Conference Presentation (After Call)

FZJ-2018-04353

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Shape optimization for interior Neumann and transmission eigenvalues

Kleefeld, A. (Corresponding author)FZJ*

2018

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 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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2018

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