  A method of adapting smoothed particle hydrodynamics (SPH) with periodic
boundary conditions for use with the special purpose device GRAPE is presented.
GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body
system by direct summation on a specially designed chip and in addition returns
the neighbour list for each particle. Due to its design, GRAPE cannot treat
periodic particle distributions directly. This limitation of GRAPESPH can be
overcome by computing a correction force for each particle due to periodicity
(Ewald correction) on the host computer using a PM-like method.
  This scheme is applied to study the fragmentation process in giant molecular
clouds. Assuming a pure isothermal model, we follow the dynamical evolution in
the interior of a molecular cloud starting from an Gaussian initial density
distribution to the formation of selfgravitating clumps until most of the gas
is consumed in these dense cores. Despite its simplicity, this model can
reproduce some fundamental properties of observed molecular clouds, like a
clump mass distribution of the form $dN/dm \propto m^n$, with $n ~ -1.5$.
