Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems

A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations

(2010) Anthony Nouy   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations

(2009) Anthony Nouy   ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING

The LATIN multiscale computational method and the Proper Generalized Decomposition

(2009) P. Ladevèze et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations

(2009) C. Le Bris et al.   CONSTRUCTIVE APPROXIMATION

A least-squares approximation of partial differential equations with high-dimensional random inputs

(2009) Alireza Doostan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Tensor Decompositions and Applications

(2009) Tamara G. Kolda et al.   SIAM REVIEW

Approximation and learning by greedy algorithms

(2008) Andrew R. Barron et al.   ANNALS OF STATISTICS

Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach

(2008) Géraud Blatman et al.   COMPTES RENDUS MECANIQUE

An extended stochastic finite element method for solving stochastic partial differential equations on random domains

(2008) A. Nouy et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Generalized spectral decomposition method for solving stochastic finite element equations: Invariant subspace problem and dedicated algorithms

(2008) Anthony Nouy   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Generalized spectral decomposition for stochastic nonlinear problems

(2008) Anthony Nouy et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

(2008) Vin de Silva et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Stochastic finite elements: Computational approaches to stochastic partial differential equations

(2008) H.G. Matthies   ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik

Global sensitivity analysis using polynomial chaos expansions

(2007) Bruno Sudret   RELIABILITY ENGINEERING & SYSTEM SAFETY