Skip to Main content Skip to Navigation
Theses

Méthode multiéchelle et réduction de modèle pour la propagation d'incertitudes localisées dans les modèles stochastiques

Abstract : In many physical problems, an uncertain model can be represented as a set of stochastic partial differential equations. We are here interested in problems with many sources of uncertainty with a localized character in space. In the context of functional approaches for uncertainty propagation, these problems present two major difficulties. The first one is that their solutions are multi-scale, which requires model reduction methods and appropriate computational strategies. The second difficulty is associated with the representation of functions of many parameters in order to take into account many sources of uncertainty. To overcome these difficulties, we first propose a multi-scale domain decomposition method that exploits the localized side of uncertainties. An iterative algorithm is proposed, which entails the alternated resolution of global and local problems, the latter being defined on patches containing localized variabilities. Tensor approximation methods are then used to deal with high dimensional functional representations. Multi-scale separation improves the conditioning of local and global problems and also the convergence of the tensor approximation methods which is related to the spectral content of functions to be decomposed. Finally, for the handling of localized geometrical variability, specific methods based on fictitious domain approaches are introduced.
Complete list of metadatas

Cited literature [98 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00798526
Contributor : Elias Safatly <>
Submitted on : Friday, March 8, 2013 - 4:44:06 PM
Last modification on : Monday, March 25, 2019 - 4:24:08 PM
Long-term archiving on: : Sunday, June 9, 2013 - 9:35:16 AM

Identifiers

  • HAL Id : tel-00798526, version 1

Collections

Citation

Elias Safatly. Méthode multiéchelle et réduction de modèle pour la propagation d'incertitudes localisées dans les modèles stochastiques. Analyse numérique [math.NA]. Université de Nantes; Ecole Centrale de Nantes (ECN), 2012. Français. ⟨tel-00798526⟩

Share

Metrics

Record views

485

Files downloads

504