  A modern approach to the evolution of a mixed (stars and gas)
self-gravitating system is the fully Lagrangian particle approach. The gaseous
(particle) phase differs from the compact because the mutual force is given by
the sum of gravity and pressure gradient. In this note we report of some
characteristics, advantages and limitations of this approach for what regards
the evaluation of forces in the system. In particular, a comparison between
classic tree-code and fast multipole algorithm to evaluate gravitational forces
is discussed.
