Труды сотрудников ИВМ СО РАН

/ V.Shaydurov, T.Liu, Z.Zheng // AIP Conference Proceedings. - 2012. - Vol. 1487: 4th International Conference on Application of Mathematics in Technical and Natural Sciences: Memorial Volume devoted to Prof. Christo I. Christov, AMiTaNS 2012 (11 June 2012 through 16 June 2012, St. Constantine and Helena) . - pp. 42-48, DOI 10.1063/1.4758940 . -
Аннотация: Computational aerodynamics is a key technology in aircraft design which is ahead of physical experiment and complements it. Of course all three components of computational modeling are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of computer architecture. Numerical algorithms are developed more conservative. More precisely, they are offered and theoretically justified for more simple mathematical problems. Nevertheless, computational mathematics now has amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. A significant step in this direction was the European Project ADIGMA whose positive experience will be used in International Project TRISTAM for further movement in the field of computational technologies for aerodynamics. This paper gives a general overview of objectives and approaches intended to use and a description of the recommended four-stage computer technology. В© 2012 American Institute of Physics.

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Доп.точки доступа:
Liu, T.; Zheng, Z.; Шайдуров, Владимир Викторович

/ V. V. Shaydurov, G. I. Shchepanovskaya, M. V. Yakubovich // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2013. - Vol. 8236 LNCS: 5th International Conference on Numerical Analysis and Applications, NAA 2012 (15 June 2013 through 20 June 2013, Lozenetz. - P122-131, DOI 10.1007/978-3-642-41515-9_11 . -
Аннотация: The algorithm for numerical solving the Navier-Stokes equations for two-dimensional motion for viscous heat-conducting gas is proposed. The discretization of equations is performed by a combination of a special version of the trajectory method for a substantial derivative and the finite element method with piecewise bilinear basis functions for other terms. The results of numerical studies of the structure of a supersonic flow in a plane channel with an obstacle for a wide range of Mach numbers and Reynolds numbers are presented. Velocity and pressure fields are investigated, and the vortex structure of flow is studied in the circulation area of the obstacle. В© 2013 Springer-Verlag.

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Держатели документа:
Institute of Computational Modeling, Siberian Branch, Russian Academy of Science, Krasnoyarsk, Russian Federation
Beihang University, Beijing, China

Доп.точки доступа:
Shaydurov, V.V.; Shchepanovskaya, G.I.; Yakubovich, M.V.

/ V. Shaydurov, T. Liu // Procedia Eng. - 2013. - Vol. 61: 25th International Conference on Parallel Computational Fluid Dynamics, ParCFD 2013 (20 May 2013 through 24 May 2013, Changsha) Conference code: 101818. - P16-22, DOI 10.1016/j.proeng.2013.07.086 . -
Аннотация: All three components of computational aerodynamics are actively developed: mathematical models of real aerodynamic processes, numerical algorithms, and high-performance computing. The most impressive progress has been made in the field of computing, though with a considerable complication of the computer architecture. Numerical algorithms developed more conservative. Nevertheless, computational mathematics now amassed a whole palette of numerical algorithms that can provide acceptable accuracy and interface between modern mathematical models in aerodynamics and high-performance computers. This paper gives a general overview of objectives and approaches of international Project TRISTAM and a description of the four-stage computer technology in the field of computational aerodynamics. © 2013 The Authors.

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Держатели документа:
Beihang University, 37# Xueyuan Road, Haidian District, Beijing, 100191, China
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Liu, T.; Шайдуров, Владимир Викторович

/ A. Efremov [et al.] // J. Appl. Math. - 2014. - Vol. 2014, DOI 10.1155/2014/610398 . - ISSN 1110-757X
Аннотация: A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture computation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation between time step and mesh size. The theoretical results are confirmed by numerical experiments. Performance of a sequential algorithm and several parallel implementations with the OpenMP and CUDA technologies in the C language has been studied.

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Держатели документа:
Institute of Computational Modeling SB RASKrasnoyarsk, Akademgorodok, Russian Federation
Siberian Federal University, Svobodny ProspectKrasnoyarsk, Russian Federation
Beihang UniversityHaidian District, Beijing, China

Доп.точки доступа:
Efremov, A.; Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaydurov, V.V.; Шайдуров, Владимир Викторович; Vyatkin, A.V.; Вяткин, Александр Владимирович

[Text] : статья / L. Gileva, V. Shaydurov, B. Dobronets // Applied Mathematics. - 2013. - Vol. 4. - p. 50-56DOI 10.4236/am.2013.412A006 . -
Аннотация: The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.

