TY  - CHAP
A1  - Abele, Daniel
A1  - Kleefeld, Andreas
A2  - Constanda, Christian
T1  - New Numerical Results for the Optimization of Neumann Eigenvalues
T2  - Computational and Analytic Methods in Science and Engineering
N2  - 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.
Y1  - 2020
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/11498
SN  - 978-3-030-48185-8 (Print)
SN  - 978-3-030-48186-5 (Online)
SP  - 1
EP  - 20
PB  - Birkhäuser
CY  - Cham
ER  -