Coupling Methods for Continuum Model with Molecular Model

This article develops coupling methods for continuum models with molecular models. Two methods are studied here: an overlapping domain decomposition method, which has overlapping domain; and an edge-to-edge decomposition method, which has an interface between the two models. These two methods enforce compatibility on the overlapping domain or interface nodes/atoms by the Lagrange multiplier method or the augmented Lagrangian method.