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We present parallel algorithms for constructing and traversing sparse octrees on graphics processing units (GPUs). The algorithms are based on parallel-scan and sort methods. To test the performance and feasibility, we implemented them in…

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…

The numerical simulations of massive collisional stellar systems, such as globular clusters (GCs), are very time-consuming. Until now, only a few realistic million-body simulations of GCs with a small fraction of binaries (5%) have been…

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…

Restricted three-body codes have a proven ability to recreate much of the disturbed morphology of actual interacting galaxies. As more sophisticated n-body models were developed and computer speed increased, restricted three-body codes fell…

We introduce our new binary tree code for neighbour search and gravitational force calculations in an N-particle system. The tree is built in a "top-down" fashion by "recursive coordinate bisection" where on each tree level we split the…

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…

We present $\texttt{Abacus}$, a fast and accurate cosmological $N$-body code based on a new method for calculating the gravitational potential from a static multipole mesh. The method analytically separates the near- and far-field forces,…

Federated learning is proposed by Google to safeguard data privacy through training models locally on users' devices. However, with deep learning models growing in size to achieve better results, it becomes increasingly difficult to…

We describe the two-dimensional TreePM method in this paper. The 2d TreePM code is an accurate and efficient technique to carry out large two-dimensional N-body simulations in cosmology. This hybrid code combines the 2d Barnes and Hut Tree…

We propose a hybrid tree algorithm for reducing calculation and communication cost of collision-less N-body simulations. The concept of our algorithm is that we split interaction force into two parts: hard-force from neighbor particles and…

We have performed fully self-consistent $N$-body simulations of star clusters near the Galactic center (GC). Such simulations have not been performed because it is difficult to perform fast and accurate simulations of such systems using…

Training and transferring learning-based policies for quadrotors from simulation to reality remains challenging due to inefficient visual rendering, physical modeling inaccuracies, unmodeled sensor discrepancies, and the absence of a…

The P$^3$T scheme is a hybrid method for simulating gravitational $N$-body systems. It combines a fast particle-tree (PT) algorithm for long-range forces with a high-accuracy particle-particle (PP, direct $N$-body) solver for short-range…

The tremendous challenge of comparing our theoretical models with the gravitational-wave observations in the new era of multimessenger astronomy requires accurate and fast numerical simulations of complicated physical systems described by…

In this paper, we report the implementation and measured performance of our extreme-scale global simulation code on Sunway TaihuLight and two PEZY-SC2 systems: Shoubu System B and Gyoukou. The numerical algorithm is the parallel Barnes-Hut…

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 present a hybrid code combining the OpenMP-parallel tree code VINE with an algorithmic chain regularization scheme. The new code, called "rVINE", aims to significantly improve the accuracy of close encounters of massive bodies with…

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…

Fast algorithms for the computation of $N$-body problems can be broadly classified into mesh-based interpolation methods, and hierarchical or multiresolution methods. To this last class belongs the well-known fast multipole method (FMM),…