Результаты поиска по 'Keldysh Institute of Applied Mathematics':
Найдено статей: 2
  1. Malinetsky G.G.
    Image of the teacher. Ten years afterward
    Computer Research and Modeling, 2015, v. 7, no. 4, pp. 789-811

    The work outlines the key ideas of Kurdyumov S.P., an outstanding specialist in applied mathematics, self-organization theory, transdisciplinary research. It considers the development of his scientific ideas in the last decade and formulates a set of open problems in synergetics which will probably stimulate the development of this approach. The article is an engaged version of the report made at Xth Kurdyumov readings held in Tver State University in 2015.

    Keywords: S.P. Kurdyumov, Keldysh Institute of Applied Mathematics, scientific school, theory of blow-up regimes, self-organiation, synergetics, problem of time, dynamic chaos, self-organized complexity, paradigma, risk managment.
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  2. Litvinov V.N., Chistyakov A.E., Nikitina A.V., Atayan A.M., Kuznetsova I.Y.
    Mathematical modeling of hydrodynamics problems of the Azov Sea on a multiprocessor computer system
    Computer Research and Modeling, 2024, v. 16, no. 3, pp. 647-672

    The article is devoted to modeling the shallow water hydrodynamic processes using the example of the Azov Sea. The article presents a mathematical model of the hydrodynamics of a shallow water body, which allows one to calculate three-dimensional fields of the velocity vector of movement of the aquatic environment. Application of regularizers according to B.N.Chetverushkin in the continuity equation led to a change in the method of calculating the pressure field, based on solving the wave equation. A discrete finite-difference scheme has been constructed for calculating pressure in an area whose linear vertical dimensions are significantly smaller than those in horizontal coordinate directions, which is typical for the geometry of shallow water bodies. The method and algorithm for solving grid equations with a tridiagonal preconditioner are described. The proposed method is used to solve grid equations that arise when calculating pressure for the three-dimensional problem of hydrodynamics of the Azov Sea. It is shown that the proposed method converges faster than the modified alternating triangular method. A parallel implementation of the proposed method for solving grid equations is presented and theoretical and practical estimates of the acceleration of the algorithm are carried out taking into account the latency time of the computing system. The results of computational experiments for solving problems of hydrodynamics of the Sea of Azov using the hybrid MPI + OpenMP technology are presented. The developed models and algorithms were used to reconstruct the environmental disaster that occurred in the Sea of Azov in 2001 and to solve the problem of the movement of the aquatic environment in estuary areas. Numerical experiments were carried out on the K-60 hybrid computing cluster of the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences.

    Keywords: mathematical modeling, hydrodynamics, iterative method, computational domain decomposition, parallel algorithm.

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