  Excited-state calculations, notably for quasiparticle band structures, are
nowadays routinely performed within the GW approximation for the electronic
self-energy. Nevertheless, certain numerical approximations and simplifications
are still employed in practice to make the computations feasible. An important
aspect for periodic systems is the proper treatment of the singularity of the
screened Coulomb interaction in reciprocal space, which results from the slow
1/r decay in real space. This must be done without introducing artificial
interactions between the quasiparticles and their periodic images in repeated
cells, which occur when integrals of the screened Coulomb interaction are
discretised in reciprocal space. An adequate treatment of both aspects is
crucial for a numerically stable computation of the self-energy. In this
article we build on existing schemes for isotropic screening and present an
extension for anisotropic systems. We also show how the contributions to the
dielectric function arising from the non-local part of the pseudopotentials can
be computed efficiently. These improvements are crucial for obtaining a fast
convergence with respect to the number of points used for the Brillouin zone
integration and prove to be essential to make GW calculations for strongly
anisotropic systems, such as slabs or multilayers, efficient.
