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We present an implementation of the hierarchical tree algorithm on the individual timestep algorithm (the Hermite scheme) for collisional $N$-body simulations, running on GRAPE-9 system, a special-purpose hardware accelerator for…
In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a…
We present a novel method for efficient direct integration of gravitational N-body systems with a large variation in characteristic time scales. The method is based on a recursive and adaptive partitioning of the system based on the…
We describe a new method (HOP) for identifying groups of particles in N-body simulations. Having assigned to every particle an estimate of its local density, we associate each particle with the densest of the N_hop particles nearest to it.…
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…
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…
Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…
Astrophysical research in recent decades has made significant progress thanks to the availability of various $N$-body simulation techniques. With the rapid development of high-performance computing technologies, modern simulations have been…
We derive a new criterion for estimating characteristic dynamical timescales in N-body simulations. The criterion uses the second, third, and fourth derivatives of particle positions: acceleration, jerk, and snap. It can be used for…
We present performance measurements of direct gravitational N -body simulation on the grid, with and without specialized (GRAPE-6) hardware. Our inter-continental virtual organization consists of three sites, one in Tokyo, one in…
Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like…
We present an algorithm named "Chamomile Scheme". The scheme is fully optimized for calculating gravitational interactions on the latest programmable Graphics Processing Unit (GPU), NVIDIA GeForce8800GTX, which has (a) small but fast shared…
We present a new implementation of the numerical integration of the classical, gravitational, N-body problem based on a high order Hermite's integration scheme with block time steps, with a direct evaluation of the particle-particle forces.…
We introduce a particle-based simulation method for granular material in interactive frame rates. We divide the simulation into two decoupled steps. In the first step, a relatively small number of particles is accurately simulated with a…
We report on resent N-body simulations of galaxy formation performed on the GRAPE-4 (GRAvity PipE) system, a special-purpose computer for astrophysical N-body simulations. We review the astrophysical motivation, the algorithm, the actual…
We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping,…
We present the results of gravitational direct $N$-body simulations using the commercial graphics processing units (GPU) NVIDIA Quadro FX1400 and GeForce 8800GTX, and compare the results with GRAPE-6Af special purpose hardware. The force…
Quantum master equations are common tools to describe the dynamics of many-body systems open to an environment. Due to the interaction with the latter, even for the case of non-interacting electrons, the computational cost to solve these…
We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than…
We present the multi-GPU realization of the StePS (Stereographically Projected Cosmological Simulations) algorithm with MPI-OpenMP-CUDA hybrid parallelization and nearly ideal scale-out to multiple compute nodes. Our new zoom-in…