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Dimension reduction in stochastic modeling of coupled problems
Author(s) -
Arnst M.,
Ghanem R.,
Phipps E.,
RedHorse J.
Publication year - 2012
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.4364
Subject(s) - multiphysics , probabilistic logic , reduction (mathematics) , dimension (graph theory) , computation , representation (politics) , computer science , context (archaeology) , dimensionality reduction , theoretical computer science , uncertainty quantification , domain (mathematical analysis) , domain decomposition methods , mathematical optimization , mathematics , algorithm , finite element method , artificial intelligence , machine learning , engineering , paleontology , mathematical analysis , geometry , structural engineering , politics , law , political science , pure mathematics , biology
SUMMARY Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced‐dimensional representation and in particular by an adaptation of the Karhunen‐Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering. Copyright © 2012 John Wiley & Sons, Ltd.