New Numerical Results for the Optimization of Neumann Eigenvalues
- 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.
Author: | Daniel Abele, Andreas KleefeldORCiD |
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DOI: | https://doi.org/10.1007/978-3-030-48186-5_1 |
ISBN: | 978-3-030-48185-8 (Print) |
ISBN: | 978-3-030-48186-5 (Online) |
Parent Title (English): | Computational and Analytic Methods in Science and Engineering |
Publisher: | Birkhäuser |
Place of publication: | Cham |
Editor: | Christian Constanda |
Document Type: | Part of a Book |
Language: | English |
Year of Completion: | 2020 |
First Page: | 1 |
Last Page: | 20 |
Link: | https://doi.org/10.1007/978-3-030-48186-5_1 |
Zugriffsart: | campus |
Institutes: | FH Aachen / Fachbereich Medizintechnik und Technomathematik |
collections: | Verlag / Birkhäuser Verlag |