  The Bethe-Salpeter equation is a widely used approach to describe optical
excitations in bulk semiconductors. It leads to spectra that are in very good
agreement with experiment, but the price to pay for such accuracy is a very
high computational burden. One of the main bottlenecks is the large number of
k-points required to obtain converged spectra. In order to circumvent this
problem we propose a strategy to solve the Bethe-Salpeter equation based on a
double-grid technique coupled to a Wannier interpolation of the Kohn-Sham band
structure. This strategy is then benchmarked for a particularly difficult case,
the calculation of the absorption spectrum of GaAs, and for the well studied
case of Si. The considerable gains observed in these cases fully validate our
approach, and open the way for the application of the Bethe-Salpeter equation
to large and complex systems.
