| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 90 | |
| Number of page(s) | 39 | |
| DOI | https://doi.org/10.1051/cocv/2024071 | |
| Published online | 17 November 2025 | |
Nonlocal approximation of the anisotropic perimeter and application to topology optimization
1
Laboratoire de Mathématiques d’Avignon, Avignon Université, 301 rue Baruch de Spinoza, BP 21239, 84916 AVIGNON Cedex 9, France
2
Centre de Mathématiques Appliquées (UMR 7641), École Polytechnique, Institut Polytechnique de Paris, 91120, PALAISEAU Cedex, France
* Corresponding author: samuel.amstutz@univ-avignon.fr
Received:
8
December
2023
Accepted:
11
September
2024
We present a Γ−convergence approximation of a class of anisotropic perimeter functionals. In contrast to other works on the topic, the construction relies on the solution of possibly nonlinear elliptic boundary value problems. We discuss theoretical and algorithmic aspects. We also show various applications in topology optimization, including multiphase partitioning and overhang penalization in a mechanical framework related to additive manufacturing.
Mathematics Subject Classification: 49Q10 / 49Q20 / 74P05
Key words: Topology optimization / perimeter / additive manufacturing
© The authors. Published by EDP Sciences, SMAI 2025
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