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The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N-body system with ~10^6 particles over many relaxation times, remains a major challenge in computational astrophysics.…
Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are…
Accurate direct $N$-body simulations help to obtain detailed information about the dynamical evolution of star clusters. They also enable comparisons with analytical models and Fokker-Planck or Monte-Carlo methods. NBODY6 is a well-known…
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…
$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or…
Special high-accuracy direct force summation N-body algorithms and their relevance for the simulation of the dynamical evolution of star clusters and other gravitating N-body systems in astrophysics are presented, explained and compared…
We present FlowPM, a Particle-Mesh (PM) cosmological N-body code implemented in Mesh-TensorFlow for GPU-accelerated, distributed, and differentiable simulations. We implement and validate the accuracy of a novel multi-grid scheme based on…
Simulations inform all aspects of modern astrophysical research, ranging in scale from 1D and 2D test problems that can run in seconds on an astronomer's laptop all the way to large-scale 3D calculations that run on the largest…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
We describe a new parallel N-body code for cosmological simulations. The code is based on a work- and data sharing scheme, and is implemented within the Cray Research Corporation's CRAFT programming environment. Different data distribution…
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…
Cosmological N-Body simulations have become an essential tool for studying formation of large scale structure. These simulations are computationally challenging even though the available computing power gets better every year. A number of…
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…
We present a novel hierarchical formulation of the fourth-order forward symplectic integrator and its numerical implementation in the GPU-accelerated direct-summation N-body code FROST. The new integrator is especially suitable for…
The gravitational N-body simulation in the Solar system was performed using different parallel approaches with the comparisons in the computational times and speed-up values being carried out under different model sizes and the number of…
Most recent progress in understanding the dynamical evolution of star clusters relies on direct N-body simulations. Owing to the computational demands, and the desire to model more complex and more massive star clusters, hardware…
The German-Russian Astroparticle Data Life Cycle Initiative is an international project launched in 2018. The Initiative aims to develop technologies that provide a unified approach to data management, as well as to demonstrate their…
This paper concentrates on four key tools for performing star cluster simulations developed during the last decade which are sufficient to handle all the relevant dynamical aspects. First we discuss briefly the Hermite integration scheme…
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,…
Astrophysical direct $N$-body methods have been one of the first production algorithms to be implemented using NVIDIA's CUDA architecture. Now, almost seven years later, the GPU is the most used accelerator device in astronomy for…