  Graphics Processing Units (GPUs) can speed up the numerical solution of
various problems in astrophysics including the dynamical evolution of stellar
systems; the performance gain can be more than a factor 100 compared to using a
Central Processing Unit only. In this work I describe some strategies to speed
up the classical $N$-body problem using GPUs. I show some features of the
$N$-body code HiGPUs as template code. In this context, I also give some hints
on the parallel implementation of a regularization method and I introduce the
code HiGPUs-R. Although the main application of this work concerns
astrophysics, some of the presented techniques are of general validity and can
be applied to other branches of physics such as electrodynamics and QCD.
