Geodesic
The three-dimensional parallel numerical code on the base of mixed Lagrange--Eulerian approach
Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 4 (2015), pp. 24-34.

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In this paper the parallel numerical code developed for integration of gas-dynamics equations in the three-dimensional case on the base of mixed Lagrange–Eulerian approach was described. The method of paralleling, allowing effective use of computation properties of computer cluster with multiprocessor nodes, was shown. The results of performance testing, which shown significant growth of computations comparing to serial version of the software was shown. For parallelization of numerical code, combination of OpenMP and MPI technologies was used: on each node of computer cluster runs multithread calculation process. Methodology of data parallelism was implemented (in other words, single instruction—multiple data). For dividing data between calculation processes, partitioning of computational domain along one axis was used. OpenMP technology leads to acceleration of calculations relative to number of processor cores with coefficient $0.93$. MPI technology leads to acceleration of calculations relative to number of computation cluster nodes with coefficient $0.9$. Combination of OpenMP+MPI leads to acceleration of calculations with coefficient $0.98$. Testing of computational performance was made on computer cluster with these characteristics: Intel(R) Core(TM) 2 CPU E 8400, 2 Gb RAM, communication media - Gigabit Ethernet 1000Base-T. The results have shown that the numerical code was effectivly parallelized: with using combination MPI+OpenMP on two-node cluster computational performance growth to approximately in $1.96$ times (computational grid size depended); on four nodes—approximately in $3.87$ times; on eight nodes—approximately in $7.86$ times. Total computational performance has grown on the average by $10$–$15\%$ instead of results obtained by using only MPI. The developed computer program can be used for numerical solving of the three-dimensional gas-dynamics equations with detailed grids with computational clusters of multiprocessor nodes.
Keywords: numerical simulation, gas-dynamics, Lagrange–Eulerian approach, parallel technologies, high-performance computations. 
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     title = {The three-dimensional parallel numerical code on the base of mixed {Lagrange--Eulerian} approach},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
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T. S. Shushkеvich; N. M. Kuz'min; M. A. Butenko. The three-dimensional parallel numerical code on the base of mixed Lagrange--Eulerian approach. Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 4 (2015), pp. 24-34. http://geodesic.mathdoc.fr/item/VVGUM_2015_4_a3/

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