Masaki Iwasawa

Evolution of Massive Black Hole Triples. I. Equal-Mass Binary-Single Systems

We present the results of N-body simulations of dynamical evolution of triple massive black hole (BH) systems in galactic nuclei. We found that in most cases two of the three BHs merge through gravitational wave (GW) radiation in a timescale much shorter than the Hubble time before ejecting one BH through a slingshot. In order for a binary BH to merge before ejecting the third one, it has to become highly eccentric, since the GW timescale would be much longer than the Hubble time unless the eccentricity is very high. We found that two mechanisms drive the increase of the eccentricity of the binary. One is the strong binary-single BH interaction, which results in the thermalization of the eccentricity. The second is the Kozai mechanism, which drives the cyclic change of the inclination and eccentricity of the inner binary of a stable hierarchical triple system. Our result implies that many supermassive BHs are binaries.

BRIDGE: A Direct-Tree Hybrid N -Body Algorithm for Fully Self-Consistent Simulations of Star Clusters and Their Parent Galaxies

We developed a new direct-tree hybrid N -body algorithm for fully self-consistent N -body simulations of star clusters in their parent galaxies. In such simulations, star clusters need high accuracy, while galaxies need a fast scheme because of the large number of particles required to model it. In our new algorithm, the internal motion of the star cluster is calculated accurately using the direct Hermite scheme with individual timesteps, and all other motions are calculated using the tree code with a second-order leapfrog integrator. The direct and tree schemes are combined using an extension of the mixed variable symplectic (MVS) scheme. Thus, the Hamiltonian corresponding to everything other than the internal motion of the star cluster is integrated with the leapfrog, which is symplectic. Using this algorithm, we performed fully self-consistent N -body simulations of star clusters in their parent galaxy. The internal and orbital evolutions of the star cluster agreed well with those obtained using the direct scheme. We also performed fully self-consistent N -body simulation for large-N models (N = 2 � 10 6 ). In this case, the calculation speed was seven-times faster than what would be if the direct scheme was used.

Automatic generation of efficient codes from mathematical descriptions of stencil computation

Programming in HPC is a tedious work. Therefore functional programming languages that generate HPC programs have been proposed. However, they are not widely used by application scientists, because of learning barrier, and lack of demonstrated application performance. We have designed Formura which adopts application-friendly features such as typed rational array indices. Formura users can describe mathematical concepts such as operation over derivative operators using functional programming. Formura allows intuitive expression over array elements while ensuring the program is a stencil computation, so that state-of-the-art stencil optimization techniques such as temporal blocking is always applied to Formura-generated program. We demonstrate the usefulness of Formura by implementing a preliminary below-ground biology simulation. Optimized C-code are generated from 672 bytes of Formura program. The simulation was executed on the full nodes of the K computer, with 1.184 Pflops, 11.62% floating-point-instruction efficiency, and 31.26% memory throughput efficiency.

FDPS: a novel framework for developing high-performance particle simulation codes for distributed-memory systems

We have developed FDPS (Framework for Developing Particle Simulator), which enables researchers and programmers to develop high-performance particle simulation codes easily. The basic idea of FDPS is to separate the program code for complex parallelization including domain decomposition, redistribution of particles, and exchange of particle information for interaction calculation between nodes, from actual interaction calculation and orbital integration. FDPS provides the former part and the users write the latter. Thus, a user can implement, for example, a high-performance N- body code, only in 120 lines. In this paper, we present the structure and implementation of FDPS, and describe its performance on two sample applications: gravitational N-body simulation and Smoothed Particle Hydrodynamics simulation. Both codes show very good parallel efficiency and scalability on the K computer. FDPS lets the researchers concentrate on the implementation of physics and mathematical schemes, without wasting their time on the development and performance tuning of their codes.

6th and 8th Order Hermite Integrator Using Snap and Crackle

We present sixth- and eighth-order Hermite integrators for astrophysical N -body simulations, which use the derivatives of accelerations up to second order ( snap ) and third order ( 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 be implemented. 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.

Global Simulation of Planetary Rings on Sunway TaihuLight

In this paper, we report the implementation and measured performance of a global simulation of planetary rings on Sunway TaihuLight. The basic algorithm is the Barnes-Hut tree, but we have made a number of changes to achieve good performance for extremely large simulations on machines with an extremely large number of cores. The measured performance is around 35% of the theoretical peak. The main limitation comes from the performance of the interaction calculation kernel itself, which is currently around 50%.

PENTACLE: Parallelized particle–particle particle-tree code for planet formation

We have newly developed a Parallelized Particle-Particle Particle-tree code for Planet formation, PENTACLE, which is a parallelized hybrid

Simulations of below-ground dynamics of fungi: 1.184 pflops attained by automated generation and autotuning of temporal blocking codes

N

EVOLUTION OF STAR CLUSTERS NEAR THE GALACTIC CENTER : FULLY SELF-CONSISTENT N-BODY SIMULATIONS

-body integrator executed on a CPU-based (super)computer. PENTACLE uses a 4th-order Hermite algorithm to calculate gravitational interactions between particles within a cutoff radius and a Barnes-Hut tree method for gravity from particles beyond. It also implements an open-source library designed for full automatic parallelization of particle simulations, FDPS (Framework for Developing Particle Simulator) to parallelize a Barnes-Hut tree algorithm for a memory-distributed supercomputer. These allow us to handle

TROJAN STARS IN THE GALACTIC CENTER

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