Speeding up the GENGA N -body integrator on consumer-grade graphics cards

Abstract

Context. Graphics processing unit (GPU) computing has become popular due to the enormous calculation potential that can be harvested from a single card. The N -body integrator Gravitational ENcounters with GPU Acceleration (GENGA) is built to harvest the computing power from such cards, but it suffers a severe performance penalty on consumer-grade Nvidia GPUs due to their artificially truncated double precision performance. Aims. We aim to speed up GENGA on consumer-grade cards by harvesting their high single-precision performance. Methods. We modified GENGA to have the option to compute the mutual long-distance forces between bodies in single precision and tested this with five experiments. First, we ran a high number of simulations with similar initial conditions of on average 6600 fully self-gravitating planetesimals in both single and double precision to establish whether the outcomes were statistically different. These simulations were run on Tesla K20 cards. We supplemented this test with simulations that (i) began with a mixture of planetesimals and planetary embryos, (ii) planetesimal-driven giant planet migration, and (iii) terrestrial planet formation with a dissipating gas disc. All of these simulations served to determine the accuracy of energy and angular momentum conservation under various scenarios with single and double precision forces. Second, we ran the same simulation beginning with 40 000 self-gravitating planetesimals using both single and double precision forces on a variety of consumer-grade and Tesla GPUs to measure the performance boost of computing the long-range forces in single precision. Results. We find that there are no statistical differences when simulations are run with the gravitational forces in single or double precision that can be attributed to the force prescription rather than stochastic effects. The accumulations in uncertainty in energy are almost identical when running with single or double precision long-range forces. However, the uncertainty in the angular momentum using single rather than double precision long-range forces is about two orders of magnitude greater, but still very low. Running the simulations in single precision on consumer-grade cards decreases running time by a factor of three and becomes within a factor of three of a Tesla A100 GPU. Additional tuning speeds up the simulation by a factor of two across all types of cards. Conclusions. The option to compute the long-range forces in single precision in GENGA when using consumer-grade GPUs dramatically improves performance at a little penalty to accuracy. There is an additional environmental benefit because it reduces energy usage.