Parametric shape optimization for the convected Helmholtz equation with a generalized Myers boundary condition
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911020851658752 |
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| author | Alami, Nabil Lucyszyn, Edward Hermier, Raphaél Pain Dit Rozanova-Pierrat, Anna |
| author_facet | Alami, Nabil Lucyszyn, Edward Hermier, Raphaél Pain Dit Rozanova-Pierrat, Anna |
| contents | We consider the convected Helmholtz equation with a generalized Myers boundary condition (a boundary condition of the second-order) and characterize the set of physical parameters for which the problem is weakly well-posed. The model comes from industrial applications to absorb acoustic noise in jet engines filled with absorbing liners (porous material). The problem is set on a 3D cylinder filled with a d-upper regular boundary measure, with a real 1 < d $\le$ 2. This setup leads to a parametric shape optimization problem, for which we prove the existence of at least one optimal distribution for any fixed volume fraction of the absorbing liner on the boundary that minimizes the total acoustic energy on any bounded wavenumber range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parametric shape optimization for the convected Helmholtz equation with a generalized Myers boundary condition Alami, Nabil Lucyszyn, Edward Hermier, Raphaél Pain Dit Rozanova-Pierrat, Anna Analysis of PDEs Functional Analysis Optimization and Control We consider the convected Helmholtz equation with a generalized Myers boundary condition (a boundary condition of the second-order) and characterize the set of physical parameters for which the problem is weakly well-posed. The model comes from industrial applications to absorb acoustic noise in jet engines filled with absorbing liners (porous material). The problem is set on a 3D cylinder filled with a d-upper regular boundary measure, with a real 1 < d $\le$ 2. This setup leads to a parametric shape optimization problem, for which we prove the existence of at least one optimal distribution for any fixed volume fraction of the absorbing liner on the boundary that minimizes the total acoustic energy on any bounded wavenumber range. |
| title | Parametric shape optimization for the convected Helmholtz equation with a generalized Myers boundary condition |
| topic | Analysis of PDEs Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2504.00658 |