Related papers: A connected component-based method for efficiently…
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 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.…
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…
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…
A wide variety of outstanding problems in astrophysics involve the motion of a large number of particles ($N\gtrsim 10^{6}$) under the force of gravity. These include the global evolution of globular clusters, tidal disruptions of stars by…
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 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 review the recent optimizations of gravitational $N$-body kernels for running them on graphics processing units (GPUs), on single hosts and massive parallel platforms. For each of the two main $N$-body techniques, direct summation and…
We give a full description of the code NBODY2 for direct integration of the gravitational N-body problem. The method of solution is based on the neighbour scheme of Ahmad & Cohen (1973) which speeds up the force calculation already for…
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…
$N$-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…
We propose an efficient method for active particle selection, working with Hermite Individual Time Steps (HITS) scheme in direct N-body simulation code $\varphi$GRAPE. For a simulation with $N$ particles, this method can reduce the…
We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed…
The time step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time step criteria commonly adopt the minimum pairwise time step, which…
This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the…
The large dynamic range in some astrophysical N-body problems led to the use of adaptive multi-time-steps; however, the search for optimal strategies is still challenging. We numerically quantify the performance of the hierarchical…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…
The method of choice for integrating the equations of motion of the general N-body problem has been to use an individual time step scheme. For the sake of efficiency, block time steps have been the most popular, where all time step sizes…