Multiscale method and model reduction for the propagation of localized uncertainties in the stochastic models.
type: Dataset
description: 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.
landing page: https://theses.hal.science/tel-00798526
keyword: approximation-de-tenseurs
keyword: decomposition-de-domaine
keyword: domain-decomposition
keyword: domaine-aleatoire
keyword: edp-stochastiques
keyword: fictitious-domain-method
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: methode-de-domaine-fictif
keyword: methodes-spectrales-stochastiques
keyword: multiechelle
keyword: multiscale
keyword: numerical-zoom
keyword: quantifications-des-incertitudes
keyword: random-domain
keyword: spectral-stochastic-methods
keyword: spimecaengineering-sciences-physicsmechanics-physicsmed-ph
keyword: stochastic-pde
keyword: tensor-approximation
keyword: theses
keyword: uncertainty-quantification
keyword: zoom-numerique
issued: 2026-05-13T05:46:48.877974
modified: 2026-05-13T05:46:48.877980
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Multiscale method and model reduction for the propagation of localized uncertainties in the stochastic models.
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00798526
issued: 2026-05-13T05:46:49.030841
modified: 2026-05-13T05:46:48.825605