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

## TL;DR

This paper explores hyper-systolic algorithms for n^2-loop problems on the Quadrics parallel computer, demonstrating significant communication efficiency improvements for molecular dynamics simulations with Coulomb or gravitational interactions.

## Contribution

It introduces hyper-systolic methods tailored for 3D interprocessor connectivity, showing potential for large-scale n-body simulations on Quadrics systems.

## Key findings

- Achieved up to 3x speedup on Q4 and 8x on QH4 systems.
- Validated the feasibility of simulating 10,000-body gravitating systems.
- Compared communication costs of standard and hyper-systolic approaches.

## Abstract

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.