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Randomized residual-based error estimators for the Proper Generalized Decomposition approximation of parametrized problems

Kathrin Smetana 1 Olivier Zahm 2
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an adjoint problem with random right-hand side, which we approximate using the PGD. The effectivity of this randomized error estimator can be arbitrarily close to unity with high probability, allowing the estimation of the error with respect to any user-defined norm as well as the error in some quantity of interest. The performance of the error estimator is demonstrated and compared with some existing error estimators for the PGD for a parametrized time-harmonic elastodynamics problem and the parametrized equations of linear elasticity with a high-dimensional parameter space.
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https://hal.inria.fr/hal-02335617
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Submitted on : Monday, October 28, 2019 - 1:42:06 PM
Last modification on : Tuesday, October 19, 2021 - 11:25:54 AM

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Kathrin Smetana, Olivier Zahm. Randomized residual-based error estimators for the Proper Generalized Decomposition approximation of parametrized problems. International Journal for Numerical Methods in Engineering, Wiley, 2020, Special Issue: Credible High‐Fidelity and Low‐Cost Simulations in Computational Engineering, 121 (23), pp.5153-5177. ⟨10.1002/nme.6339⟩. ⟨hal-02335617⟩

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