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Доп.точки доступа:
Shaydurov, V.V.; Шайдуров, Владимир Викторович; Dobronets, B.S.; Добронец, Борис Станиславович; Гилева, Лидия Викторовна

[Text] / A. V. Vyatkin, V. V. Shaydurov // Zbornik radova konferencije MIT 2013. - Beograd : Uiverziteta u Pristini, 2014. - P739-745 . - ISBN 978-86-80795-20-1

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Доп.точки доступа:
Shaydurov, V.V.; Шайдуров, Владимир Викторович; Вяткин, Александр Владимирович

[Text] : научное издание / S. Chang [et al.] // Computational Research. - 2014. - Vol. 2, Is. 3. - p. 49-53DOI 10.13189/cr.2014.020303 . -
Аннотация: In this paper, fitted finite volume method is developed to solve a nonlinear degenerate Black-Scholes equation applied in the valuation of unit-linked policy with surrender option, based on the fitting idea in S. Wang [IMA J. Numer. Anal., 24 (2004), 699-720]. Unlike the conventional pricing method mentioned in [1] which is using the free boundary method to calibrate the valuation PDE, here we develop a power penalty method to solve numerically the linear complimentary problem in the variational inequality arising from the valuation of unit-linked policy with surrender option. With the degenerate boundary and non-smooth final condition, we will show that it is essential to refine the mesh to remain the convergence and super-convergence order.

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Доп.точки доступа:
Chang, Shuhua; Добронец, Борис Станиславович; Fang, Zhiwei; Liu, Xin; Shaydurov, V.V.; Шайдуров, Владимир Викторович

[Text] / V. Shaydurov, A. Vyatkin // AIP Conference Proceedings. - 2015. - Vol. 1648: International Conference on Numerical Analysis and Applied Mathematics (SEP 22-28, 2014, Rhodes, GREECE). - Ст. UNSP 85004, DOI 10.1063/1.4913096. - Cited References:11 . - ISSN 0094-243XРУБ Mathematics, Applied + Physics, Applied

Аннотация: We consider a semi-Lagrangian algorithm and formulate the basic equality for a local temporal-spatial domain. This equality involves integrals over domains at neighboring temporal levels. To get the numerical scheme, we approximate each component of the equality within second-order accuracy. To compute an integral at the previous time level, we make the change of variables. After that the quadrature formulas are implemented with nodes and weights defined with the help of the Cauchy problem for a system of ordinary differential equations.

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Держатели документа:
Siberian Fed Univ, Krasnoyarsk 660041, Svobodny Prospe, Russia
Inst Computat Modeling SB RAS, Akademgorodok 660036, Russia

Доп.точки доступа:
Vyatkin, Alexander; Вяткин, Александр Владимирович; Шайдуров, Владимир Викторович

/ V. V. Shaydurov, T. Xu // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . - 2015. - Vol. 9045: 6th International Conference on Finite Difference Methods, FDM 2014; Lozenetz; Bulgaria; 18 June 2014 through 23 June 2014; Code 156479. - P84-95, DOI 10.1007/978-3-319-20239-6_8 . -
Аннотация: This paper deals with the calculation of linear and quadratic functionals of approximate solutions obtained by the finite element method. It is shown that under certain conditions the output functionals of an approximate solution are computed with higher order of accuracy than that of the solution itself. These abstract results are illustrated by two numerical examples for the Poisson equation. © Springer International Publishing Switzerland 2015.

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Держатели документа:
Institute of Computational Modeling of Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, Russian Federation
Beihang University, Beijing, China

Доп.точки доступа:
Xu, T.; Шайдуров, Владимир Викторович

[Text] / V. Shaydurov [et al.] ; ed. M. D. Todorov // APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES : AMER INST PHYSICS, 2015. - Vol. 1684: 7th International Conference on Application of Mathematics in Technical (JUN 28-JUL 03, 2015, Albena, BULGARIA). - Ст. UNSP 090011. - (AIP Conference Proceedings), DOI 10.1063/1.4934336. - Cited References:16 . - РУБ Mathematics, Applied + Physics, Applied

Аннотация: In the paper, a semi-Lagrangian approximation is presented for the numerical solution of the two-dimensional time-dependent Navier-Stokes equations for viscous heat-conducting gas. In each equation, a combination of three first-order derivatives describing the transfer of a corresponding substance (density, velocity components, or internal energy) along trajectories is interpreted as the "transfer derivative" in the transfer direction. The other terms of the equations are written in the Euler form. On the sought-for time level, the standard conforming finite element method is realized for them with the linear elements on triangles and the bilinear ones on rectangles. The stencil adaptation along trajectories enables us to avoid the Courant-Friedrichs-Lewy upper limit which describes the dependence of the time step on the mesh-size of the space triangulation. At the end of the paper, a numerical example illustrates the implementation of the described algorithms.

