A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations

A new adaptive method based on an optimal control approach is proposed for adaptive modeling of an atomic-to-continuum coupling method constructed from the Arlequin framework. The coupling method provides for an approximation of the solution to a fully atomic model in which errors may arise due to the misplacement of the overlap region. The objective is thus to determine, a posteriori, the best position of this overlap region. More precisely, the problem is to find the optimal size of the atomic region that one needs to consider in the coupled formulation in order to accurately estimate predefined quantities of interest. In this new adaptive process, the position of the overlapping domain between the two models is conveniently parameterized and iteratively determined by searching for the optimal parameters. The performance of the method is demonstrated on one-dimensional and two-dimensional test problems. In particular, it is observed that the approach yields better convergence with respect to quantities of interest when compared to a classical adaptive approach based on a posteriori estimates of the modeling error.