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arXiv · 2109.13239

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

Harald Garcke·Sourav Mitra·Vanja Nikolić
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Abstract

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.

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Harald Garcke, Sourav Mitra, Vanja Nikolić. 2021-09-27. A phase-field approach to shape and topology optimization of acoustic waves in dissipative media. https://arxiv.org/abs/2109.13239

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