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High performance computing for classic gravitational N-body systems

The role of gravity is crucial in astrophysics. It determines the evolution of any system, over an enormous range of time and space scales. Astronomical stellar systems as composed by N interacting bodies represent examples of self-gravitating systems, usually treatable with the aid of newtonian gravity but for particular cases. In this note I will briefly discuss some of the open problems in the dynamical study of classic self-gravitating N-body systems, over the astronomical range of N. I will also point out how modern research in this field compulsorily requires a heavy use of large scale computations, due to the contemporary requirement of high precision and high computational speed.