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

Abstract

The presented adaptive modeling approach aims to jointly control the level of refinement for each of the building blocks employed in a typical chain of finite element approximations for stochastically parametrized systems, namely: (i) finite error approximation of the spatial fields, (ii) surrogate modeling 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 the only tunable parameter. At each stage of the greedy-based algorithm for spatial discretization, the mesh is selectively refined 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 discretization 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 sufficient confidence or (b) the fact that the computational model requires further mesh refinement is statistically established. The efficiency of the proposed approach is discussed for a frequency-domain vibration structural dynamics problem with forward uncertainty propagation. Results show that locally adapted finite element solutions converge faster than those obtained using uniformly refined grids.