Coarse-graining molecular dynamics models using an extended Galerkin projection method

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. To effectively reduce artificial reflections of phonons at the interface, we construct extended subspaces with increasing accuracy by adding more coarse-grained variables near the interface between lattice defects and the surrounding region. This approach is equivalent to the generalized Langevin model. But it eliminates the need to precompute the memory function, a well-known practical difficulty. Further, the variational formulation preserves the stability of the molecular models.