  Within the mode-coupling theory (MCT) of the glass transition, we reconsider
the numerical schemes to evaluate the MCT functional. Here we propose
nonuniform discretizations of the wave number, in contrast to the standard
equidistant grid, in order to decrease the number of grid points without losing
accuracy. We discuss in detail how the integration scheme on the new grids has
to be modified from standard Riemann integration. We benchmark our approach by
solving the MCT equations numerically for mono-disperse hard disks and hard
spheres and by computing the critical packing fraction and the nonergodicity
parameters. Our results show that significant improvements in performance can
be obtained by employing a nonuniform grid.
