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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.