%0 Conference Paper
%A Kleefeld, Andreas
%A Abele, Daniel
%T New Numerical Results for the Optimization of Neumann Eigenvalues
%C Basel
%I Birkhäuser
%M FZJ-2020-02035
%P 1-19
%D 2020
%< Computational and Analytic Methods in Science and Engineering
%X 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.
%B Computational and Mathematical Methods in Science and Engineering
%C 30 Jun 2019 - 6 Jul 2019, Cadiz (Spain)
Y2 30 Jun 2019 - 6 Jul 2019
M2 Cadiz, Spain
%F PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
%9 Contribution to a conference proceedingsContribution to a book
%U https://juser.fz-juelich.de/record/875440