Contribution to a conference proceedings/Contribution to a book

FZJ-2020-02035

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png New Numerical Results for the Optimization of Neumann Eigenvalues

Kleefeld, A. (Corresponding author)FZJ* ; Abele, D.FZJ*

2020
Birkhäuser Basel

Please use a persistent id in citations: http://hdl.handle.net/2128/24939

Abstract: We 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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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 2020

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Database coverage:

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