  We present an efficient framework to numerically treat infinite periodic
vortex lattices in rotating superfluids described by the Gross-Pitaevskii
theory. The commonly used split-step Fourier (SSF) spectral methods are
inapplicable to such systems as the standard Fourier transform does not respect
the boundary conditions mandated by the magnetic translation group. We present
a generalisation of the SSF method which incorporates the correct boundary
conditions by employing the so-called magnetic Fourier transform. We test the
method and show that it reduces to known results in the lowest-Landau-level
regime. While we focus on rotating scalar superfluids for simplicity, the
framework can be naturally extended to treat multicomponent systems and systems
under more general `synthetic' gauge fields.

Quantum Gases;Superconductivity;Quantum Physics