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We present implementations of a fourth-order symplectic integrator on graphicprocessing units for three $N$-body models with long-range interactions ofgeneral interest: the Hamiltonian Mean Field, Ring and two-dimensionalself-gravitating models. We discuss the algorithms, speedups and errors usingone and two GPU units. Speedups can be as high as 140 compared to a serialcode, and the overall relative error in the total energy is of the same orderof magnitude as for the CPU code. The number of particles used in the testsrange from 10,000 to 50,000,000 depending on the model.

Molecular dynamics for long-range interacting systems on Graphic Processing Units