  Coarse-grained molecular dynamics (CGMD) is a technique developed as a
concurrent multiscale model that couples conventional molecular dynamics (MD)
to a more coarse-grained description of the periphery. The coarse-grained
regions are modeled on a mesh in a formulation that generalizes conventional
finite element modeling (FEM) of continuum elasticity. CGMD is derived solely
from the MD model, however, and has no continuum parameters. As a result, it
provides a coupling that is smooth and provides control of errors that arise at
the coupling between the atomistic and coarse-grained regions. In this article,
we elaborate on the formulation of CGMD, describing in detail how CGMD is
applied to anharmonic solids and finite temperature simulations. As tests of
CGMD, we present in detail the calculation of the phonon spectra for solid
argon and tantalum in 3D, demonstrating how CGMD provides a better description
of the elastic waves than that provided by FEM. We also present elastic wave
scattering calculations that show the elastic wave scattering is more benign in
CGMD than FEM. We also discuss the dependence of scattering on the properties
of the mesh. We introduce a rigid approximation to CGMD that eliminates
internal relaxation, similar to the Quasicontinuum technique, and compare it to
the full CGMD.
