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Reduced chaos expansions with random coefficientsin reduced‐dimensional stochastic modeling of coupled problems
Author(s) -
Arnst M.,
Ghanem R.,
Phipps E.,
RedHorse J.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4595
Subject(s) - polynomial chaos , curse of dimensionality , mathematics , dimension (graph theory) , representation (politics) , mathematical optimization , projection (relational algebra) , dimensionality reduction , multiphysics , uncertainty quantification , polynomial expansion , polynomial , stochastic process , monte carlo method , computer science , algorithm , mathematical analysis , finite element method , statistics , artificial intelligence , politics , political science , law , pure mathematics , physics , thermodynamics
SUMMARY 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. Copyright © 2013 John Wiley & Sons, Ltd.