International audienceA tensor-based method is proposed for the solution of partial differential equations defined on uncertain parameterized domains. It provides an accurate solution which is explicit with respect to parameters defining the shape of the domain, thus allowing efficient a posteriori probabilistic or parametric analyses. In the proposed method, a fictitious domain approach is first adopted for the reformulation of the parametric problem on a fixed domain, yielding a weak formulation in a tensor product space (product of space functions and parametric functions). The paper is limited to the case of Neumann conditions on uncertain parts of the boundary. The Proper Generalized Decomposition method is then introduced for the construction...
Projet MENUSINFictitious domain approach is a technique to solve partial differential equations on a...
A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework....
A domain decomposition approach exploiting the localization of random parameters in high-dimensional...
We consider the numerical solution of elliptic boundary-value problems on uncertain two-dimensional ...
This thesis makes several contributions to the resolution of high dimensional problems in scientific...
This paper aims at handling high dimensional uncertainty propagation problems by proposing a tensor ...
In many physical problems, an uncertain model can be represented as a set of stochastic partial diff...
This paper examines a completely non-intrusive, sample-based method for the computation of functiona...
Part 2: UQ TheoryInternational audienceComputational uncertainty quantification in a probabilistic s...
International audienceA priori model reduction methods based on separated representations are introd...
Computational uncertainty quantication in a probabilistic setting is a special case of a parametric ...
Computing statistical quantities of interest of the solution of PDE on random domains is an importan...
International audienceModel reduction techniques based on the construction of separated representati...
International audienceThis contribution presents a numerical strategy to evaluate the effective prop...
International audienceWe here propose a multiscale numerical method for the solution of stochastic p...
Projet MENUSINFictitious domain approach is a technique to solve partial differential equations on a...
A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework....
A domain decomposition approach exploiting the localization of random parameters in high-dimensional...
We consider the numerical solution of elliptic boundary-value problems on uncertain two-dimensional ...
This thesis makes several contributions to the resolution of high dimensional problems in scientific...
This paper aims at handling high dimensional uncertainty propagation problems by proposing a tensor ...
In many physical problems, an uncertain model can be represented as a set of stochastic partial diff...
This paper examines a completely non-intrusive, sample-based method for the computation of functiona...
Part 2: UQ TheoryInternational audienceComputational uncertainty quantification in a probabilistic s...
International audienceA priori model reduction methods based on separated representations are introd...
Computational uncertainty quantication in a probabilistic setting is a special case of a parametric ...
Computing statistical quantities of interest of the solution of PDE on random domains is an importan...
International audienceModel reduction techniques based on the construction of separated representati...
International audienceThis contribution presents a numerical strategy to evaluate the effective prop...
International audienceWe here propose a multiscale numerical method for the solution of stochastic p...
Projet MENUSINFictitious domain approach is a technique to solve partial differential equations on a...
A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework....
A domain decomposition approach exploiting the localization of random parameters in high-dimensional...