Development of error criteria for adaptive multi-element polynomial chaos approaches

B Chouvion (1) , Emmanuelle Sarrouy (2)

1 M&S - Matériaux et Structures
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper presents and compares different methodologies to create an adaptive stochastic space partitioning in polynomial chaos applications which use a multi-element approach. To implement adaptive partitioning, Wan and Karniadakis first developed a criterion based on the relative error in local variance. We propose here two different error criteria: one based on the residual error and the other on the local variance discontinuity created by partitioning. The methods are applied to classical differential equations with long-term integration difficulties, including the Kraichnan–Orszag three-mode problem, and to simple linear and nonlinear mechanical systems whose stochastic dynamic responses are investigated. The efficiency and robustness of the approaches are investigated by comparison with Monte-Carlo simulations. For the different examples considered, they show significantly better convergence characteristics than the original error criterion used.

Mots clés: Polynomial chaos; MEgPC; Uncertainty modelling; Stochastic Galerkin method

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

B Chouvion, Emmanuelle Sarrouy. Development of error criteria for adaptive multi-element polynomial chaos approaches. Mechanical Systems and Signal Processing, 2016, 66--67, pp.201--222. ⟨10.1016/j.ymssp.2015.05.007⟩. ⟨hal-01183750⟩