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We describe a new algorithm for the integration of self-gravitating fluidsystems using SPH method. We split the Hamiltonian of a self-gravitating fluidsystem to the gravitational potential and others (kinetic and internalenergies) and use different time-steps for their integrations. The timeintegration is done in the way similar to that used in the mixed variable ormultiple stepsize symplectic schemes. We performed three test calculations. Onewas the spherical collapse and the other was an explosion. We also performed arealistic test, in which the initial model was taken from a simulation ofmerging galaxies. In all test calculations, we found that the number oftime-steps for gravitational interaction were reduced by nearly an order ofmagnitude when we adopted our integration method. In the case of the realistictest, in which the dark matter potential dominates the total system, the totalcalculation time was significantly reduced. Simulation results were almost thesame with those of simulations with the ordinary individual time-step method.Our new method achieves good performance without sacrificing the accuracy ofthe time integration.

FAST: A Fully Asynchronous Split Time-Integrator for Self-Gravitating Fluid