[Text]. - Electronic data (249 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=788. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/788gorban_AMLappr98.pdf (Полный текст) : статья / A.N. Gorban. - Electronic data (249 Kb) // Applied Mathematics Letters. - 1998. - Vol. 11, № 3. - p. 45-49
Перевод заглавия: Аппроксимация непрерывных функций нескольких переменных с помощью произвольной нелинейной непрерывной функции одного переменного, линейных функций и их суперпозиций
Аннотация: Linear spaces of continuous functions of real variables closed under the superposition operation are considered. It has been proved that when such a space contains constants, linear functions, and at least one nonlinear function, it is dense in the space of all continuous functions in the topology of uniform convergence on compact sets. So, the approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions is possible.
http://icm.krasn.ru/refextra.php?id=788,
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Горбань, Александр Николаевич
Труды сотрудников ИВМ СО РАН
w10=
Найдено документов в текущей БД: 44
В16
G65
G65
Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions .
Peculiarities of Alfven wave propagation along a nonuniform magnetic flux tube
[Text] / N. V. Erkaev [et al.] // Phys. Plasmas. - 2005. - Vol. 12, Is. 1. - Ст. 12905, DOI 10.1063/1.1833392. - Cited References: 18
. - ISSN 1070-664X
РУБ Physics, Fluids & Plasmas
Аннотация: Within the framework of the assumption of large azimuthal wave numbers, the equations for Alfven and slow magnetosonic waves are obtained using frozen-in material coordinates. These equations are specified for the case of a nonuniform magnetic field with axial symmetry. Assuming a meridional polarization of the magnetic field and velocity perturbations, the effects of Alfven wave propagation are analyzed which are related to geometric characteristics of a nonuniform magnetic field: (a) A finite curvature radius of the magnetic field lines and (b) convergence of magnetic field lines. The interaction between the Alfven and magnetosonic waves is found to be strongly dependent on the curvature radius of the magnetic tube and the local plasma beta parameter. The electric field amplitude and the length scale of a wave front are found to increase very strongly in the course of the Alfven wave propagation along a converging magnetic flux tube. Also studied is a temporal decrease of the wave perturbations which is caused by dissipation at the conducting boundary. (C) 2005 American Institute of Physics.
Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Shaidurov, V.A.; Semenov, V.S.; Langmayr, D.; Biernat, H.K.
Аннотация: Within the framework of the assumption of large azimuthal wave numbers, the equations for Alfven and slow magnetosonic waves are obtained using frozen-in material coordinates. These equations are specified for the case of a nonuniform magnetic field with axial symmetry. Assuming a meridional polarization of the magnetic field and velocity perturbations, the effects of Alfven wave propagation are analyzed which are related to geometric characteristics of a nonuniform magnetic field: (a) A finite curvature radius of the magnetic field lines and (b) convergence of magnetic field lines. The interaction between the Alfven and magnetosonic waves is found to be strongly dependent on the curvature radius of the magnetic tube and the local plasma beta parameter. The electric field amplitude and the length scale of a wave front are found to increase very strongly in the course of the Alfven wave propagation along a converging magnetic flux tube. Also studied is a temporal decrease of the wave perturbations which is caused by dissipation at the conducting boundary. (C) 2005 American Institute of Physics.
Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Shaidurov, V.A.; Semenov, V.S.; Langmayr, D.; Biernat, H.K.
Convergence of a full multigrid algorithm for quadratic finite elements in a domain with a curvilinear boundary
[Text] / L. V. Gileva, V. V. Shaidurov // Russ. J. Numer. Anal. Math. Model. - 2009. - Vol. 24, Is. 5. - P425-438, DOI 10.1515/RJNAMM.2009.027. - Cited References: 11. - This analysis was partially supported by Grant 08-01-00621 of the Russian Foundation of Basic Research.
. - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied
Аннотация: In this paper, a full multigrid algorithm with a symmetric V-cycle for a grid problem obtained by discretization of a second-order elliptic equation with quadratic finite elements on triangles is studied. The multigrid complexity of the algorithm is proved. This means that the number of arithmetic operations required to achieve the order of accuracy of an approximate solution equal to that of the discretization error linearly depends on the number of unknowns. The rate of convergence is found to be higher than that for linear finite elements in spite of the higher order of accuracy.
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Гилева, Лидия Викторовна; Russian Foundation [08-01-00621]
Аннотация: In this paper, a full multigrid algorithm with a symmetric V-cycle for a grid problem obtained by discretization of a second-order elliptic equation with quadratic finite elements on triangles is studied. The multigrid complexity of the algorithm is proved. This means that the number of arithmetic operations required to achieve the order of accuracy of an approximate solution equal to that of the discretization error linearly depends on the number of unknowns. The rate of convergence is found to be higher than that for linear finite elements in spite of the higher order of accuracy.
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Гилева, Лидия Викторовна; Russian Foundation [08-01-00621]
Electric field generation at the magnetospheric boundary for northward IMF
/ N. V. Erkaev [et al.] // Journal of Atmospheric and Terrestrial Physics. - 1994. - Vol. 56, Is. 2. - P153-166
. - ISSN 0021-9169
Аннотация: We discuss three different processes which generate electric fields at the magnetopause during northward interplanetary magnetic field (IMF) conditions. These are (1) Petschek-type magnetic field reconnection, (2) magnetic field diffusion, and (3) viscous-like interaction resulting from the Kelvin-Helmholtz instability. For northward IMF all three processes lead to the formation of a boundary layer on closed magnetic field lines adjacent to the magnetospheric boundary. The thickness of the boundary layer depend on Petschek's parameter in the first case, the magnetic Reynolds number in the second case, and an effective Reynolds number in the third case. In each case coupling between the boundary layer and the ionosphere occurs via field-aligned currents. These field-aligned currents result from the penetration into the polar ionosphere of the electric field generated at the magnetospheric boundary. These currents are closed by a transverse current in the boundary layer and the associated Lorentz force causes a decrease of the kinetic energy of the solar wind plasma inside the boundary layer. As a result of this velocity decrease the thickness of the boundary layer increases on both flanks of the magnetosphere near the equatorial plane. The convergence of the boundary layer on the dawn and dusk sides leads to antisunward plasma flow in the magnetospheric tail. В© 1994.
Scopus
Держатели документа:
Computing Center, Siberian Branch, the Academy of Sciences, Krasnoyarsk, Russian Federation
Arctic and Antarctic Research Institute, St Petersburg, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Mezentsev, A.V.; Denisenko, V.V.; Денисенко, Валерий Васильевич; Zamay, S.S.; Troshichev, O.A.
Аннотация: We discuss three different processes which generate electric fields at the magnetopause during northward interplanetary magnetic field (IMF) conditions. These are (1) Petschek-type magnetic field reconnection, (2) magnetic field diffusion, and (3) viscous-like interaction resulting from the Kelvin-Helmholtz instability. For northward IMF all three processes lead to the formation of a boundary layer on closed magnetic field lines adjacent to the magnetospheric boundary. The thickness of the boundary layer depend on Petschek's parameter in the first case, the magnetic Reynolds number in the second case, and an effective Reynolds number in the third case. In each case coupling between the boundary layer and the ionosphere occurs via field-aligned currents. These field-aligned currents result from the penetration into the polar ionosphere of the electric field generated at the magnetospheric boundary. These currents are closed by a transverse current in the boundary layer and the associated Lorentz force causes a decrease of the kinetic energy of the solar wind plasma inside the boundary layer. As a result of this velocity decrease the thickness of the boundary layer increases on both flanks of the magnetosphere near the equatorial plane. The convergence of the boundary layer on the dawn and dusk sides leads to antisunward plasma flow in the magnetospheric tail. В© 1994.
