TY  - CONF
AU  - Kleefeld, Andreas
AU  - Abele, Daniel
TI  - New Numerical Results for the Optimization of Neumann Eigenvalues
CY  - Basel
PB  - Birkhäuser
M1  - FZJ-2020-02035
SP  - 1-19
PY  - 2020
AB  - 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.
T2  - Computational and Mathematical Methods in Science and Engineering
CY  - 30 Jun 2019 - 6 Jul 2019, Cadiz (Spain)
Y2  - 30 Jun 2019 - 6 Jul 2019
M2  - Cadiz, Spain
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
UR  - https://juser.fz-juelich.de/record/875440
ER  -