GRAPE-6: Massively-Parallel Special-Purpose Computer for Astrophysical Particle Simulations

Makino, Junichiro; Fukushige, Toshiyuki; Koga, M.; Namura, Ken

doi:10.1093/pasj/55.6.1163

Cited by 184 publications

(186 citation statements)

References 31 publications

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“…Each node of the FIRST cluster is equipped with Blade-GRAPE, a special purpose computer for N -body simulations (Sugimoto et al, 1990;Makino et al, 2003;Makino, 2008).…”

Section: N -Body Simulationmentioning

confidence: 99%

Unexpected formation modes of the first hard binary in core collapse

2012

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The conventional wisdom for the formation of the first hard binary in core collapse is that three-body interactions of single stars form many soft binaries, most of which are quickly destroyed, but eventually one of them survives. We report on direct N-body simulations to test these ideas, for the first time. We find that both assumptions are often incorrect: 1) quite a few three-body interactions produce a hard binary from scratch; 2) and in many cases there are more than three bodies directly and simultaneously involved in the production of the first binary. The main reason for the discrepancies is that the core of a star cluster, at the first deep collapse, contains typically only five or so stars. Therefore, the homogeneous background assumption, which still would be reasonable for, say, 25 stars, utterly breaks down. There have been some speculations in this direction, but we demonstrate this result here explicitly, for the first time.

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“…Each node of the FIRST cluster is equipped with Blade-GRAPE, a special purpose computer for N -body simulations (Sugimoto et al, 1990;Makino et al, 2003;Makino, 2008).…”

Section: N -Body Simulationmentioning

confidence: 99%

Unexpected formation modes of the first hard binary in core collapse

2012

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“…Another milestone in the history of N-body simulations was the introduction of special purpose hardware, responsible only for the calculation A&A 522, A70 (2010) of the gravitational forces. The GRAPE series of computers (Makino et al 1997(Makino et al , 2003a were designed to perform only this type of calculation. The next step was GRAPE-DR 3 (Makino 2008), which is a more general purpose hardware specialized for N-body codes which operates faster than a normal CPU.…”

Section: Introductionmentioning

confidence: 99%

MYRIAD: a newN-body code for simulations of star clusters

Konstantinidis

Kokkotas

2010

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Aims. We present a new C++ code for collisional N-body simulations of star clusters. Methods. The code uses the Hermite fourth-order scheme with block time steps, to advance the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, and binary or multiple subsystems that form either dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions, and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware such as the graphics processing units (GPUs).Results. Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t 17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 10 −3 . Comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t 0.17 ± 0.05 half-mass relaxation times, which is slightly earlier than expected from previous work. Finally, the code accuracy becomes comparable to and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is because of the high accuracy of the method that is used for close binary and multiple subsystems. Conclusions. The code can be used for evolving star clusters containing equal-mass stars or star clusters with an initial mass function (IMF) containing an intermediate mass black hole (IMBH) at the center and/or a fraction of primordial binaries, which are systems of particular astrophysical interest.

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“…Researchers in Japan, under the auspices of the Grape project, have also sought to develop special hardware, similar to the GPU, for performing N body calculations (see e.g., [17,15]). However, the substantial investments required to create special purpose hardware have meant that the progress in new generations has been slow (about 7 years since the previous Grape version was introduced).…”

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confidence: 99%

Fast multipole methods on graphics processors

Gumerov

Duraiswami

2008

Journal of Computational Physics

157

131

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The Fast Multipole Method allows the rapid evaluation of sums of radial basis functions centered at points distributed inside a computational domain at a large number of evaluation points to a specified accuracy . The method scales as O (N ) in both time and memory compared to the direct method with complexity O(N 2 ), which allows the solution of larger problems with given resources. Graphical processing units (GPU) are now increasingly viewed as data parallel compute coprocessors that can provide significant computational performance at low price. We describe acceleration of the FMM using the data parallel GPU architecture.The FMM has a complex hierarchical (adaptive) structure, which is not easily implemented on dataparallel processors. We described strategies for parallelization of all components of the FMM, develop a model to explain the performance of the algorithm on the GPU architecture; and determined optimal settings for the FMM on the GPU, which are different from those on usual CPUs. Some innovations in the FMM algorithm, including the use of modified stencils, real polynomial basis functions for the Laplace kernel, and decompositions of the translation operators, are also described.We obtained accelerations of the Laplace kernel FMM on a single NVIDIA GeForce 8800 GTX GPU in the range of 30-60 compared to a serial CPU FMM implementation. For a problem with a million sources, the summations involved are performed in approximately one second. This performance is equivalent to solving of the same problem at a 43 Teraflop rate if we use straightforward summation.

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GRAPE-6: Massively-Parallel Special-Purpose Computer for Astrophysical Particle Simulations

Cited by 184 publications

References 31 publications

Unexpected formation modes of the first hard binary in core collapse

Unexpected formation modes of the first hard binary in core collapse

MYRIAD: a newN-body code for simulations of star clusters

Fast multipole methods on graphics processors

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