Connecting atomistic-to-continuum coupling and domain decomposition

Many atomistic/continuum coupling algorithms utilize an overlapping subdomain method, where boundary data for local solves in atomistic and discretized continuum subdomains is provided from local solves in neighboring subdomains. Such coupling algorithms are closely related to the classical alternating Schwarz domain decomposition method, although little to no convergence or error analysis exists for such methods in an atomistic/continuum framework. We consider a specific alternating Schwarz algorithm for coupling a nonlocal atomistic model with a local finite element model and carry out a convergence and error analysis along with supporting numerical experiments.