相关论文: Fast Multipole Methods for $N$-body Simulations of…

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…

We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…

We present the novel algorithmically regularised integration method MSTAR for high accuracy ($|\Delta E/E| \gtrsim 10^{-14}$) integrations of N-body systems using minimum spanning tree coordinates. The two-fold parallelisation of the…

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 present tests of comparison between our versions of the Fast Multipole Algorithm (FMA) and ``classic'' tree-code to evaluate gravitational forces in particle systems. We have optimized the Greengard's original version of FMA allowing for…

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 summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-called Multi-particle collision…

Context. Simulating stellar dynamics in a molecular cloud environment is numerically challenging due to the strong coupling between young stars and their surrounding gas, and the large range of length and time scales. Aims. This paper is…

We present a new scheme to compensate for the small-scales approximations resulting from Particle-Mesh (PM) schemes for cosmological N-body simulations. This kind of simulations are fast and low computational cost realizations of the large…

Due to the variety and importance of applications of treecodes and FMM, the combination of algorithmic acceleration with hardware acceleration can have tremendous impact. Alas, programming these algorithms efficiently is no piece of cake.…

One of the computational challenges of cluster formation simulations is resolving individual stars and simulating massive clusters with masses of more than $10^4 M_{\odot}$ without gravitational softening. Combining direct $N$-body code…

This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a…

We report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up…

We have developed a parallel Particle-Particle, Particle-Mesh (P^3M) simulation code for the T3E well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in cosmological contexts. The…

Particle-in-cell methods with stochastic collision models are commonly used to simulate collisional plasma dynamics, with applications ranging from hypersonic flight to semiconductor manufacturing. Code verification of such methods is…

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.…

The gravitational $N$-body problem is a nearly universal problem in astrophysics which, despite its deceptive simplicity, still presents a significant computational challenge. For collisional systems such as dense star clusters, the need to…

Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…

The fast multipole method (FMM) performs fast approximate kernel summation to a specified tolerance $\epsilon$ by using a hierarchical division of the domain, which groups source and receiver points into regions that satisfy local…

We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the…