Year: 2025
Type: article
Abstract: . In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic function in the Robin-type boundary condition associated with the Helmholtz equation. A Robin boundary condition can be given on a part or the entire boundary of a bounded [Formula: see text]-domain of [Formula: see text]. The geometry of the partially absorbing boundary is fixed, but allowed to be non-Lipschitz, for example, fractal. It is defined as the support of a [Formula: see text]-upper regular measure with [Formula: see text]. Using the well-posedness properties of the model, for any fixed volume fraction of the absorbing material, we establish the existence of at least one optimal distribution minimizing the acoustical energy on a fixed frequency range of the relaxation problem. Thanks to the shape derivative of the energy functional, also existing for non-Lipschitz boundaries, we implement (in the two-dimensional case) the gradient descent method and find the optimal distribution with [Formula: see text] of the absorbent material on a frequency range with better performances than the [Formula: see text] absorbent boundary. The same type of performance is also obtained by the genetic method.
DOI: 10.1137/24m1691296
Institutions: Université Paris-Saclay, CentraleSupélec
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409550743