Numerical studies of a coarse-grained approximation for dynamics of an atomic chain
P. Lin and P. Plechac
International Journal for Multiscale Computational Engineering, 5, 351-367 (2007).

ABSTRACT
in many applications, materials are modeled by a large number of particles (or
atoms) where each particle interacts with all others. Near or nearest-neighbor
interaction is considered to be a good simplification of the full interaction in
the engineering community. However, the resulting system is still too large to
be solved under the existing computer power. In this paper we shall use the
finite element and/or quasicontinuum idea to both position and velocity
variables in order to reduce the number of degrees of freedom. The original and
approximate particle systems are related to the discretization of the virtual
internal bond model (continuum model). We focus more on the discrete system
since the continuum description may not be physically complete because the
stress-strain relation is not monotonically increasing and thus not necessarily
well posed. We provide numerical justification on how well the coarse-grained
solution is close to the fine grid solution in either a viscosity-demping or a
temporal-average sense.