New Numerical Results for the Optimization of Neumann Eigenvalues

Daniel Abele () and Andreas Kleefeld ()
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Daniel Abele: Jülich Supercomputing Centre, Forschungszentrum Jülich
Andreas Kleefeld: Jülich Supercomputing Centre, Forschungszentrum Jülich

Chapter Chapter 1 in Computational and Analytic Methods in Science and Engineering, 2020, pp 1-20 from Springer

Abstract: Abstract We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-48186-5_1

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DOI: 10.1007/978-3-030-48186-5_1

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