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Тезисы докладов

Параллельные численные алгоритмы

The evolution of self-gravitating systems such as accretion discs is of great interest to astrophysics. The aim of this work is to give a robust method for gravitational potential evaluation in the problem of accretion disc simulation. Disc structure formation is the 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 physical problem is to be solved with very high spatial accuracy because the the evolution of the disc is affected by small peculiarities of its structure. It results in large size of the computational grid. The memory required for a real physical task is not available on a sequetial workstation and due to this reason the program has to be parallel. The main difficulty here is the evaluation of gravitational potential which is given by the three-dimensional Poisson equation. The equation is approximated on the grid in cylindrical coordinate system resulting in a system of linear algebraic equations. For the Poisson equation solver to be fast, it should deal with the peculiarities of the physical problem and be highly paralellizable. Employed to solve the equation is the combined numerical scheme based on iterational methods which suit the best the above two requirements. Despite of their inefficiency in the general case, they show high speed of computation for this non-stationary problem. Furthermore the simpler iterational methods are better paralellized, and the gain from parallelization on a system with rather big number of processors exceed the loss in computational efficiency. The parallel scheme of the algorithm was designed for MIMD computers in assembly technology. The values of grid potential are distributed between the processor elements uniformly in the radial direction. As the potential evaluation takes the main time, the distribution of particles is of little importance here. Moreover, the workload of all the processors is generally uniform. Test computations conducted on the ICT cluster of Pentium-III workstations also on MVS-1000M supercomputer showed the speedup close to linear and, which is more important, the ability of solving the Poisson equation with high accuracy on large grids.

Примечание. Тезисы докладов публикуются в авторской редакции

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