Reduced basis techniques for stochastic problems
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Patera_Reduced basis.pdf
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Author(s)
Boyaval, S.
Le Bris, C.
Lelievre, T.
Maday, Yvon
Nguyen, Ngoc Cuong
Patera, Anthony T.
Date Issued
October 2010
Journal
Archives of Computational Methods in Engineering
Publisher
International Center for Numerical Methods in Engineering
Citation
Boyaval, S. et al. “Reduced Basis Techniques for Stochastic Problems.” Archives of Computational Methods in Engineering 17.4 (2010) : 435-454-454.
Version
Author's final manuscript
Abstract
We report here on the recent application of a now classical general reduction technique, the Reduced-Basis (RB) approach initiated by C. Prud’homme et al. in J. Fluids Eng. 124(1), 70–80, 2002, to the specific context of differential equations with random coefficients. After an elementary presentation of the approach, we review two contributions of the authors: in Comput. Methods Appl. Mech. Eng. 198(41–44), 3187–3206, 2009, which presents the application of the RB approach for the discretization of a simple second order elliptic equation supplied with a random boundary condition, and in Commun. Math. Sci., 2009, which uses a RB type approach to reduce the variance in the Monte-Carlo simulation of a stochastic differential equation. We conclude the review with some general comments and also discuss possible tracks for further research in the direction.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s11831-010-9056-z
