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Measure transformation and efficient quadrature in reduced‐dimensional 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.4368
Subject(s) - probabilistic logic , multiphysics , computer science , measure (data warehouse) , transformation (genetics) , theoretical computer science , computation , reduction (mathematics) , dimension (graph theory) , dimensionality reduction , representation (politics) , context (archaeology) , mathematical optimization , uncertainty quantification , algorithm , mathematics , data mining , finite element method , artificial intelligence , machine learning , law , chemistry , biology , paleontology , biochemistry , geometry , political science , thermodynamics , physics , politics , pure mathematics , gene
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. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. Copyright © 2012 John Wiley & Sons, Ltd.