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An adaptation of the ``Particle-Particle/Particle-Mesh'' (${\rm P^3M}$) code to the special purpose hardware ``GRAPE'' is presented.
GRAPE (for ``GRAvity piPE'') is the generic name for a series of computer chip boards designed by the University of Tokyo to handle ``N-body'' computations at the speed of supercomputers. It is coupled to a workstation used for other calculations.
Specifically, the ``PP'' part is done by a four chip GRAPE-3A, while the ``PM'' part is done on a Sun Sparc 10/51 workstation. The substantial modifications of the original code needed for this implementation are described in detail. The resulting combination achieves about one third of the speed of a Cray C-90 for the fully vectorized ${\rm P^3M}$.
Applications to cosmological simulations are discussed.
