  We present a new framework for coarse-graining molecular dynamics models for
crystalline solids. The reduction method is based on a Galerkin projection to a
subspace, whose dimension is much smaller than that of the full atomistic
model. The subspace is expanded by adding more coarse-grain variables near the
interface between lattice defects and the surrounding regions. This effectively
minimizes reflection of phonons at the interface. In this approach, there is no
need to pre-compute the memory function in the generalized Langevin equations,
a typical model of interface conditions. Moreover, the variational formulation
preserves the stability of mechanical equilibria.