Scopus
Держатели документа:
Computing Center, Siberian Branch, the Academy of Sciences, Krasnoyarsk, Russian Federation
Arctic and Antarctic Research Institute, St Petersburg, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Mezentsev, A.V.; Denisenko, V.V.; Денисенко, Валерий Васильевич; Zamay, S.S.; Troshichev, O.A.
Some estimates of the rate of convergence for the cascadic conjugate-gradient method
/ V. V. Shaidurov // Computers and Mathematics with Applications. - 1996. - Vol. 31, Is. 4-5. - P161-171
. - ISSN 0898-1221
Аннотация: The paper deals with a cascadic conjugate-gradient method (shortly called the CCG-algorithm) which was proposed by P. Deuflhard and can be considered as a simpler version of a multigrid (multilevel) method. We define it recurrently for discrete self-adjoint positive-definite problems on a sequence of grids. On the coarsest grid, the linear discrete algebraic system is solved directly. On the finer grids, the system is iteratively solved by the conjugate-gradient method where the starting guess is an interpolation of the approximated solution on the previous grid. Any preconditioning or restriction to coarser grids is not implemented. Nevertheless, the CCG-algorithm has the same optimal property compared to multigrid methods; namely, the algorithm converges with a rate which is independent of the number of unknowns and the number of grids. As an example, this property is proved for elliptic second order Dirichlet problems in two-dimensional, convex, polygonal bounded domains. For ensuring convergence, the number of iterations on each grid level has to increase from finer to coarser grids. The optimal dependence of these numbers is established with respect to the mesh size and the number of unknowns. The theory has been presented in an abstract setting which allows the application to both finite element and finite difference methods. CopyrightВ©1996 Elsevier Science Ltd. All rights reserved.
Scopus
Держатели документа:
Computing Center, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович
Аннотация: The paper deals with a cascadic conjugate-gradient method (shortly called the CCG-algorithm) which was proposed by P. Deuflhard and can be considered as a simpler version of a multigrid (multilevel) method. We define it recurrently for discrete self-adjoint positive-definite problems on a sequence of grids. On the coarsest grid, the linear discrete algebraic system is solved directly. On the finer grids, the system is iteratively solved by the conjugate-gradient method where the starting guess is an interpolation of the approximated solution on the previous grid. Any preconditioning or restriction to coarser grids is not implemented. Nevertheless, the CCG-algorithm has the same optimal property compared to multigrid methods; namely, the algorithm converges with a rate which is independent of the number of unknowns and the number of grids. As an example, this property is proved for elliptic second order Dirichlet problems in two-dimensional, convex, polygonal bounded domains. For ensuring convergence, the number of iterations on each grid level has to increase from finer to coarser grids. The optimal dependence of these numbers is established with respect to the mesh size and the number of unknowns. The theory has been presented in an abstract setting which allows the application to both finite element and finite difference methods. CopyrightВ©1996 Elsevier Science Ltd. All rights reserved.
Scopus
Держатели документа:
Computing Center, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович
Engineering, Multidisciplinary
A35
A35
Algebraic approach to the analysis of linear static systems with interval uncertainty
/ S. P. Shary // Russ. J. Numer. Anal. Math. Model. - 1996. - Vol. 11, Is. 3. - P259-274, DOI 10.1515/rnam.1996.11.3.259. - Cited References: 19
. - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied
Аннотация: We propose a new algebraic approach to the analysis of linear static systems with interval uncertainty. Its mathematical basis is replacement of the original problem by a problem of seeking the algebraic interval solution of an auxiliary system of equations in Kaucher extended interval arithmetic. We investigate the existence and uniqueness of algebraic interval solutions, develop some computational algorithms for obtaining them (in particular, Newton's subdifferential method), and prove the convergence of these algorithms.
WOS,
Scopus
Держатели документа:
Computer Center, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shary, S.P.; Шарый С.П.
