  We present a method for evolving the projected Gross-Pitaevskii equation in
an infinite rotating Bose-Einstein condensate, the ground state of which is a
vortex lattice. We use quasi-periodic boundary conditions to investigate the
behaviour of the bulk superfluid in this system, in the absence of boundaries
and edge effects. We also give the Landau gauge expression for the phase of a
BEC subjected to these boundary conditions. Our spectral representation uses
the eigenfunctions of the one-body Hamiltonian as basis functions. Since there
is no known exact quadrature rule for these basis functions we approximately
implement the projection associated with the energy cut-off, but show that by
choosing a suitably fine spatial grid the resulting error can be made
negligible. We show how the convergence of this model is affected by simulation
parameters such as the size of the spatial grid and the number of Landau
levels. Adding dissipation, we use our method to find the lattice ground state
for $N$ vortices. We can then perturb the ground-state, in order to investigate
the melting of the lattice.
