GOTHIC: Gravitational oct-tree code accelerated by hierarchical time step controlling

Abstract

The tree method is a widely implemented algorithm for collisionless $N$-body simulations in astrophysics well suited for GPU(s). Adopting hierarchical time stepping can accelerate $N$-body simulations; however, it is infrequently implemented and its potential remains untested in GPU implementations. We have developed a Gravitational Oct-Tree code accelerated by HIerarchical time step Controlling named \texttt{GOTHIC}, which adopts both the tree method and the hierarchical time step. The code adopts some adaptive optimizations by monitoring the execution time of each function on-the-fly and minimizes the time-to-solution by balancing the measured time of multiple functions. Results of performance measurements with realistic particle distribution performed on NVIDIA Tesla M2090, K20X, and GeForce GTX TITAN X, which are representative GPUs of the Fermi, Kepler, and Maxwell generation of GPUs, show that the hierarchical time step achieves a speedup by a factor of around 3--5 times compared to the shared time step. The measured elapsed time per step of \texttt{GOTHIC} is 0.30~s or 0.44~s on GTX TITAN X when the particle distribution represents the Andromeda galaxy or the NFW sphere, respectively, with $2^{24}=$~16,777,216 particles. The averaged performance of the code corresponds to 10--30\% of the theoretical single precision peak performance of the GPU.

22 pages, 10 figures, 4 tables, accepted for publication in New Astronomy

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Cited by in corpus (13)

• Cusp-to-core transition in low-mass dwarf galaxies induced by dynamical heating of cold dark matter by primordial black holes
• MAGI: many-component galaxy initialiser
• Fornax globular cluster distributions: implications for the cusp-core problem
• Embedding globular clusters in dark matter minihalos solves the cusp-core and timing problems in the Fornax dwarf galaxy
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• Properties of globular clusters formed in dark matter mini-halos
• Absence of obvious tidal tails around the globular cluster NGC 6397
• The nature of the progenitor of the M31 North-western stream: globular clusters as milestones of its orbit
• Flattening of dark matter cusps during mergers: model of M31
• Direct N-body simulations of NGC 6397 and its tidal tails
• The origin of the black hole offset in M31
• MatRox: Modular approach for improving data locality in Hierarchical (Mat)rix App(Rox)imation
• Gravitational octree code performance evaluation on Volta GPU