Аннотация: We propose a new algebraic approach to the analysis of linear static systems with interval uncertainty. Its mathematical basis is replacement of the original problem by a problem of seeking the algebraic interval solution of an auxiliary system of equations in Kaucher extended interval arithmetic. We investigate the existence and uniqueness of algebraic interval solutions, develop some computational algorithms for obtaining them (in particular, Newton's subdifferential method), and prove the convergence of these algorithms.
WOS,
Scopus
Держатели документа:
Computer Center, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shary, S.P.; Шарый С.П.
Engineering, Multidisciplinary
H99
H99
Information technology of mathematical modelling of a three-dimensional supersonic flow on the basis of particular solutions of hydrodynamic problems
/ V. A. Shchepanovskii // Russ. J. Numer. Anal. Math. Model. - 1997. - Vol. 12, Is. 4. - P373-397, DOI 10.1515/rnam.1997.12.4.373. - Cited References: 47
. - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied
Аннотация: We propose the formalized methods of mathematical modelling of a three-dimensional supersonic flow on the basis of solutions of smaller dimensionality. We separate a base algorithm for constructing the solution and derive an equation for the streamlined space surface. We introduce concrete techniques, viz. the procedures of superposition, completion, and convergence. We construct test forms for debugging the multidimensional computational algorithms and study various parts of hypersonic aircraft.
WOS,
Scopus
Держатели документа:
Computer Center, Siberian Br. Russ. Acad. of Sci., Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shchepanovskii, V.A.; Щепановский, Владимир Александрович
Аннотация: We propose the formalized methods of mathematical modelling of a three-dimensional supersonic flow on the basis of solutions of smaller dimensionality. We separate a base algorithm for constructing the solution and derive an equation for the streamlined space surface. We introduce concrete techniques, viz. the procedures of superposition, completion, and convergence. We construct test forms for debugging the multidimensional computational algorithms and study various parts of hypersonic aircraft.
WOS,
Scopus
Держатели документа:
Computer Center, Siberian Br. Russ. Acad. of Sci., Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shchepanovskii, V.A.; Щепановский, Владимир Александрович
The evolution of the thermocapillary motion of three fluids in a plane layer
[Text] : статья / V. K. Andreev, Ye. N. Lemeshkhova // PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS. - 2014. - Vol. 78, Iss. 4. - p. 341-347DOI 10.1016/j.jappmathmech.2014.12.004
. -
Аннотация: The unidirectional motion of three immiscible incompressible viscous heat-conducting liquids in a plane layer is considered. It is assumed that the motion occurs only under the action of thermocapillary forces from a state of rest. The analysis of the motion is reduced to solving linear conjugate initial boundary value problems for a system of parabolic equations. A non-stationary solution is sought by the Laplace transformation method and is obtained in the form of finite analytical expressions in transforms. It is proved that, as the time increases, the solution always reaches the steady state obtained earlier and an exponential estimate of the rate of convergence is given with an indicator which depends on the physical properties of the media and the layer thicknesses. The evolution of the velocity and temperature perturbation fields to a steady state for specific liquid media is obtained by numerical inversion of the Laplace transformation. (C) 2015 Elsevier Ltd. All rights reserved.
Доп.точки доступа:
Lemeshkhova, Ye.N.; Лемешкова, Елена Николаевна; Андреев, Виктор Константинович
Аннотация: The unidirectional motion of three immiscible incompressible viscous heat-conducting liquids in a plane layer is considered. It is assumed that the motion occurs only under the action of thermocapillary forces from a state of rest. The analysis of the motion is reduced to solving linear conjugate initial boundary value problems for a system of parabolic equations. A non-stationary solution is sought by the Laplace transformation method and is obtained in the form of finite analytical expressions in transforms. It is proved that, as the time increases, the solution always reaches the steady state obtained earlier and an exponential estimate of the rate of convergence is given with an indicator which depends on the physical properties of the media and the layer thicknesses. The evolution of the velocity and temperature perturbation fields to a steady state for specific liquid media is obtained by numerical inversion of the Laplace transformation. (C) 2015 Elsevier Ltd. All rights reserved.
