ANALYSIS OF AN OPTIMIZATION-BASED ATOMISTIC-TO-CONTINUUM COUPLING METHOD FOR POINT DEFECTS

Abstract. We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-based atomistic model, which enables accurate simulation of the defect. Away from the core, where site energies become nearly inde-pendent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and contin-uum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates