[en] We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed method entails a partitioned iterative solution algorithm that relies on a reduced-dimensional representation of information exchanged between subproblems to allow each subproblem to be solved within its own stochastic dimension while interacting with a reduced projection of the other subproblems. The proposed method extends previous work by the authors by introducing a reduced chaos expansion with random coefficients. The representation of the exchanged information by using this reduced chaos expansion with random coefficients enables an expeditious construction of doubly stochastic polynomial chaos expansions that separate the effect of uncertainty local to a subproblem from the effect of statistically independent uncertainty coming from other subproblems through the coupling. After laying out the theoretical framework, we apply the proposed method to a multiphysics problem from nuclear engineering.
Disciplines :
Mechanical engineering
Author, co-author :
Arnst, Maarten ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational and stochastic modeling
Ghanem, Roger; University of Southern California > Department of Civil and Environmental Engineering
Phipps, Eric; Sandia National Laboratories
Red-Horse, John; Sandia National Laboratories
Language :
English
Title :
Reduced chaos expansions with random coefficients in reduced-dimensional stochastic modeling of coupled problems
Publication date :
2014
Journal title :
International Journal for Numerical Methods in Engineering
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