Доп.точки доступа:
Lemeshkhova, Ye.N.; Лемешкова, Елена Николаевна; Андреев, Виктор Константинович
A Fitted Finite Volume Method for Unit-linked Policy with Surrender Option
[Text] : научное издание / S. Chang [et al.] // Computational Research. - 2014. - Vol. 2, Is. 3. - p. 49-53DOI 10.13189/cr.2014.020303
. -
Кл.слова (ненормированные):
Insurance -- Unit-linked Policy -- Power Penalty Method -- Finite Volume Method
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.
Полный текст на сайте правообладателя
Доп.точки доступа:
Chang, Shuhua; Добронец, Борис Станиславович; Fang, Zhiwei; Liu, Xin; Shaydurov, V.V.; Шайдуров, Владимир Викторович
Кл.слова (ненормированные):
Insurance -- Unit-linked Policy -- Power Penalty Method -- Finite Volume Method
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.
Полный текст на сайте правообладателя
Доп.точки доступа:
Chang, Shuhua; Добронец, Борис Станиславович; Fang, Zhiwei; Liu, Xin; Shaydurov, V.V.; Шайдуров, Владимир Викторович
Superconvergence of some linear and quadratic functionals for higher-order finite elements
/ 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
. -
Кл.слова (ненормированные):
Bogner-Fox-Schmit element -- Convergence order -- Dual problems -- Finite element method -- Hermite finite elements -- Output functional -- Finite difference method -- Poisson equation -- Bogner-Fox-Schmit element -- Convergence order -- Dual problem -- Hermite finite elements -- Output functional -- Finite element method
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.
Scopus,
WOS
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
Кл.слова (ненормированные):
Bogner-Fox-Schmit element -- Convergence order -- Dual problems -- Finite element method -- Hermite finite elements -- Output functional -- Finite difference method -- Poisson equation -- Bogner-Fox-Schmit element -- Convergence order -- Dual problem -- Hermite finite elements -- Output functional -- Finite element method
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.
Scopus,
WOS
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
A Study of (m,k)-methods for solving differential-algebraic systems of index 1
/ A. I. Levykin, E. A. Novikov // Communications in Computer and Information Science . - 2015. - Vol. 549: 8th International Conference on Mathematical Modeling of Technological Processes, CITech 2015; Almaty; Kazakhstan; 24 September 2015 through 27 September 2015; Code 159049. - P94-107, DOI 10.1007/978-3-319-25058-8_10
. -
Кл.слова (ненормированные):
Differential-algebraic systems of index 1 -- Numerical methods -- Stiff systems -- Differential equations -- Initial value problems -- Numerical methods -- Ordinary differential equations -- Differential algebraic systems -- Implicit systems -- Numerical solution -- Order conditions -- Schemes optimal -- Stiff systems -- Algebra
Аннотация: A class (m,k)-methods is discussed for the numerical solution of the initial value problems for implicit systems of ordinary differential equations. The order conditions and convergence of the numerical solution in the case of implementation of the scheme with the time-lagging of matrices derivatives for systems of index 1 are obtained. At k ? 4 the order conditions are studied and schemes optimal computing costs are obtained. © Springer International Publishing Switzerland 2015.
Scopus
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics, Academy of Sciences, Siberian Branch, pr. Ak. Lavrent’eva 6, Akademgorodok, Novosibirsk, Russian Federation
Institute of Computational Modeling, Academy of Sciences, Siberian Branch, Akademgorodok 50, Str. 4, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Novikov, E. A.; Новиков, Евгений Александрович
Кл.слова (ненормированные):
Differential-algebraic systems of index 1 -- Numerical methods -- Stiff systems -- Differential equations -- Initial value problems -- Numerical methods -- Ordinary differential equations -- Differential algebraic systems -- Implicit systems -- Numerical solution -- Order conditions -- Schemes optimal -- Stiff systems -- Algebra
Аннотация: A class (m,k)-methods is discussed for the numerical solution of the initial value problems for implicit systems of ordinary differential equations. The order conditions and convergence of the numerical solution in the case of implementation of the scheme with the time-lagging of matrices derivatives for systems of index 1 are obtained. At k ? 4 the order conditions are studied and schemes optimal computing costs are obtained. © Springer International Publishing Switzerland 2015.
