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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},
}