Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 274, Issue -, Pages 103-124Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.02.004
Keywords
Uncertainty quantification; Separated representation; Stochastic decoupling; Coupled problem; Domain decomposition; FETI
Funding
- Department of Energy under Advanced Scientific Computing Research Early Career Research Award [DE-SC0006402]
- National Science Foundation grant [CMMI-1201207]
- Deutsche Forschungsgemeinschaft (DFG) [SFB 880]
- National Science Foundation [CNS-0821794]
- University of Colorado Boulder
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1201207] Funding Source: National Science Foundation
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This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned treatment of the uncertainty space. The construction of the coupled domain solution is achieved though a sequence of approximations with respect to the dimensionality of the random inputs associated with each individual sub-domain and not the combined dimensionality, hence drastically reducing the overall computational cost. The coupling between the sub-domain solutions is done via the classical finite element tearing and interconnecting (FETI) method, thus providing a well suited framework for parallel computing. Two high-dimensional stochastic problems, a 2D elliptic PDE with random diffusion coefficient and a stochastic linear elasticity problem, have been considered to study the performance and accuracy of the proposed stochastic coupling approach. (C) 2014 Elsevier B.V. All rights reserved.
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