GOAL-ORIENTED MODEL ADAPTIVITY IN STOCHASTIC ELASTODYNAMICS: SIMULTANEOUS CONTROL OF DISCRETIZATION, SURROGATE MODEL AND SAMPLING ERRORS

Abstract

The presented adaptive modelling approach aims to jointly control the level of renement for each of the building-blocks employed in a typical chain of nite element approximations for stochastically parametrized systems, namely: (i) nite error approximation of the spatial elds (ii) surrogate modelling to interpolate quantities of interest(s) in the parameter domain and (iii) Monte-Carlo sampling of associated probability distribution(s). The control strategy seeks accurate calculation of any statistical measure of the distributions at minimum cost, given an acceptable margin of error as only tunable parameter. At each stage of the greedy-based algorithm for spatial discretisation, the mesh is selectively rened in the subdomains with highest contribution to the error in the desired measure. The strictly incremental complexity of the surrogate model is controlled by enforcing preponderant discretisation error integrated across the parameter domain. Finally, the number of Monte-Carlo samples is chosen such that either (a) the overall precision of the chain of approximations can be ascertained with sucient condence, or (b) the fact that the computational model requires further mesh renement is statistically established. The eciency of the proposed approach is discussed for a frequency-domain vibration structural dynamics problem with forward uncertainty propagation. Results show that locally adapted nite element solutions converge faster than those obtained using uniformly rened grids.