| Title: |
A phase-field approach to shape and topology optimization of acoustic waves in dissipative media |
| Authors: |
Garcke, Harald, Mitra, Sourav, Nikolić, Vanja |
| Publication Year: |
2021 |
| Collection: |
Mathematics
Mathematical Physics |
| Subject Terms: |
Mathematics - Optimization and Control, Mathematical Physics, Mathematics - Analysis of PDEs, 35L72, 49J20 |
| More Details: |
We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field formulation of this problem through diffuse interfaces between the lenses and the surrounding fluid. The resulting formulation is shown to be well-posed and we prove that the corresponding optimization problem has a minimizer. By analyzing properties of the reduced objective functional and well-posedness of the adjoint problem, we rigorously derive first-order optimality conditions for this problem. Additionally, we consider the $\Gamma$-limit of the reduced objective functional and in this way establish a relation between the diffuse interface problem and a perimeter-regularized sharp interface shape optimization problem. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2109.13239 |
| Accession Number: |
edsarx.2109.13239 |
| Database: |
arXiv |
