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Multiscale Model Reduction for the Solution of Stochastic Partial Differential Equations With Localized Sources of Uncertainties

[+] Author Affiliations
Elias Safatly, Mathilde Chevreuil, Anthony Nouy

Université de Nantes, Nantes, France

Paper No. ESDA2012-82389, pp. 197-203; 7 pages
doi:10.1115/ESDA2012-82389
From:
  • ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control
  • Nantes, France, July 2–4, 2012
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4484-7
  • Copyright © 2012 by ASME

abstract

The presence of numerous localized sources of uncertainties in stochastic models leads to high dimensional and multiscale problems. A numerical strategy is here proposed to propagate the uncertainties through such models. It is based on a multiscale domain decomposition method that exploits the localized side of uncertainties. The separation of scales has the double benefit of improving the conditioning of the problem as well as the convergence of tensor based methods (namely Proper Generalized Decomposition methods) used within the strategy for the separated representation of high dimensional stochastic parametric solutions.

Copyright © 2012 by ASME

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