PERFORMANCE AND ACCURACY OF A GRAPE-3 SYSTEM FOR COLLISIONLESS N-BODYSIMULATIONS

The performance and accuracy of a GRAPE-3 system for collisionless N-b ody simulations is discussed. After an initial description of the hard ware configurations available to us at Marseille, and the usefulness o f on-line analysis, we concentrate on the actual performance and accur acy of direct summation and of tree code software. For the former we d iscuss the sources of round-off errors. The standard Barnes-Hut tree c ode cannot be used as such on a GRAPE-3 system. Instead particles are divided into blocks and the tree traversal is performed for the whole block, instead of for each particle in the block separately. The force s are then calculated by direct summation over the whole interaction l ist. The performance of the tree code depends on the number of particl es in the block, the optimum number depending on the speed of the fron t end and the number of boards. We find that the code scales as O(N) a nd explain this behaviour. The time per step decreases as the toleranc e increases, but the dependence is much weaker than for the standard t ree code. Finally, we find that, contrary to what is expected for the standard version, the speed of our tree code increases with the cluste ring of the configuration. We discuss the effect of the front end and compare the performance of direct summation and of tree code on GRAPE- 3 with that of other software on general purpose computers. The accura cy of both direct summation and the tree code is discussed as a functi on of number of particles and softening. For this we consider the accu racy of the force calculation as well as the energy conservation durin g a simulation. Because of the increased role of the direct summation in the force calculation, our tree code is much more accurate than the standard one. Finally, we follow the evolution of an isolated barred galaxy using different hardware and software in order to assess the re liability and reproducibility of our results. We find excellent agreem ent between the pattern speed of the bar in direct summation simulatio ns run on the high-precision GRAPE-4 machines and that in direct summa tion simulations run on our GRAPE-3 system. The agreement with the tre e code is also very good provided the tolerance values are smaller tha n about 1.0. We conclude that GRAPE-3 systems are well suited for coll isionless simulations and in particular for those of galaxies. This is due to their good accuracy and their high speed, which allows the use of a large number of particles.