Distributed N-body Simulation on the Grid Using Dedicated Hardware

We present performance measurements of direct gravitational N -body simulation on the grid, with and without specialized (GRAPE-6) hardware. Our inter-continental virtual organization consists of three sites, one in Tokyo, one in Philadelphia and one in Amsterdam. We run simulations with up to 196608 particles for a variety of topologies. In many cases, high performance simulations over the entire planet are dominated by network bandwidth rather than latency. With this global grid of GRAPEs our calculation time remains dominated by communication over the entire range of N, which was limited due to the use of three sites. Increasing the number of particles will result in a more efficient execution. Based on these timings we construct and calibrate a model to predict the performance of our simulation on any grid infrastructure with or without GRAPE. We apply this model to predict the simulation performance on the Netherlands DAS-3 wide area computer. Equipping the DAS-3 with GRAPE-6Af hardware would achieve break-even between calculation and communication at a few million particles, resulting in a compute time of just over ten hours for 1 N -body time unit. Key words: high-performance computing, grid, N-body simulation, performance modellingComment: (in press) New Astronomy, 24 pages, 5 figure

Systolic and Hyper-Systolic Algorithms for the Gravitational N-Body Problem, with an Application to Brownian Motion

A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic algorithms minimize memory requirements by distributing the particles between processors. We show that the performance of systolic routines can be greatly enhanced by the use of non-blocking communication, which allows particle coordinates to be communicated at the same time that force calculations are being carried out. Hyper-systolic algorithms reduce the communication complexity at the expense of increased memory demands. As an example of an application requiring large N, we use the systolic algorithm to carry out direct-summation simulations using 10^6 particles of the Brownian motion of the supermassive black hole at the center of the Milky Way galaxy. We predict a 3D random velocity of 0.4 km/s for the black hole.Comment: 33 pages, 10 postscript figure