  First principles calculations based on many-electron perturbation theory
methods, such as the \textit{ab initio} GW and GW plus Bethe-Salpeter equation
(GW-BSE) approach, are reliable ways to predict quasiparticle and optical
properties of materials, respectively. However, these methods involve more care
in treating the electron-electron interaction and are considerably more
computationally demanding when applied to systems with reduced dimensionality,
since the electronic confinement leads a slower convergence of sums over the
Brillouin zone due to a much more complicated screening environment that
manifests in the "head" and "neck" elements of the dielectric matrix. Here, we
present two new schemes to sample the Brillouin zone for GW and GW-BSE
calculations: the non-uniform neck subsampling method and the clustered
sampling interpolation method, which can respectively be used for a family of
single-particle problems, such as GW calculations, and for problems involving
the scattering of two-particle states, such as when solving the BSE. We tested
these methods on several few-layer semiconductors and graphene and show that
they perform a much more efficient sampling of the Brillouin zone and yield two
to three orders of magnitude reduction in the computer time. These two methods
can be readily incorporated into several \textit{ab initio} packages that
compute electronic and optical properties through the GW and GW-BSE approaches.
