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v1 (2012-07-30)

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Goal-oriented error estimation for reduced basis method, with application to certified sensitivity analysis

Alexandre Janon 1, 2, Maëlle Nodet 1, 2, Clémentine Prieur 1, 2

(2012-07-28)

The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parameterized partial differential equations (PDEs). We consider a quantity of interest, which is a linear functional of the parameterized PDE solution. Compared to the original quantity of interest, the quantity of interest computed using the reduced model is tainted by a reduction error. We present a new, efficiently and explicitly computable bound for this error, and we show on different examples that this error bound is more precise than existing ones. We also present an application of our work to certified sensitivity analysis studies.

1:	MOISE (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
	CNRS : UMR5224 – INRIA – Laboratoire Jean Kuntzmann – Université Joseph Fourier - Grenoble I – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
2:	GdR MASCOT-NUM ((Méthodes d'Analyse Stochastique des Codes et Traitements Numériques))
	CNRS : GDR3179

Subject

:

Mathematics/Analysis of PDEs Statistics/Computation Mathematics/Numerical Analysis

Keyword(s): reduced basis method – surrogate model – reduced order modelling – response surface method – scientific computation – sensitivity analysis – Sobol index computation – Monte-Carlo method

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From: Alexandre Janon <>

Submitted on: Saturday, 28 July 2012 16:29:20

Updated on: Monday, 30 July 2012 20:03:04