Garcke, Harald and Mitra, Sourav and Nikolic, Vanja (2022) A PHASE-FIELD APPROACH TO SHAPE AND TOPOLOGY OPTIMIZATION OF ACOUSTIC WAVES IN DISSIPATIVE MEDIA. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 60 (4). pp. 2297-2319. ISSN 0363-0129, 1095-7138
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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 I.-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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | WESTERVELT; LENS; shape and topology optimization; nonlinear acoustics; phase-field method; opti-mality conditions; I-convergence |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 10:50 |
| Last Modified: | 07 Feb 2024 10:50 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57274 |
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