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Hyper-Systolic Processing on APE100/Quadrics: N^2-Loop Computations

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.