  A new type of absorbing boundary conditions for molecular dynamics
simulations are presented. The exact boundary conditions for crystalline solids
with harmonic approximation are expressed as a dynamic Dirichlet- to-Neumann
(DtN) map. It connects the displacement of the atoms at the boundary to the
traction on these atoms. The DtN map is valid for a domain with general
geometry. To avoid evaluating the time convo- lution of the dynamic DtN map, we
approximate the associated kernel function by rational functions in the Laplace
domain. The parameters in the approximations are determined by interpolations.
The explicit forms of the zeroth, first, and second order approximations will
be presented. The stability of the molecular dynamics model, supplemented with
these absorbing boundary conditions is established. Two numerical simulations
are performed to demonstrate the effectiveness of the methods.
