A multi-scale patch approximation for Poisson problems with a small inhomogeneous inclusion
The paper deals with the multi-scale approximation of the influence of a small inhomogeneity of arbitrary shape in an elastic medium. A new multi-scale patch method is introduced, whose caracteristic is to deal with a large scale problem without inclusion, a small-scale problem on a patch surrounding the inclusion defining a corrector and an iterative procedure between these two problems. Theoretical results of convergence of the iterations, a posteriori error estimate and comparison of the corrector with the asymptotic expansion are provided. The finite element approximation is also addressed together with some numerical tests.
Authors
- Mohamed Khaled Gdoura
- Yves Renard (ORCID: https://orcid.org/0000-0003-4701-4488)
- Thomas Homolle
- Arnaud Heibig
- Saber Amdouni (ORCID: https://orcid.org/0000-0002-4489-6019)
- Nidhal Mannai
- Adrien Petrov (ORCID: https://orcid.org/0009-0001-7699-5214)
Institutions
- Université Claude Bernard Lyon 1 (FR)
- Tunis University (TN)
- Michelin (United States) (US)
- Centre National de la Recherche Scientifique (FR)
- Université de Lyon (FR)
- Michelin (France) (FR)
- Institut Camille Jordan (FR)
- National Engineering School of Tunis (TN)
- Laboratoire de Mécanique des Contacts et des Structures (FR)
- National Institute of Applied Science and Technology (TN)
- Institut National des Sciences Appliquées de Lyon (FR)
- Tunis El Manar University (TN)
Publication Details
- Journal
- SMAI Journal of Computational Mathematics
- Published
- 2025-03-24
- DOI
- https://doi.org/10.5802/smai-jcm.121
- Primary Topic
- Composite Material Mechanics
- Type
- article
- Field-Weighted Citation Impact
- 0.00