A Domain Decomposition Approach for Uncertainty Analysis
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Liao-2015-Domain Decomposition.pdf
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684.22 KB
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Author(s)
Liao, Qifeng
Willcox, Karen E.
Date Issued
January 2015
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Liao, Qifeng, and Karen Willcox. “A Domain Decomposition Approach for Uncertainty Analysis.” SIAM Journal on Scientific Computing 37, no. 1 (January 2015): A103–A133. © 2015, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
This paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equations (PDEs). The system is split into local components using domain decomposition. Our domain-decomposed uncertainty quantification (DDUQ) approach performs uncertainty analysis independently on each local component in an “offline" phase, and then assembles global uncertainty analysis results using precomputed local information in an “online" phase. At the heart of the DDUQ approach is importance sampling, which weights the precomputed local PDE solutions appropriately so as to satisfy the domain decomposition coupling conditions. To avoid global PDE solves in the online phase, a proper orthogonal decomposition reduced model provides an efficient approximate representation of the coupling functions.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/140980508
