COMPUTATIONAL EXPERIMENTS ON SOLVING GRID ELLIPTIC EQUATIONS BY SOME PARALLEL ITERATIVE METHODS ON THE K60 CLUSTER
https://doi.org/10.23947/2587-8999-2022-1-3-121-136
Abstract
The paper deals with the problem of preserving natural water systems, as well as maintaining their integrity, not only through the enterprise of organizational, engineering and technical solutions, but also through the development of highly effective mathematical modeling techniques that make it possible quickly and efficiently, based on interconnected high-precision models of hydrophysics and hydrobiology, predict the processes of pollution spreading and the occurrence of hazardous phenomena in coastal systems. The article considers algorithms for solving grid equations developed for high-performance cluster systems. A model of parallel computations is proposed, which makes it possible, when choosing the appropriate method for solving the problem of aquatic ecology, to estimate the cost of calculations, which is defined as the product of the time of parallel solution of the problem and the number of processors used. An estimate of the optimal amount of information packet for exchange between processors is obtained. The adaptive modified alternating-triangular method of minimum corrections is described, the results of numerical experiments for the parallel variant of this one are presented.
Keywords
mathematical modeling,
adaptive alternating-triangular method,
parallel algorithms for solving grid equations,
MPI,
OpenMP
Supporting agencies: The study was financially supported by the Council for Grants of the President of the Russian Federation within the framework of the scientific project No. MD-3624.2021.1.1
About the Authors
A. M. Atayan
Don State Technical University
Russian Federation
Russian Federation
Atayan Asya Mikhailovna, Senior Lecturer of the Department of Computer Engineering and Automated Systems Software
Gagarin square, 1, Rostov-on-Don, Russia
A. E. Chistyakov
Don State Technical University
Russian Federation
Russian Federation
Chistyakov Alexander Evgenyevich, Doctor of Science in Physics and Maths, Professor of the Department of Computer Engineering and Automated Systems Software
Gagarin square, 1, Rostov-on-Don, Russia
References
1. Sukhinov A.I., Chistyakov A.E., Protsenko E.A., Sidoryakina V.V., Protsenko S.V. Parallel algorithms for solving the problem of coastal bottom relief dynamics // Num. Meth. Prog.. ‒ 2020. ‒ Vol.21, №3. ‒ P.196–206.
2. Voevodin V.V. Parallelism in large software packages (why is it difficult to create efficient software) // Chebyshevskii Sb. – 2017. – Vol.18, №3, P. 188–201 (in Russian).
3. Gorobets A.V., Sukov S.A., Zheleznyakov A.O., Bogdanov P.B., Chetverushkin B.N. / The use of GPUs in the framework of hybrid two-level parallelization MPI + OpenMP on heterogeneous scientific computing resources // Proceedings of the international conference. PCT2011– 2011. – P.452–460 (in Russian).
4. Gur'eva, Ya.L. Il'in V.P. On acceleration technologies of parallel decomposition methods // Num. Meth. Prog. – 2015. - Vol.16, №1, P. 146–154 (in Russian).
5. Atayan A.M., Nikitina A.V., Sukhinov A.I., Chistyakov A.E. Mathematical modeling of hazardous natural phenomena in a shallow basin // Comput. Math. Math. Phys. – 2022. – Vol.61, № 2.– P. 269–286.
6. Sukhinov А.I., Chistyakov A.E., Alekseenko E.V. Numerical realization of three-dimensional model of hydrodynamics for shallow water basins on high-performance system // Math. Models Comput. Simul. ‒ 2011. ‒ Vol.3, №5. ‒ P. 562–574.
7. Alekseenko E., Roux B., Fougere D., Chen P.G. The effect of wind induced bottom shear stress and salinity on Zostera noltii replanting in a Mediterranean coastal lagoon. Estuarine // Coastal and Shelf Science. ‒ 2017. ‒ Vol.187. ‒ P.293–305.
8. Belotserkovskii O.M., Gushchin V.A., Shchennikov V.V. Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid // Comput. Math. Math. Phys.‒ 1975. ‒ Vol.15, №1. ‒ P. 190–200.
9. Sukhinov A.I., Chistyakov A.E., Kuznetsova I.Y., Atayan A.M., Nikitina A.V. Regularized difference scheme for solving hydrodynamic problems // Math. Models Comput. Simul. ‒ 2022. ‒ Vol.14, №5. ‒ P. 745–754.
10. Sukhinov A.I., Chistyakov A.E. Adaptive analog-SSOR iterative method for solving grid equations with nonselfadjoint operators // Math. Models Comput. Simul. ‒ 2012. ‒ Vol.4, №4. ‒ P.398–409.
Review
For citations:
Atayan A.M., Chistyakov A.E. COMPUTATIONAL EXPERIMENTS ON SOLVING GRID ELLIPTIC EQUATIONS BY SOME PARALLEL ITERATIVE METHODS ON THE K60 CLUSTER. Computational Mathematics and Information Technologies. 2022;6(3):121-136. https://doi.org/10.23947/2587-8999-2022-1-3-121-136
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