A parallel algorithm for solving the unsteady 3D problems of collisionless dynamics in the case of more than 10⁹ bodies in a self-consistent gravitational field in Cartesian coordinates is proposed. The algorithm is based on the computational domain decomposition method. The parallel code that implements this algorithm can be used to perform computations on grids of more than 1000³ nodes. Some results of supercomputer simulation obtained by the code are discussed.

Keywords: mathematical simulation, supercomputer, parallel programming, astrophysics

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