arXiv subjects

Keigo Nitadori

Publications and source records attributed to Keigo Nitadori.

29 records · Page 2Linked to original sources

arXiv2013

The Cosmogrid Simulation: Statistical Properties of Small Dark Matter Halos

We present the results of the "Cosmogrid" cosmological N-body simulation suites based on the concordance LCDM model. The Cosmogrid simulation was performed in a 30Mpc box with 2048^3 particles. The mass of each particle is 1.28x10^5 Msun, which is sufficient to resolve ultra-faint dwarfs. We found that the halo mass function shows good agreement with the Sheth & Tormen fitting function down to ~10^7 Msun. We have analyzed the spherically averaged density profiles of the three most massive halos which are of galaxy group size and contain at least 170 million particles. The slopes of these density profiles become shallower than -1 at the inner most radius. We also find a clear correlation of halo concentration with mass. The mass dependence of the concentration parameter cannot be expressed by a single power law, however a simple model based on the Press-Schechter theory proposed by Navarro et al. gives reasonable agreement with this dependence. The spin parameter does not show a correlation with the halo mass. The probability distribution functions for both concentration and spin are well fitted by the log-normal distribution for halos with the masses larger than ~10^8 Msun. The subhalo abundance depends on the halo mass. Galaxy-sized halos have 50% more subhalos than ~10^{11} Msun halos have.

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arXiv2012

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

(Abridged) We have developed a numerical software library for collisionless N-body simulations named "Phantom-GRAPE" which highly accelerates force calculations among particles by use of a new SIMD instruction set extension to the x86 architecture, AVX, an enhanced version of SSE. In our library, not only the Newton's forces, but also central forces with an arbitrary shape f(r), which has a finite cutoff radius r_cut (i.e. f(r)=0 at r>r_cut), can be quickly computed. Using an Intel Core i7--2600 processor, we measure the performance of our library for both the forces. In the case of Newton's forces, we achieve 2 x 10^9 interactions per second with 1 processor core, which is 20 times higher than the performance of an implementation without any explicit use of SIMD instructions, and 2 times than that with the SSE instructions. With 4 processor cores, we obtain the performance of 8 x 10^9 interactions per second. In the case of the arbitrarily shaped forces, we can calculate 1 x 10^9 and 4 x 10^9 interactions per second with 1 and 4 processor cores, respectively. The performance with 1 processor core is 6 times and 2 times higher than those of the implementations without any use of SIMD instructions and with the SSE instructions. These performances depend weakly on the number of particles. It is good contrast with the fact that the performance of force calculations accelerated by GPUs depends strongly on the number of particles. Substantially weak dependence of the performance on the number of particles is suitable to collisionless N-body simulations, since these simulations are usually performed with sophisticated N-body solvers such as Tree- and TreePM-methods combined with an individual timestep scheme. Collisionless N-body simulations accelerated with our library have significant advantage over those accelerated by GPUs, especially on massively parallel environments.

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arXiv2012

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 $N$-body simulations. Over the years, the $N^2$ 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 $10^4-2 \times 10^5$ for a dual GPU system attached to a standard PC.

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arXiv2012

Formation and Hardening of Supermassive Black Hole Binaries in Minor Mergers of Disk Galaxies

We model for the first time the complete orbital evolution of a pair of Supermassive Black Holes (SMBHs) in a 1:10 galaxy merger of two disk dominated gas-rich galaxies, from the stage prior to the formation of the binary up to the onset of gravitational wave emission when the binary separation has shrunk to 1 milli parsec. The high-resolution smoothed particle hydrodynamics (SPH) simulations used for the first phase of the evolution include star formation, accretion onto the SMBHs as well as feedback from supernovae explosions and radiative heating from the SMBHs themselves. Using the direct N-body code ϕ-GPU we evolve the system further without including the effect of gas, which has been mostly consumed by star formation in the meantime. We start at the time when the separation between two SMBHs is ~ 700 pc and the two black holes are still embedded in their galaxy cusps. We use 3 million particles to study the formation and evolution of the SMBH binary till it becomes hard. After a hard binary is formed, we reduce (reselect) the particles to 1.15 million and follow the subsequent shrinking of the SMBH binary due to 3-body encounters with the stars. We find approximately constant hardening rates and that the SMBH binary rapidly develops a high eccentricity. Similar hardening rates and eccentricity values are reported in earlier studies of SMBH binary evolution in the merging of dissipation-less spherical galaxy models. The estimated coalescence time is ~ 2.9 Gyr, significantly smaller than a Hubble time. We discuss why this timescale should be regarded as an upper limit. Since 1:10 mergers are among the most common interaction events for galaxies at all cosmic epochs, we argue that several SMBH binaries should be detected with currently planned space-borne gravitational wave interferometers, whose sensitivity will be especially high for SMBHs in the mass range considered here.

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arXiv2012

PSDF: Particle Stream Data Format for N-Body Simulations

We present a data format for the output of general N-body simulations, allowing the presence of individual time steps. By specifying a standard, different N-body integrators and different visualization and analysis programs can all share the simulation data, independent of the type of programs used to produce the data. Our Particle Stream Data Format, PSDF, is specified in YAML, based on the same approach as XML but with a simpler syntax. Together with a specification of PSDF, we provide background and motivation, as well as specific examples in a variety of computer languages. We also offer a web site from which these examples can be retrieved, in order to make it easy to augment existing codes in order to give them the option to produce PSDF output.

