High Precision, High Performance Simulations of Astrophysical Stellar Systems

The main target of this work is the discussion of the modern techniques (software and hardware) apt to solve numerically the $N$-body problem in order to develop a numerical code with highest as possible speed and accuracy performance. In particular, we will introduce a new high precision, high performance, code (called \code) which solves the $N$-body problem exploiting both a high order time integration algorithm (the Hermite's 6th order integrator) and the modern hardware represented by Graphics Processing Units (GPUs), which work as powerful computing accelerators. I will describe in details \code showing how GPUs can be efficiently exploited for gravitational $N$-body simulations up to a large number of particles ($N\simeq 10^7$) with a degree of precision and speed impossible to reach until 5 years ago. Being quite new technologies, the GPUs have not been fully exploited so far; this is why, in this Thesis, I will discuss modern numerical techniques associated with the $N$-body problem, starting from the set up of initial conditions up to the computation of the dynamical evolution of dense and populous stellar systems using GPUs and the two main languages (OpenCL and CUDA) apt to program them. I will present also results of the application of \code to study the emerging state, and rapid mass segregation, of intermediate-$N$, young, stellar systems after their violent relaxation process. These objects have been investigated simulating systems composed by stars of different masses, including a central star-mass black hole as well as a model of gas residual of the mother cloud, starting from \lq cold\rq to \lq warm\rq initial conditions. Moreover, thanks to the high adaptability of the developed software, our group is investigating the formation and the evolution of the innermost region of galaxies (Nuclear Star Clusters). This is, surely, a modern topic, which has not yet received an adequate self-consistent explanation neither from theoretical nor a numerical point of view.