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Communication Dans Un Congrès Année : 2002

Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations

Résumé

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations -- Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -- relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -- methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage -- in which, given a new parameter value, we calculate the output of interest and associated error bound -- depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.
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Dates et versions

hal-00798352 , version 1 (11-03-2013)

Identifiants

  • HAL Id : hal-00798352 , version 1

Citer

Christophe Prud'Homme, D.V Rovas, K. Veroy, L. Machiels, Yvon Maday, et al.. Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations. Proceedings SMA Symposium, 2002, Saarbrücken, Germany. pp.1. ⟨hal-00798352⟩
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