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The reproducibility of experiments is one of the main principles of the scientific method. However, numerical N-body experiments, especially those of planetary systems, are currently not reproducible. In the most optimistic scenario, they…
We present a novel $N$-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach…
We introduce FastPM, a highly-scalable approximated particle mesh N-body solver, which implements the particle mesh (PM) scheme enforcing correct linear displacement (1LPT) evolution via modified kick and drift factors. Employing a…
In cosmological $N$-body simulations, the representation of dark matter as discrete "macroparticles" suppresses the growth of structure, such that simulations no longer reproduce linear theory on small scales near $k_{\rm Nyquist}$. Marcos…
Direct gravitational simulations of n-body systems have a time complexity O(n^2), which gets computationally expensive as the number of bodies increases. Distributing this workload to multiple cores significantly speeds up the computation…
We describe a new implementation of a parallel N-body tree code. The code is load-balanced using the method of orthogonal recursive bisection to subdivide the N-body system into independent rectangular volumes each of which is mapped to a…
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…
Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…
In this contribution a broad overview of the methodologies of cosmological N-body simulations and a short introduction explaining the general idea behind such simulations is presented. After explaining how to set up the initial conditions…
Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range…
Approximate N-body methods, such as FastPM and COLA, have been successful in modelling halo and galaxy clustering statistics, but their low resolution on small scales is a limitation for applications that require high precision. Full N-body…
Direct $N$-body simulations of star clusters are accurate but expensive, largely due to the numerous $\mathcal{O} (N^2)$ pairwise force calculations. To solve the post-million-body problem, it will be necessary to use approximate force…
The integration of the equations of motion of N interacting particles, represents a classical problem in many branches of physics and chemistry. The direct N-body problem is at the heart of simulations studying Coulomb Crystals. We present…
We report on the performance of our cold-dark matter cosmological N-body simulation which was carried out concurrently using supercomputers across the globe. We ran simulations on 60 to 750 cores distributed over a variety of supercomputers…
Constraining neutrino mass remains an elusive challenge in modern physics. Precision measurements are expected from several upcoming cosmological probes of large-scale structure. Achieving this goal relies on an equal level of precision…
We describe the TreePM method for carrying out large N-Body simulations to study formation and evolution of the large scale structure in the Universe. This method is a combination of Barnes and Hut tree code and Particle-Mesh code. It…
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…
In this article, we apply a new methodology for precision tuning to the N-body problem. Our technique, implemented in a tool named POP, makes it possible to optimize the numerical data types of a program performing floating-point…
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 the public data release of the AbacusSummit cosmological $N$-body simulation suite, produced with the $\texttt{Abacus}$ $N$-body code on the Summit supercomputer of the Oak Ridge Leadership Computing Facility. $\texttt{Abacus}$…