Keigo Nitadori

Accelerating nbody6 with graphics processing units

We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct

42 TFlops hierarchical N -body simulations on GPUs with applications in both astrophysics and turbulence

N

4.45 Pflops astrophysical N -body simulation on K computer: the gravitational trillion-body problem

-body simulations. Over the years, the

Sixth- and eighth-order Hermite integrator for N-body simulations

N^2

190 TFlops Astrophysical N-body Simulation on a Cluster of GPUs

nature of the direct force calculation has proved a barrier for extending the particle number. Following an early introduction of force polynomials and individual time-steps, the calculation cost was first reduced by the introduction of a neighbour scheme. After a decade of GRAPE computers which speeded up the force calculation further, we are now in the era of GPUs where relatively small hardware systems are highly cost-effective. A significant gain in efficiency is achieved by employing the GPU to obtain the so-called regular force which typically involves some 99 percent of the particles, while the remaining local forces are evaluated on the host. However, the latter operation is performed up to 20 times more frequently and may still account for a significant cost. This effort is reduced by parallel SSE/AVX procedures where each interaction term is calculated using mainly single precision. We also discuss further strategies connected with coordinate and velocity prediction required by the integration scheme. This leaves hard binaries and multiple close encounters which are treated by several regularization methods. The present nbody6-GPU code is well balanced for simulations in the particle range

Astrophysical weighted particle magnetohydrodynamics

10^4-2 \times 10^5

Phantom-GRAPE: Numerical software library to accelerate collisionless N-body simulation with SIMD instruction set on x86 architecture

for a dual GPU system attached to a standard PC.

nbody6++gpu: ready for the gravitational million-body problem

As an entry for the 2009 Gordon Bell price/performance prize, we present the results of two different hierarchical N-body simulations on a cluster of 256 graphics processing units (GPUs). Unlike many previous N-body simulations on GPUs that scale as O(N2), the present method calculates the O(N log N) treecode and O(N) fast multipole method (FMM) on the GPUs with unprecedented efficiency. We demonstrate the performance of our method by choosing one standard application -a gravitational N-body simulation- and one non-standard application -simulation of turbulence using vortex particles. The gravitational simulation using the treecode with 1,608,044,129 particles showed a sustained performance of 42.15 TFlops. The vortex particle simulation of homogeneous isotropic turbulence using the periodic FMM with 16,777,216 particles showed a sustained performance of 20.2 TFlops. The overall cost of the hardware was 228,912 dollars. The maximum corrected performance is 28.1TFlops for the gravitational simulation, which results in a cost performance of 124 MFlops/

24.77 Pflops on a gravitational tree-code to simulate the Milky Way Galaxy with 18600 GPUs

. This correction is performed by counting the Flops based on the most efficient CPU algorithm. Any extra Flops that arise from the GPU implementation and parameter differences are not included in the 124 MFlops/

Simulating the Universe on an Intercontinental Grid

.