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000875440 005__ 20210130004932.0
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000875440 037__ $$aFZJ-2020-02035
000875440 041__ $$aEnglish
000875440 1001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b0$$eCorresponding author$$ufzj
000875440 1112_ $$aComputational and Mathematical Methods in Science and Engineering$$cCadiz$$d2019-06-30 - 2019-07-06$$gCMMSE2019$$wSpain
000875440 245__ $$aNew Numerical Results for the Optimization of Neumann Eigenvalues
000875440 260__ $$aBasel$$bBirkhäuser$$c2020
000875440 29510 $$aComputational and Analytic Methods in Science and Engineering
000875440 300__ $$a1-19
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000875440 520__ $$aWe present new numerical results for shape optimization problems ofinterior Neumann eigenvalues. This field is not well understood from a theoreticalstandpoint. The existence of shape maximizers is not proven beyond the firsttwo eigenvalues, so we study the problem numerically. We describe a method tocompute the eigenvalues for a given shape that combines the boundary elementmethod with an algorithm for nonlinear eigenvalues. As numerical optimizationrequires many such evaluations, we put a focus on the efficiency of the methodand the implemented routine. The method is well suited for parallelization. Usingthe resulting fast routines and a specialized parametrization of the shapes, we foundimproved maxima for several eigenvalues.
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000875440 7001_ $$0P:(DE-Juel1)177946$$aAbele, Daniel$$b1$$ufzj
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