A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient
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Author(s)
Bris, Claude Le
Maday, Yvon
Nguyen, Ngoc Cuong
Patera, Anthony T.
Boyaval, Sebastien
Date Issued
June 2009
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier
Citation
Boyaval, Sebastien, Claude Le Bris, Yvon Maday, Ngoc Cuong Nguyen, and Anthony T. Patera. “A Reduced Basis Approach for Variational Problems with Stochastic Parameters: Application to Heat Conduction with Variable Robin Coefficient.” Computer Methods in Applied Mechanics and Engineering 198, no. 41–44 (September 2009): 3187–3206.
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Author's final manuscript
Abstract
In this work, a Reduced Basis (RB) approach is used to solve a large number of boundary value problems parametrized by a stochastic input – expressed as a Karhunen–Loève expansion – in order to compute outputs that are smooth functionals of the random solution fields. The RB method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the RB approach developed previously for deterministic systems. However, the stochastic framework requires the development of new a posteriori estimates for “statistical” outputs – such as the first two moments of integrals of the random solution fields; these error bounds, in turn, permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many-query context.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1016/j.cma.2009.05.019
