  A polymer model given in terms of beads, interacting through Hookean springs
and hydrodynamic forces, is studied. Brownian dynamics description of this
bead-spring polymer model is extended to multiple resolutions. Using this
multiscale approach, a modeller can efficiently look at different regions of
the polymer in different spatial and temporal resolutions with scalings given
for the number of beads, statistical segment length and bead radius in order to
maintain macro-scale properties of the polymer filament. The Boltzmann
distribution of a Gaussian chain for differing statistical segment lengths
gives a Langevin equation for the multi-resolution model with a mobility tensor
for different bead sizes. Using the pre-averaging approximation, the
translational diffusion coefficient is obtained as a function of the inverse of
a matrix and then in closed form in the long-chain limit. This is then
confirmed with numerical experiments.
