| Title: |
Gradient Flow Dynamical System for Solution of Shape Optimization Problems |
| Authors: |
Tan, Yixin; Plotnikov, Pavel; Sokolowski, Jan; Stingl, Michael; Uihlein, Andrian |
| Contributors: |
Systems Research Institute Warsaw (IBS PAN); Polska Akademia Nauk = Polish Academy of Sciences = Académie polonaise des sciences (PAN); East China Normal University Shangaï (ECNU); Lavrentyev Institute of Hydrodynamics (LIH); SBRAS; Institut Élie Cartan de Lorraine (IECL); Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS); Friedrich-Alexander Universität Erlangen-Nürnberg = University of Erlangen-Nuremberg (FAU) |
| Source: |
https://hal.science/hal-05530950 ; 2026. |
| Publisher Information: |
CCSD |
| Publication Year: |
2026 |
| Collection: |
Université de Lorraine: HAL |
| Subject Terms: |
Gradient flow; Shape optimization; Inverse problem; Kohn-Vogelius functional; Random data; Shape gradient; [MATH]Mathematics [math] |
| Description: |
The convergent method of shape optimization is proposed for a class of inverse problems. The form of the Gradient Flow Dynamical System is obtained for the inverse problems with the Kohn-Vogelius shape functional. The interface between two materials with different properties is identified from the boundary observations. In the case of the deterministic data, the convergence of the proposed method at the continuous level is recently established by Pavel Plotnikov and Jan Sokolowski. In the case of random data, the convergence result is still to be shown; however, our numerical results confirm the convergence. The convergence of such a method in the case of stochastic PDEs is an open and difficult problem, it seems. |
| Document Type: |
report |
| Language: |
English |
| Availability: |
https://hal.science/hal-05530950; https://hal.science/hal-05530950v1/document; https://hal.science/hal-05530950v1/file/JSokolowski.pdf |
| Rights: |
https://creativecommons.org/licenses/by/4.0/ ; info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.7ACE4E32 |
| Database: |
BASE |