Archives of Computational Methods in Engineering

, Volume 17, Issue 4, pp 435–454 | Cite as

Reduced Basis Techniques for Stochastic Problems

  • S. Boyaval
  • C. Le Bris
  • T. Lelièvre
  • Y. Maday
  • N. C. Nguyen
  • A. T. Patera
Original Paper

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.

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Copyright information

© CIMNE, Barcelona, Spain 2010

Authors and Affiliations

  • S. Boyaval
    • 1
    • 2
  • C. Le Bris
    • 1
    • 2
  • T. Lelièvre
    • 1
    • 2
  • Y. Maday
    • 3
    • 4
  • N. C. Nguyen
    • 5
  • A. T. Patera
    • 5
  1. 1.CERMICS, Ecole des ponts ParisTechUniversité Paris-EstMarne la Vallée Cedex 2France
  2. 2.MICMAC project teamINRIALe Chesnay CedexFrance
  3. 3.UMR 7598, Laboratoire Jacques-Louis LionsUPMC Univ Paris 06ParisFrance
  4. 4.Division of Applied MathematicsBrown UniversityProvidenceUSA
  5. 5.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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