  The study of polycrystalline materials requires theoretical and computational
techniques enabling multiscale investigations. The amplitude expansion of the
phase field crystal model (APFC) allows for describing crystal lattice
properties on diffusive timescales by focusing on continuous fields varying on
length scales larger than the atomic spacing. Thus, it allows for the
simulation of large systems still retaining details of the crystal lattice.
Fostered by the applications of this approach, we present here an efficient
numerical framework to solve its equations. In particular, we consider a real
space approach exploiting the finite element method. An optimized
preconditioner is developed in order to improve the convergence of the linear
solver. Moreover, a mesh adaptivity criterion based on the local rotation of
the polycrystal is used. This results in an unprecedented capability of
simulating large, three-dimensional systems including the dynamical description
of the microstructures in polycrystalline materials together with their
dislocation networks.
