title     = {New Numerical Results for the Optimization of Neumann Eigenvalues},
  series = {Computational and Analytic Methods in Science and Engineering},
  booktitle = {Computational and Analytic Methods in Science and Engineering},
  editor    = {Constanda, Christian},
  publisher = {Birkh{\"a}user},
  address   = {Cham},
  isbn      = {978-3-030-48185-8 (Print)},
  doi       = {10.1007/978-3-030-48186-5_1},
  pages     = {1 -- 20},
  year      = {2020},
  abstract  = {We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.},
  language  = {en}
}