Geodesic
Application of high performance computing systems to simulate the
Numerical methods and programming, Tome 11 (2010) no. 2, pp. 176-183

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The Farley-Buneman instability is observed in the E-region of the Earth's ionosphere at altitudes about $100$ km. A mathematical model is used to describe this instability. The model includes the ion kinetic equation dependent on five independent variables (two space coordinates, two velocity coordinates, and time), the fluid equations for electron density and temperature (these equations depend on three independent variables: two space coordinates and time), and the two-dimensional Poisson equation for the potential of the turbulent electric field. The problem is solved numerically on multidimensional grids containing $10^9$ points on average. A software package was designed to solve the problem on supercomputing systems. Computations were performed on the supercomputers SKIF MGU Chebyshev and IBM Blue Gene/P installed at the VMK faculty of Moscow State University. A comparative analysis of numerical results is given. A good scalability of the software package is shown. An almost linear acceleration is achieved for large data sets (about $100$ Gb of memory is used) and for a number of computational nodes about 2000. The work was performed as a part of the SKIG GRID project and was supported by the state contracts No. P-958 (August 20, 2009) and No. 02.740.11.0196 of the Federal Special-Purpose Program “Scientific and scientific-educational personnel of innovative Russia” and by the Russian Foundation for Basic Research (project No. 08-01-00721).
Keywords: ionosphere; plasma modeling; instability in plasma; kinetic equation; high performance computing. 
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D. V. Kovalev; A. P. Smirnov; A. B. Shmelev. Application of high performance computing systems to simulate the. Numerical methods and programming, Tome 11 (2010) no. 2, pp. 176-183. http://geodesic.mathdoc.fr/item/VMP_2010_11_2_a3/