Phantom-GRAPE is a numerical software library to accelerate collisionless $N$-body simulation with SIMD instruction set on x86 architecture. The Newton's forces and also central forces with an arbitrary shape f(r), which have a finite cutoff radius r_cut (i.e. f(r)=0 at r>r_cut), can be quickly computed.

FDPS provides the necessary functions for efficient parallel execution of particle-based simulations as templates independent of the data structure of particles and the functional form of the interaction. It is used to develop particle-based simulation programs for large-scale distributed-memory parallel supercomputers. FDPS includes templates for domain decomposition, redistribution of particles, and gathering of particle information for interaction calculation. It uses algorithms such as Barnes-Hut tree method for long-range interactions; methods to limit the calculation to neighbor particles are used for short-range interactions. FDPS reduces the time and effort necessary to write a simple, sequential and unoptimized program of O(N^2) calculation cost, and produces compiled programs that will run efficiently on large-scale parallel supercomputers.

SDAR (Slow-Down Algorithmic Regularization) simulates the long-term evolution of few-body systems such as binaries and triples. The algorithm used provides a few orders of magnitude faster performance than the classical N-body method. The secular evolution of hierarchical systems, e.g. Kozai-Lidov oscillation, can be well reproduced. The code is written in the C++ language and can be used either as a stand-alone tool or a library to be plugged in other N-body codes. The high precision of the floating point to 62 digits is also supported.

The N-body code PETAR (ParticlE Tree & particle-particle & Algorithmic Regularization) combines the methods of Barnes-Hut tree, Hermite integrator and slow-down algorithmic regularization (SDAR). It accurately handles an arbitrary fraction of multiple systems (e.g. binaries, triples) while keeping a high performance by using the hybrid parallelization methods with MPI, OpenMP, SIMD instructions and GPU. PETAR has very good agreement with NBODY6++GPU results on the long-term evolution of the global structure, binary orbits and escapers and is significantly faster when used on a highly configured GPU desktop computer. PETAR scales well when the number of cores increase on the Cray XC50 supercomputer, allowing a solution to the ten million-body problem which covers the region of ultra compact dwarfs and nuclear star clusters.

The fast N-body code SCF-FDPS (Self-Consistent Field-Framework for Developing Particle Simulators) simulates disk-halo systems. It combines a self-consistent field (SCF) code, which provides scalability, and a tree code that is parallelized using the Framework for Developing Particle Simulators (FDPS) (ascl:1604.011). SCF-FDPS handles a wide variety of halo profiles and can be used to study extensive dynamical problems of disk-halo systems.

The phi-GPU (Parallel Hermite Integration on GPU) high-order N-body parallel dynamic code uses the fourth-order Hermite integration scheme with hierarchical individual block time-steps and incorporates external gravity. The software works directly with GPU, using only NVIDIA GPU and CUDA code. It creates numerical simulations and can be used to study galaxy and star cluster evolution.