Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields

Régis Cottereau (1) , Pedro Diez (2)

1 MSSMat - Laboratoire de mécanique des sols, structures et matériaux
2 LaCàN - Laboratori de Càlcul Numèric (LACAN)

We present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented.

Mots clés: Stochastic mechanics; Monte Carlo method; Stochastic collocation method; Error Estimation; r-adaptivity

Domaines: Analyse numérique [math.NA]; Probabilités [math.PR]; Analyse numérique [cs.NA]; Mécanique [physics.med-ph]

Régis Cottereau, Pedro Diez. Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields. Computational Mechanics, 2015, 56 (4), pp.601-612. ⟨10.1007/s00466-015-1190-x⟩. ⟨hal-01200721⟩