We consider a linear damped wave equation defined on a two-dimensional domain ?, with a dissipative term localized in a subset ?. We address the shape design problem which consists in optimizing the shape of ? in order to minimize the energy of the system at a given time T. By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ?. ; Expressed as a boundary integral on ??, this derivative is then used as an advection velocity in a Hamilton-Jacobi equation for shape changes. We use the level-set methodology on a fixed working Eulerian mesh as well as the notion of the topological derivative. We also consider optimization with respect to the value of the damping parameter. The numerical approximation is presented in detail and several numerical experiments are performed which relate the over-damping phenomenon to the well-posedness of the problem.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 19, number 1 (2009) ; click here to follow the link
Biblioteka Uniwersytetu Zielonogórskiego
Nov 5, 2024
Apr 8, 2024
43
https://www.zbc.uz.zgora.pl/publication/88521
Edition name | Date |
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Optimal internal dissipation of a damped wave equation using a topological approach | Nov 5, 2024 |
Fulmański, Piotr Laurain, Antoine Scheid, Jean-Francois Sokołowski, Jan Sokołowski, Jan - ed. Sonnendrücker, Eric - ed.
Iguernane, Mohamed Nazarov, Serguei A. Roche, Jean-Rodolphe Sokołowski, Jan Szulc, Katarzyna Korbicz, Józef (1951- ) - ed.
Emambakhsh, Mehryar Ebrahimnezhad, Hossein Sedaaghi, Mohammad Hossein Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.
Singh, Baljeet Verma, Shailja Jurczak, Paweł - red.
Madan, Dinesh Kumar Kumar, Naveen Rani, Annu Jurczak, Paweł - red.
Majumder, D.P. Dhar, Asoke Kumar Jurczak, Paweł - red.
Dhar, Asoke Kumar Mondal, J. Jurczak, Paweł - red.
Eppler, Karsten Korbicz, Józef (1951- ) - red. Uciński, Dariusz - red.