This title appears in the Scientific Report :
2019
Please use the identifier:
http://dx.doi.org/10.1007/978-3-030-16077-7_15 in citations.
Please use the identifier: http://hdl.handle.net/2128/22510 in citations.
Shape Optimization for Interior Neumann and Transmission Eigenvalues
Shape Optimization for Interior Neumann and Transmission Eigenvalues
Shape optimization problems for interior eigenvalues is a very challenging task since already the computation of interior eigenvalues for a given shape is far from trivial. For example, a concrete maximizer with respect to shapes of fixed area is theoretically established only for the first two non-...
Saved in:
Personal Name(s): | Kleefeld, Andreas (Corresponding author) |
---|---|
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: |
Integral Methods in Science and Engineering |
Imprint: |
Cham
Springer International Publishing
2019
|
Physical Description: |
185-196 |
ISBN: |
978-3-030-16076-0 |
DOI: |
10.1007/978-3-030-16077-7_15 |
Document Type: |
Contribution to a book |
Research Program: |
Computational Science and Mathematical Methods |
Link: |
OpenAccess OpenAccess OpenAccess OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://hdl.handle.net/2128/22510 in citations.
Shape optimization problems for interior eigenvalues is a very challenging task since already the computation of interior eigenvalues for a given shape is far from trivial. For example, a concrete maximizer with respect to shapes of fixed area is theoretically established only for the first two non-trivial Neumann eigenvalues. The existence of such a maximizer for higher Neumann eigenvalues is still unknown. Hence, the problem should be addressed numerically. Better numerical results are achieved for the maximization of some Neumann eigenvalues using boundary integral equations for a simplified parametrization of the boundary in combination with a non-linear eigenvalue solver. Shape optimization for interior transmission eigenvalues is even more complicated since the corresponding transmission problem is non-self-adjoint and non-elliptic. For the first time numerical results are presented for the minimization of interior transmission eigenvalues for which no single theoretical result is yet available. |