Abstract
This work is concerned with the propagation of uncertainty across coupled 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 solution is achieved though a sequence of approximations with respect to the dimensionality of the random inputs associated with each individual subproblem 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. A high-dimensional stochastic problem, a coupled 2D elliptic PDE with random diffusion coefficient, has been considered in this paper to study the performance and accuracy of the proposed stochastic coupling approach.
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Acknowledgments
The authors are indebted for the fruitful discussions they had with Prof. K.C. Park from University of Colorado, Boulder. AD gratefully acknowledges the financial support of the Department of Energy under Advanced Scientific Computing Research Early Career Research Award DE-SC0006402. MH’s work was supported by the National Science Foundation grant CMMI-1201207. The work of HGM and RN has been partly supported by the German Research Foundation “Deutsche Forschungsgemeinschaft” (DFG).
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Hadigol, M., Doostan, A., Matthies, H.G., Niekamp, R. (2014). Partitioned Solution of Coupled Stochastic Problems. In: Idelsohn, S. (eds) Numerical Simulations of Coupled Problems in Engineering. Computational Methods in Applied Sciences, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-06136-8_16
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DOI: https://doi.org/10.1007/978-3-319-06136-8_16
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