Coarse-graining molecular dynamics models using an extended Galerkin   projection
  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. 
Xiantao Li
math.NA