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Держатели документа:
SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Beihang Univ, Beijing 100191, Peoples R China.

Доп.точки доступа:
Shaydurov, V.V.; Шайдуров, Владимир Викторович; Liu, Tiegang; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович; Todorov, M.D. \ed.\

[Text] / V. Shaydurov, G. Shchepanovskaya, M. Yakubovich ; ed. M. D. Todorov // APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES : AMER INST PHYSICS, 2015. - Vol. 1684: 7th International Conference on Application of Mathematics in Technical (JUN 28-JUL 03, 2015, Albena, BULGARIA). - Ст. UNSP 020003. - (AIP Conference Proceedings), DOI 10.1063/1.4934284. - Cited References:23 . - РУБ Mathematics, Applied + Physics, Applied

Аннотация: In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth's atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) and the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.

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Держатели документа:
SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660041, Russia.

Доп.точки доступа:
Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович; Todorov, M.D. \ed.\; Шайдуров, Владимир Викторович

/ B. Dobronets, V. Shaydurov // Lobachevskii J. Math. - 2016. - Vol. 37, Is. 5. - P527-533, DOI 10.1134/S1995080216050036 . - ISSN 1995-0802
Аннотация: We discuss the Hermitian finite elements of high-order accuracy for solving boundary value problems for partial differential equations in domains with curvilinear boundaries. New elements are constructed in such a way that they can be used in conjunction with the Bogner–Fox–Schmit rectangular elements. © 2016, Pleiades Publishing, Ltd.

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Держатели документа:
Siberian Federal University, Svobodnyi pr. 79, Krasnoyarsk, Russian Federation
Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences, Akademgorodok 40/55, Krasnoyarsk, Russian Federation
Beihang University, Xueyuan Road 37, Beijing, China

Доп.точки доступа:
Dobronets, B.S.; Добронец, Борис Станиславович; Shaydurov, V.V.

/ A. Korneeva, V. Shaydurov ; ed.: A. . Ashyralyev, A. . Lukashov // INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM : AMER INST PHYSICS, 2016. - Vol. 1759: 3rd International Conference on Analysis and Applied Mathematics (ICAAM) (SEP 07-10, 2016, Almaty, KAZAKHSTAN). - Ст. 020048. - (AIP Conference Proceedings), DOI 10.1063/1.4959662. - Cited References:1 . - РУБ Mathematics, Applied + Physics, Applied

Аннотация: In the paper, the data analysis is considered for thin-film thermoresistors coated on to a radio-electronic printed circuit board to determine possible zones of its overheating. A mathematical model consists in an underdetermined system of linear algebraic equations with an infinite set of solutions. For computing a more real solution, two additional conditions are used: the smoothness of a solution and the positiveness of an increase of temperature during overheating. Computational experiments demonstrate that an overheating zone is determined exactly with a tolerable accuracy of temperature in it.

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Держатели документа:
Siberian Fed Univ, Krasnoyarsk 660041, Russia.
Russian Acad Sci, Inst Computat Modeling, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Korneeva, Anna; Shaydurov, V.V.; Шайдуров, Владимир Викторович

/ V. Shaydurov, G. Shchepanovskaya, M. Yakubovich // AIP Conference Proceedings. - 2016. - Vol. 1773: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 (22 June 2016 through 27 June 2016, ) Conference code: 124420, DOI 10.1063/1.4964960 . -
Аннотация: In the paper, a mathematical model and a numerical algorithm are proposed for modeling an air flow. The proposed model is based on the time-dependent Navier-Stokes equations for viscous heat-conducting gas. The energy equation and the state equations are modified to account for two kinds of 'internal' energy. The first one is the usual translational and rotational energy of molecules which defines the thermodynamical temperature and the pressure. The second one is the subgrid energy of small turbulent eddies. A numerical algorithm is proposed for solving the formulated initial-boundary value problem as a combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. A numerical example illustrates these approaches. © 2016 Author(s).

