An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations

An adaptive approach to control modeling error in multiscale simulations that involve molecular and continuum scales is presented. The modeling error is defined as the difference between the solution of a reference particle model, which is considered intractable in practice, and the solution of a manageable multiscale surrogate problem based on the Arlequin framework. The method relies on computable error estimates of the modeling error in specific outputs of interest that require the solution of an adjoint problem. These are the so-called goal-oriented error estimates, which are used to adapt the surrogate model, i.e. to find the optimal configuration of the overlap region between the molecular and continuum models, in order to deliver approximations of quantities of interest within some preset accuracy. Performance of the adaptive strategy is demonstrated on two-dimensional numerical examples.