Adaptive modeling and simulation for coupling methods

We present in this work an alternative approach to classical adaptive modeling usually based on a posteriori error estimation: the new adaptive method is founded on the concept of optimal control and is applied to the simulation of atomistic-to-continuum coupled models developed using the Arlequin framework. The solutions of the coupled model represent approximations of the solutions to fully atomistic models. The coupled solutions may indeed contain errors due to the misplacement of the overlap region defined in the Arlequin framework. Since the position of the overlap region is not known a priori and may depend on the goal of the simulation, our objective here is to determine, a posteriori, its best position, or equivalently, the optimal size of the atomic region that needs to be retained in the coupling formulation in order to accurately predict prescribed quantities of interest. In this new adaptive process, the position of the overlap between the particle and continuum models is conveniently parameterized and iteratively identified by searching for the optimal parameters. The performance of the method is illustrated on two-dimensional test problems.