Description
CLIQUER ICI POUR REJOINDRE LA SALLE 1
Président.e de session : Nicolas Forcadel
Modérateur.trice : Thierry Horsin
A multi-scale finite element method (MsFEM) is a finite element approach that allows to solve partial differential equations (PDEs) with highly oscillatory coefficients on a coarse mesh, that is, a mesh with elements of size much larger than the characteristic scale of the oscillations [1, 2]. To do so, MsFEMs use pre-computed basis functions adapted to the differential operator that comprizes...
Dans cette communication, je considérerai un problème d'homogénéisation pour l'équation de diffusion $-div\left(a(./\varepsilon) \nabla u_{\varepsilon} \right) = f$ où le coefficient $a$ décrit une géométrie périodique perturbée par un défaut non localisé mais devenant rare à l'infini. Plus précisément, l'ensemble des coefficients étudiés s'écriront comme la somme d'un coefficient périodique...
The objective of this talk is to study the homogenization of the Poisson equation in a non periodically perforated domain (see [1]). In this setting, the size of the perforations is proportional to the distance between neighbouring cells and scales like $\varepsilon \ll 1$. More precisely, we consider the problem
$$
\begin{cases}
\begin{aligned}
- \Delta u_{\varepsilon} & = f \quad...
In our work, the three-scale homogenization methods are proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities at two different levels. The first level associated with the mesoscopic structure such that the cardiac tissue is composed at extracellular $\Omega_e$ and intracellular $\Omega_i$ domains separated by cellular membrane $ \Gamma=\partial...
In this talk, we formalize the approach originally introduced in [Cottereau, R. (2013). Numerical strategy for unbiased homogenization of random materials. International journal for numerical methods in engineering, 95(1), 71-90]. The approach aims at evaluating the effective (a.k.a. homogenized) coefficient of a medium with some fine-scale structure. It combines, using the Arlequin coupling...
