The research of parallel computation efficiency when modeling collisionless gravitating systems

$N$-body model is widely used for a wide range of problems in which the important role is played by collective processes. Interaction in the $N$-body problem is defined between pairs of particles. The force acting on one i-particle is the sum of contributions from all other particles. Each body of system is characterized by a set of parameters (weight, speed, position in space).
Calculation of the acceleration caused by power influence of other particles on it is necessary for definition of the law of all particles movement. Calculations on algorithm are quite demanding: for $N$ particles the volume of calculations grows as $O(N^2)$. The direct methods and difficult schemes allowing to reduce the volume of calculations to $O (N \log{N})$ are used for effective modeling. An alternative way to reduce time of calculations is the use of technologies of parallel computing on GPUs.
The CUDA technology is considered the most advanced now. The parallel program is constructed taking into account alignment and use of the shared memory. The mechanism of interaction of threads among themselves in CUDA is realized by means of the built-in syncthreads function.
The results of numerical experiments of the dynamics of gravitationally interacting $N$-particles are presented using a different graphics processors as a part of the algorithm "Particle-Particle" and using technology CUDA.