Dual tree traversal on integrated GPUs for astrophysical <i>N</i>-body simulations

Fortin, Pierre; Touche, Maxime

doi:10.1177/1094342019840806

Cited by 7 publications

(4 citation statements)

References 27 publications

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“…For this purpose state-of-the-art hardware infrastructure (like GPUs) is required to carry out parallel processing. Another approach is to exploit distributed or cloud computing in order to achieve parallelism [19,20].…”

Section: Related Workmentioning

confidence: 99%

N-Body Simulation Inspired by Metaheuristics Optimization

Ismail¹,

Waqas²,

Sadiq³

2022

Computer Systems Science and Engineering

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Section: Related Workmentioning

confidence: 99%

N-Body Simulation Inspired by Metaheuristics Optimization

Ismail¹,

Waqas²,

Sadiq³

2022

Computer Systems Science and Engineering

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“…However, these codes still scale like O(N 2 ) and there is great interest in implementing the sub-quadratic scaling tree-based methods on GPUs, although this is challenging due to the complexity of these methods in comparison with direct summation. In this direction there have been several GPU implementations of the TC and FMM [39,40,41,42,36,43,44,45,46,47], but we know of only a few GPU implementations of the DTT [48,49].…”

Section: Gpu Implementationsmentioning

confidence: 99%

A GPU-Accelerated Fast Summation Method Based on Barycentric Lagrange Interpolation and Dual Tree Traversal

Wilson,

Vaughn,

Krasny

2020

Preprint

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We present the barycentric Lagrange dual tree traversal (BLDTT) fast summation method for particle interactions. The scheme replaces well-separated particle-particle interactions by adaptively chosen particlecluster, cluster-particle, and cluster-cluster approximations given by barycentric Lagrange interpolation at proxy particles on a Chebyshev grid in each cluster. The BLDTT is kernel-independent and the approximations can be efficiently mapped onto GPUs, where target particles provide an outer level of parallelism and source particles provide an inner level of parallelism. We present an OpenACC GPU implementation of the BLDTT with MPI remote memory access for distributed memory parallelization. The performance of the GPU-accelerated BLDTT is demonstrated for calculations with different problem sizes, particle distributions, geometric domains, and interaction kernels, as well as for unequal target and source particles.Comparison with our earlier particle-cluster barycentric Lagrange treecode (BLTC) demonstrates the superior performance of the BLDTT. In particular, on a single GPU for problem sizes ranging from N =1E5 to 1E8, the BLTC has O(N log N ) scaling, while the BLDTT has O(N ) scaling. In addition, MPI strong scaling results are presented for the BLTC and BLDTT using N =64E6 particles on up to 32 GPUs.

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“…We use OpenMP to speed up the dual-tree walk using task model with atomic clause used to update of multipole moments (Fortin & Touche 2019). The near field contribution is handled by a direct summation kernel, which is vectorized using AVX intrinsics as in Zhu (2020).…”

Section: )mentioning

confidence: 99%

Fast Multipole Methods for $N$-body Simulations of Collisional Star Systems

Mukherjee,

Zhu,

Trac

et al. 2020

Preprint

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Direct N -body simulations of star clusters are accurate but expensive largely due to the numerous O(N 2 ) pairwise force calculations. State-of-the-art N -body codes can take nearly 6 months of computer wall time to simulate a single N = 10 6 globular cluster over a single relaxation time. To solve the post-million body problem, it will be necessary to use approximated force solvers, such as tree codes. In this work, we adapt a tree-based, optimized Fast Multipole Method (FMM) to the collisional N -body problem. The use of a rotation-accelerated translation operator and an error-controlled cell opening criteria leads to a code which can be tuned to arbitrary accuracy. We demonstrate that our code, Taichi, can be as accurate as direct summation when N > 10 4 . This opens up the possibility of performing large-N , star-by-star simulations of massive stellar clusters, and would permit large parameter space studies that would require years with the current generation of direct summation codes. Using a series of tests and idealized models, we show that Taichi can accurately model collisional effects, such as dynamical friction and the core-collapse time of idealized clusters, producing results in strong agreement with benchmarks from other collisional codes such as NBODY6++GPU or PeTar. Parallelized using OpenMP and AVX, Taichi is nearly 70 times faster on a 28-core single machine than its direct integration counterpart. With future improvements to the handling of close encounters and binary evolution, we clearly demonstrate the potential of an optimized FMM for the modelling of collisional stellar systems, opening the door to accurate simulations of massive globular clusters, super star clusters, and even galactic nuclei.

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Dual tree traversal on integrated GPUs for astrophysical N-body simulations

Cited by 7 publications

References 27 publications

N-Body Simulation Inspired by Metaheuristics Optimization

N-Body Simulation Inspired by Metaheuristics Optimization

A GPU-Accelerated Fast Summation Method Based on Barycentric Lagrange Interpolation and Dual Tree Traversal

Fast Multipole Methods for $N$-body Simulations of Collisional Star Systems

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