This title appears in the Scientific Report :
2020
Please use the identifier:
http://hdl.handle.net/2128/24939 in citations.
New Numerical Results for the Optimization of Neumann Eigenvalues
New Numerical Results for the Optimization of Neumann Eigenvalues
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...
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Personal Name(s): | Kleefeld, Andreas (Corresponding author) |
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Abele, Daniel | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: |
Computational and Analytic Methods in Science and Engineering |
Imprint: |
Basel
Birkhäuser
2020
|
Physical Description: |
1-19 |
Conference: | Computational and Mathematical Methods in Science and Engineering, Cadiz (Spain), 2019-06-30 - 2019-07-06 |
Document Type: |
Contribution to a book Contribution to a conference proceedings |
Research Program: |
Computational Science and Mathematical Methods |
Link: |
OpenAccess OpenAccess |
Publikationsportal JuSER |
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. |