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 |
|---|---|
| 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 |
| Date of the Publication (Server): | 2024/07/11 |
| 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 |
