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000850311 037__ $$aFZJ-2018-04353
000850311 041__ $$aEnglish
000850311 1001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b0$$eCorresponding author$$ufzj
000850311 1112_ $$a15th International Conference on Integral Methods in Science and Engineering$$cBrighton$$d2018-07-16 - 2018-07-20$$gIMSE2018$$wUnited Kingdom
000850311 245__ $$aShape optimization for interior Neumann and transmission eigenvalues
000850311 260__ $$c2018
000850311 3367_ $$033$$2EndNote$$aConference Paper
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000850311 3367_ $$0PUB:(DE-HGF)6$$2PUB:(DE-HGF)$$aConference Presentation$$bconf$$mconf$$s1532936269_32706$$xAfter Call
000850311 520__ $$aShape optimization problems for interior eigenvalues is a very challenging task since already the computation of interior eigenvalues for a given shape is far from trivial. For example, a maximizer with respect to shapes of fixed area is theoretically established only for the first two non-trivial Neumann eigenvalues. The existence of such a maximizer for higher Neumann eigenvalues is still unknown. Hence, the problem should be addressed numerically. Better numerical results are achieved for the maximization of some Neumann eigenvalues using boundary integral equations for a simplified parametrization of the boundary in combination with a non-linear eigenvalue solver. Shape optimization for interior transmission eigenvalues is even more complicated since the corresponding transmission problem is non-self-adjoint and non-elliptic.For the first time numerical results are presented for the minimization of interior transmission eigenvalues for which no single theoretical result is yet available.
000850311 536__ $$0G:(DE-HGF)POF3-511$$a511 - Computational Science and Mathematical Methods (POF3-511)$$cPOF3-511$$fPOF III$$x0
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000850311 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)169421$$aForschungszentrum Jülich$$b0$$kFZJ
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000850311 9141_ $$y2018
000850311 920__ $$lno
000850311 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0
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