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arXiv2011

N-body simulation for self-gravitating collisional systems with a new SIMD instruction set extension to the x86 architecture, Advanced Vector eXtensions

We present a high-performance N-body code for self-gravitating collisional systems accelerated with the aid of a new SIMD instruction set extension of the x86 architecture: Advanced Vector eXtensions (AVX), an enhanced version of the Streaming SIMD Extensions (SSE). With one processor core of Intel Core i7-2600 processor (8 MB cache and 3.40 GHz) based on Sandy Bridge micro-architecture, we implemented a fourth-order Hermite scheme with individual timestep scheme (Makino and Aarseth, 1992), and achieved the performance of 20 giga floating point number operations per second (GFLOPS) for double-precision accuracy, which is two times and five times higher than that of the previously developed code implemented with the SSE instructions (Nitadori et al., 2006b), and that of a code implemented without any explicit use of SIMD instructions with the same processor core, respectively. We have parallelized the code by using so-called NINJA scheme (Nitadori et al., 2006a), and achieved 90 GFLOPS for a system containing more than N = 8192 particles with 8 MPI processes on four cores. We expect to achieve about 10 tera FLOPS (TFLOPS) for a self-gravitating collisional system with N 105 on massively parallel systems with at most 800 cores with Sandy Bridge micro-architecture. This performance will be comparable to that of Graphic Processing Unit (GPU) cluster systems, such as the one with about 200 Tesla C1070 GPUs (Spurzem et al., 2010). This paper offers an alternative to collisional N-body simulations with GRAPEs and GPUs.

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arXiv2010

Astrophysical Weighted Particle Magnetohydrodynamics

This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magneto-rotational instability in accretion disks.

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arXiv2010

Simulating the universe on an intercontinental grid of supercomputers

Understanding the universe is hampered by the elusiveness of its most common constituent, cold dark matter. Almost impossible to observe, dark matter can be studied effectively by means of simulation and there is probably no other research field where simulation has led to so much progress in the last decade. Cosmological N-body simulations are an essential tool for evolving density perturbations in the nonlinear regime. Simulating the formation of large-scale structures in the universe, however, is still a challenge due to the enormous dynamic range in spatial and temporal coordinates, and due to the enormous computer resources required. The dynamic range is generally dealt with by the hybridization of numerical techniques. We deal with the computational requirements by connecting two supercomputers via an optical network and make them operate as a single machine. This is challenging, if only for the fact that the supercomputers of our choice are separated by half the planet, as one is located in Amsterdam and the other is in Tokyo. The co-scheduling of the two computers and the 'gridification' of the code enables us to achieve a 90% efficiency for this distributed intercontinental supercomputer.

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arXiv2008

6th and 8th Order Hermite Integrator for N-body Simulations

We present sixth- and eighth-order Hermite integrators for astrophysical $N$-body simulations, which use the derivatives of accelerations up to second order ({\it snap}) and third order ({\it crackle}). These schemes do not require previous values for the corrector, and require only one previous value to construct the predictor. Thus, they are fairly easy to implemente. The additional cost of the calculation of the higher order derivatives is not very high. Even for the eighth-order scheme, the number of floating-point operations for force calculation is only about two times larger than that for traditional fourth-order Hermite scheme. The sixth order scheme is better than the traditional fourth order scheme for most cases. When the required accuracy is very high, the eighth-order one is the best. These high-order schemes have several practical advantages. For example, they allow a larger number of particles to be integrated in parallel than the fourth-order scheme does, resulting in higher execution efficiency in both general-purpose parallel computers and GRAPE systems.

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arXiv2006

High-Performance Small-Scale Simulation of Star Clusters Evolution on Cray XD1

In this paper, we describe the performance of an $N$-body simulation of star cluster with 64k stars on a Cray XD1 system with 400 dual-core Opteron processors. A number of astrophysical $N$-body simulations were reported in SCxy conferences. All previous entries for Gordon-Bell prizes used at least 700k particles. The reason for this preference of large numbers of particles is the parallel efficiency. It is very difficult to achieve high performance on large parallel machines, if the number of particles is small. However, for many scientifically important problems the calculation cost scales as $O(N^{3.3})$, and it is very important to use large machines for relatively small number of particles. We achieved 2.03 Tflops, or 57.7% of the theoretical peak performance, using a direct $O(N^2)$ calculation with the individual timestep algorithm, on 64k particles. The best efficiency previously reported on similar calculation with 64K or smaller number of particles is 12% (9 Gflops) on Cray T3E-600 with 128 processors. Our implementation is based on highly scalable two-dimensional parallelization scheme, and low-latency communication network of Cray XD1 turned out to be essential to achieve this level of performance.

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arXiv2005

Performance Tuning of N-Body Codes on Modern Microprocessors: I. Direct Integration with a Hermite Scheme on x86_64 Architecture

The main performance bottleneck of gravitational N-body codes is the force calculation between two particles. We have succeeded in speeding up this pair-wise force calculation by factors between two and ten, depending on the code and the processor on which the code is run. These speedups were obtained by writing highly fine-tuned code for x86_64 microprocessors. Any existing N-body code, running on these chips, can easily incorporate our assembly code programs. In the current paper, we present an outline of our overall approach, which we illustrate with one specific example: the use of a Hermite scheme for a direct N^2 type integration on a single 2.0 GHz Athlon 64 processor, for which we obtain an effective performance of 4.05 Gflops, for double precision accuracy. In subsequent papers, we will discuss other variations, including the combinations of N log N codes, single precision implementations, and performance on other microprocessors.

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