An optional hypercube direct N-body solver on the connection machine

Authors:
Jean-Philippe Brunet;Alan Edelman;Jill P. Mesirov
Affiliations:
Thinking Machines Corporation, 245 First Street, Cambridge, MA;42 Avenue Gustave Coriolis, 31057 Toulouse CEDEX, France;Thinking Machines Corporation, 245 First Street, Cambridge, MA
Venue:
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Year:
1990

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Abstract

The direct method for solving N-body problems maps perfectly onto hypercube architectures. Unlike other hypercube implementations, we have implemented a direct N-body solver on the Connection Machine CM-2 which makes optimum use of the full bandwidth of the hypercube. When N ≫ P, where P is the number of floating-point processors, the communication time of the algorithm is negligible, and the execution time is that of the arithmetic time giving a P-fold speed-up for real problems. To obtain this performance, we use “rotated and translated Gray codes” which result in time-wise edge disjoint Hamiltonian paths on the hypercube. We further propose that this communication pattern has unexplored potential for other types of algorithms. Timings are presented for a collection of interacting point vortices in two dimensions. The computation of the velocities of 14,000 vortices in 32-bit precision takes 2 seconds on a 16K CM-2.