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Держатели документа:
Institute of Computational Modeling of SB RAS, 50/44 Akademgorodok, Krasnoyarsk, Russian Federation
Beihang University, 37# Xueyuan Rd., Haidian District, Beijing, China

Доп.точки доступа:
Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович; Шайдуров, Владимир Викторович

/ A. Efremov [et al.] // AIP Conference Proceedings. - 2016. - Vol. 1773: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 (22 June 2016 through 27 June 2016, ) Conference code: 124420, DOI 10.1063/1.4964997 . -
Аннотация: In the paper, the semi-Lagrangian method is considered for the numerical solution of the advection problem. A numerical solution is constructed as a piecewise constant function on a rectangular grid. The proposed method is stable and gives an approximate solution with the first order of accuracy. To reduce the effect of smoothing an approximate solution because of numerical viscosity, a mesh refinement is applied in the vicinity of large gradients of the approximate solution. The localization of the smoothing effect is illustrated by a numerical example. In contrast to the traditional Eulerian schemes, semi-Lagrangian algorithms do not involve a time step restriction. © 2016 Author(s).

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Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Efremov, A.; Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaydurov, V.V.; Шайдуров, Владимир Викторович; Vyatkin, A.

/ L. Gileva, E. Karepova, V. Shaydurov // AIP Conference Proceedings. - 2016. - Vol. 1773: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 (22 June 2016 through 27 June 2016, ) Conference code: 124420, DOI 10.1063/1.4964999 . -
Аннотация: In the paper, we propose new biquadratic and bicubic Hermite elements on a rectangle. These elements involve the values of a function and its second-order derivatives as degrees of freedom. The proposed elements are more efficient than Lagrange elements of the same degree. Numerical results confirm the theoretical estimates of convergence. © 2016 Author(s).

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Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Shaydurov, V.V.; Шайдуров, Владимир Викторович

/ V. V. Shaydurov, G. I. Shchepanovskaya, M. V. Yakubovich // Lobachevskii J. Math. - 2018. - Vol. 39, Is. 7. - P936-948, DOI 10.1134/S1995080218070193. - Cited References:20. - The work was partially supported by the Russian Foundation for Basic Research to projects nos. 17-01-000270 and No 16-41-243029 which is also supported by the Krasnoyarsk Regional Government and the Krasnoyarsk Regional Fund for the Support of Scientific and Technical Activities. . - ISSN 1995-0802. - ISSN 1818-9962РУБ Mathematics

Аннотация: In the paper, the numerical modeling of a supersonic flow around a wedge by viscous heat-conducting gas is considered. A numerical algorithm is proposed for the initial boundary-value problem for the Navier-Stokes equations. These equations are modified and amplified by new boundary conditions to provide the conservation law for the full energy: kinetic and inner. Then the combination of the Lagrangian approximation for the transfer operators and the conforming finite element method for other terms provides an efficient algorithm. Particular attention has been given to the approximation providing the conservation laws for mass and full energy at discrete level. Test calculations have been performed for a wide range of Mach and Reynolds numbers.

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Держатели документа:
Russian Acad Sci, Siberian Branch, Inst Computat Modeling, Akademgorodok 50-44, Krasnoyarsk 660036, Russia.
Tianjin Univ Finance & Econ, Zhujiang Rd 25, Tianjin 300222, Peoples R China.

Доп.точки доступа:
Shaydurov, V. V.; Shchepanovskaya, G. I.; Yakubovich, M. V.; Russian Foundation for Basic Research [17-01-000270, 16-41-243029]; Krasnoyarsk Regional Government; Krasnoyarsk Regional Fund for the Support of Scientific and Technical Activities

/ V. V. Shaydurov, V. S. Kornienko // AIP Conference Proceedings : American Institute of Physics Inc., 2019. - Vol. 2164: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2019 (20 June 2019 through 25 June 2019, ) Conference code: 153460. - Ст. 110012, DOI 10.1063/1.5130857 . -
Аннотация: The paper presents a computational scheme for solving economic problems formulated in terms of Mean Field Game theory. The equilibrium of the Mean Field leads to a coupled system of two parabolic partial differential equations: Fokker-Planck-Kolmogorov and Hamilton-Jacobi-Bellman ones. The article is devoted to the discrete approximation of these equations and the application of the Mean Field theory directly at the discrete level. Contrary to other studies, the monotonic algorithm constructed here is applicable to problem with more general control function. This algorithm is applied to the problem of heating insulation. © 2019 Author(s).

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Держатели документа:
Tianjin University of Finance and Economics, Tianjin, China
Institute of Computational Modeling of Federal Research Center KSC SB RAS, Krasnoyarsk, Russian Federation
Siberian Federal University, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Shaydurov, V. V.; Kornienko, V. S.