A phase-field approach to shape and topology optimization of acoustic waves in dissipative media

0562002 - MÚ 2023 RIV US eng J - Journal Article
Garcke, H. - Mitra, Sourav - Nikolić, V.
A phase-field approach to shape and topology optimization of acoustic waves in dissipative media.
SIAM Journal on Control and Optimization. Roč. 60, č. 4 (2022), s. 2297-2319. ISSN 0363-0129. E-ISSN 1095-7138
Institutional support: RVO:67985840
Keywords : nonlinear acoustics * optimality conditions * phase-field method * shape and topology optimization
OECD category: Pure mathematics
Impact factor: 2.2, year: 2022
Method of publishing: Limited access
https://doi.org/10.1137/21M1449294

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 Γ-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.
Permanent Link: https://hdl.handle.net/11104/0334432