Geodesic
Numerical simulation of N-body gravitational dynamics by PIC method: a~parallel implementation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 1, pp. 25-36

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The evolution of self-gravitating systems such as the accretion discs is of great interest to astrophysics. The aim of this work is to create a parallel program for the accretion disc simulation on high-performance multiprocessor computers. The disc structure formation is N-body problem in a self-consistent gravity field. A good approximation to the problem is the Vlasov–Liouville kinetic equation. In the present work, the equation is solved by the PIC method. The main difficulty here is the evaluation of gravitational potential which is given by the 3D Poisson equation. The parallel scheme of the algorithm was designed for the MIMD computers in an assembly technology. This means that the program is assembled of minimal fragments, each being a readymade program containing potential values and the particles from one or more grid layers. The values of a grid potential are uniformly distributed among the processor elements uniformly in the radial direction. As the potential evaluation takes the main time, the distribution of particles is of minor importance here. Test computations conducted on the ICT cluster of Pentium-III workstations showed the linear acceleration as compared to the sequential version. 
@article{SJVM_2003_6_1_a2,
     author = {V. A. Vshivkov and V. \`E. Malyshkin and A. V. Snytnikov and V. N. Snytnikov},
     title = {Numerical simulation of {N-body} gravitational dynamics by {PIC} method: a~parallel implementation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {25--36},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2003_6_1_a2/}
}
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V. A. Vshivkov; V. È. Malyshkin; A. V. Snytnikov; V. N. Snytnikov. Numerical simulation of N-body gravitational dynamics by PIC method: a~parallel implementation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 1, pp. 25-36. http://geodesic.mathdoc.fr/item/SJVM_2003_6_1_a2/