High performance computing for self-gravitating systems

A peculiarity of astrophysics with respect to terrestrial physics is the unavoidable presence of self-gravity. This makes astrophysical simulations very hard to be done, because self-gravity induces, by mean of the fine grain structure superposed to the coarse grain, a multitude of space and time scales. In this report I give (i) a brief overview of the simulation problems to be faced in astrophysics and cosmology, with particular emphasis on the classic gravitational N-body problem and (ii) some results on the evolution of a typical example of intermediate N-body system, like a globular cluster moving in an external galactic field.