A non-iterative reconstruction method for an inverse problem modeled by a Stokes-Brinkmann equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2019
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908502374481920 |
|---|---|
| author | Hrizi, Mourad Malek, Rakia Hassine, Maatoug |
| author_facet | Hrizi, Mourad Malek, Rakia Hassine, Maatoug |
| contents | This article is concerned with the reconstruction of obstacle $Ø$ immersed in a fluid flowing in a bounded domain $Ω$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make an internal measurement and then have a least-square approach to locate the obstacle. The idea is to rewrite the reconstruction problem as a topology optimization problem. The existence and the stability of the optimization problem are demonstrated. We use here the concept of the topological gradient in order to determine the obstacle and it's rough location. The topological gradient is computed using a straightforward way based on a penalization technique without the truncation method used in the literature. The unknown obstacle is reconstructed using a level-set curve of the topological gradient. Finally, we make some numerical examples exploring the efficiency of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_07265 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A non-iterative reconstruction method for an inverse problem modeled by a Stokes-Brinkmann equations Hrizi, Mourad Malek, Rakia Hassine, Maatoug Optimization and Control Mathematical Physics Fluid Dynamics This article is concerned with the reconstruction of obstacle $Ø$ immersed in a fluid flowing in a bounded domain $Ω$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make an internal measurement and then have a least-square approach to locate the obstacle. The idea is to rewrite the reconstruction problem as a topology optimization problem. The existence and the stability of the optimization problem are demonstrated. We use here the concept of the topological gradient in order to determine the obstacle and it's rough location. The topological gradient is computed using a straightforward way based on a penalization technique without the truncation method used in the literature. The unknown obstacle is reconstructed using a level-set curve of the topological gradient. Finally, we make some numerical examples exploring the efficiency of the method. |
| title | A non-iterative reconstruction method for an inverse problem modeled by a Stokes-Brinkmann equations |
| topic | Optimization and Control Mathematical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/1905.07265 |