  We present Particle-Particle-Particle-Mesh (PPPM) and Tree Particle-Mesh
(TreePM) implementations on GRAPE-5 and GRAPE-6A systems, special-purpose
hardware accelerators for gravitational many-body simulations. In our PPPM and
TreePM implementations on GRAPE, the computational time is significantly
reduced compared with the conventional implementations without GRAPE,
especially under the strong particle clustering, and almost constant
irrespective of the degree of particle clustering. We carry out the survey of
two simulation parameters, the PM grid spacing and the opening parameter for
the most optimal combination of force accuracy and computational speed. We also
describe the parallelization of these implementations on a PC-GRAPE cluster, in
which each node has one GRAPE board, and present the optimal configuration of
simulation parameters for good parallel scalability.
