  We present an effective and simple multiscale method for equilibrating Kremer
Grest model polymer melts of varying stiffness. In our approach, we
progressively equilibrate the melt structure above the tube scale, inside the
tube and finally at the monomeric scale. We make use of models designed to be
computationally effective at each scale. Density fluctuations in the melt
structure above the tube scale are minimized through a Monte Carlo simulated
annealing of a lattice polymer model. Subsequently the melt structure below the
tube scale is equilibrated via the Rouse dynamics of a force-capped
Kremer-Grest model that allows chains to partially interpenetrate. Finally the
Kremer-Grest force field is introduced to freeze the topological state and
enforce correct monomer packing. We generate $15$ melts of $500$ chains of
$10.000$ beads for varying chain stiffness as well as a number of melts with
$1.000$ chains of $15.000$ monomers. To validate the equilibration process we
study the time evolution of bulk, collective and single-chain observables at
the monomeric, mesoscopic and macroscopic length scales. Extension of the
present method to longer, branched or polydisperse chains and/or larger system
sizes is straight forward.

Soft Condensed Matter