Reduced Basis Techniques for Stochastic Problems

• Autores: Sébastien Boyaval, Claude Le Bris, Tony Lelièvre, Yvon Maday, Ngoc-Cuong Nguyen, Anthony T. Patera
• Localización: Archives of computational methods in engineering: state of the art reviews, ISSN 1134-3060, Vol. 17, Nº. 4, 2010, págs. 435-454
• Idioma: inglés
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• Resumen

  • 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