A Bayesian approach for uncertainty quantification in elliptic Cauchy problem

Renaud Ferrier (1) , Mohamed Larbi Kadri (2) , Pierre Gosselet (1) , Hermann G. Matthies (3)

1 LMT - Laboratoire de Mécanique et Technologie
2 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
3 WiRe - Institut für Wissenschaftliches Rechnen

We study the Cauchy problem in the framework of static linear elasticity and its resolution via the Steklov-Poincaré approach. In the linear Gaussian framework, the straightforward application of Bayes theory leads to formulas allowing to deduce the uncertainty on the identified field from the noise level. We use a truncated Ritz decomposition of the Steklov-Poincaré operator, which reduces the number of degrees of freedom and significantly lowers the computational cost.

Domaines: Mécanique des structures [physics.class-ph]

Renaud Ferrier, Mohamed Larbi Kadri, Pierre Gosselet, Hermann G. Matthies. A Bayesian approach for uncertainty quantification in elliptic Cauchy problem. Virtual design and validation, Springer, pp.293-308, 2020, 978-3-030-38156-1. ⟨10.1007/978-3-030-38156-1_15⟩. ⟨hal-02344209⟩