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Numerical investigation on the Total Sensitivity Index influence in the solution of stochastic partial differential equations

Remi Abgrall 1, 2 Pietro Marco Congedo 1 Gianluca Geraci 1
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : In the present work a criterion on the reduction of the stochastic dimensions has been investigated in the context of the stochastic partial differential equations. Three different types of equations have been analyzed: elliptical, parabolic and an hyperbolic. For each equation, both mean and variance have been computed on some scalar output of interest. The complete and the reduced models have been compared in terms of statistical moments. The validity and the efficiency of a criterion based on TSI index has been investigated, and an error correlation has been found between the error on the variance and the TSI, that will be validated in a future work for more complex equations.
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Remi Abgrall, Pietro Marco Congedo, Gianluca Geraci. Numerical investigation on the Total Sensitivity Index influence in the solution of stochastic partial differential equations. [Research Report] RR-7911, INRIA Bordeaux, équipe CARDAMOM. 2012, pp.19. ⟨hal-00681405v2⟩

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