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Partitioned Solution of Coupled Stochastic Problems

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Numerical Simulations of Coupled Problems in Engineering

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 33))

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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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Authors and Affiliations

  1. University of Colorado, CO, 80309, , Boulder, USA

    Mohammad Hadigol & Alireza Doostan

  2. TU Braunschweig, 38092 , Braunschweig, Germany

    Hermann G. Matthies & Rainer Niekamp

Authors
  1. Mohammad Hadigol
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  2. Alireza Doostan
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  3. Hermann G. Matthies
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  4. Rainer Niekamp
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Corresponding author

Correspondence to Hermann G. Matthies .

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Editors and Affiliations

  1. Centre Internacional de Mètodes Numerics en l'Enginyeria (CIMNE), Catalan Institution for Research and Advanced Studies (ICREA), and International Center for Numercial Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio R. Idelsohn

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06135-1

  • Online ISBN: 978-3-319-06136-8

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