  We investigate the performance gains from hyper-systolic implementations of
n^2-loop problems on the massively parallel computer Quadrics, exploiting its
3-dimensional interprocessor connectivity. For illustration we study the
communication aspects of an exact molecular dynamics simulation of n particles
with Coulomb (or gravitational) interactions. We compare the interprocessor
communication costs of the standard-systolic and the hyper-systolic approaches
for various granularities. We predict gain factors as large as 3 on the Q4 and
8 on the QH4 and measure actual performances on these machine configurations.
We conclude that it appears feasable to investigate the thermodynamics of a
full gravitating n-body problem with O(10000) particles using the new method on
a QH4 system.
