Digital Library of Zielona Góra contains 9 272 digital objects
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Title: Optimal internal dissipation of a damped wave equation using a topological approach
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Abstract:
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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
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DOI:
Pages:
Source:
AMCS, volume 19, number 1 (2009) ; click here to follow the link
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License CC BY 4.0:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Repository > Types of work > Articles
- Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2009)
Last modified:
Jul 14, 2025
In our library since:
Apr 8, 2024
Number of object content hits:
131
All available object's versions:
https://zbc.uz.zgora.pl/repozytorium/publication/88521
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19, number 1 (2009)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19, number 2 (2009)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19, number 3 (2009)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19, number 4 (2009)
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| Edition name | Date |
|---|---|
| Optimal internal dissipation of a damped wave equation using a topological approach | Jul 14, 2025 |
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