Scopus
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics, Academy of Sciences, Siberian Branch, pr. Ak. Lavrent’eva 6, Akademgorodok, Novosibirsk, Russian Federation
Institute of Computational Modeling, Academy of Sciences, Siberian Branch, Akademgorodok 50, Str. 4, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Novikov, E. A.; Новиков, Евгений Александрович
Longwave stability of two-layer fluid flow in the inclined plane
/ V. B. Bekezhanova, A. V. Rodionova // Fluid Dyn. - 2015. - Vol. 50, Is. 6. - P723-736, DOI 10.1134/S0015462815060010
. - ISSN 0015-4628
Кл.слова (ненормированные):
interface -- spectrum of characteristic perturbations -- stability -- Capillary flow -- Convergence of numerical methods -- Eigenvalues and eigenfunctions -- Fluid dynamics -- Interfaces (materials) -- Machinery -- Inclined planes -- Long-wave stabilities -- Oscillatory regimes -- Spectral problem -- spectrum of characteristic perturbations -- Thermocapillary flow -- Two layer fluid -- Zeroth approximations -- Flow of fluids
Аннотация: The exact invariantOstroumov–Birikh solution of the Oberbeck–Bussinesq equationswhich describes two-layer advective thermocapillary flows in the inclined plane is analyzed. The spectrum of the characteristic perturbations of all classes of the flows is investigated and analytical representations of the eigennumbers and eigenfunctions of the corresponding spectral problem are obtained in the zeroth approximation. Stability of the flows with respect to longwave perturbations and the possibility of existence of oscillatory regimes are proved. © 2015, Pleiades Publishing, Ltd.
Scopus,
WOS
Держатели документа:
Institute of Computational Modelling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, Krasnoyarsk, Russian Federation
Institute of Mathematics and Basic Informatics of the Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Rodionova, A. V.; Бекежанова, Виктория Бахытовна
Кл.слова (ненормированные):
interface -- spectrum of characteristic perturbations -- stability -- Capillary flow -- Convergence of numerical methods -- Eigenvalues and eigenfunctions -- Fluid dynamics -- Interfaces (materials) -- Machinery -- Inclined planes -- Long-wave stabilities -- Oscillatory regimes -- Spectral problem -- spectrum of characteristic perturbations -- Thermocapillary flow -- Two layer fluid -- Zeroth approximations -- Flow of fluids
Аннотация: The exact invariantOstroumov–Birikh solution of the Oberbeck–Bussinesq equationswhich describes two-layer advective thermocapillary flows in the inclined plane is analyzed. The spectrum of the characteristic perturbations of all classes of the flows is investigated and analytical representations of the eigennumbers and eigenfunctions of the corresponding spectral problem are obtained in the zeroth approximation. Stability of the flows with respect to longwave perturbations and the possibility of existence of oscillatory regimes are proved. © 2015, Pleiades Publishing, Ltd.
Scopus,
WOS
Держатели документа:
Institute of Computational Modelling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, Krasnoyarsk, Russian Federation
Institute of Mathematics and Basic Informatics of the Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Rodionova, A. V.; Бекежанова, Виктория Бахытовна
Вопросы сходимости конечно-элементных оценок напряженного состояния силовых конструкций с концентраторами напряжений
[Текст] : статья / А. Н. Рогалев, С. В. Доронин // Современные технологии. Системный анализ. Моделирование. - 2015. - № 1. - С. 8-13
. - ISSN 1813-9108
Перевод заглавия: ISSUES OF CONVERGENCE OF THE FINITE ELEMENT ESTIMATIONS OF STRESS STATE OF LOAD-BEARING STRUCTURES WITH STRESS CONCENTRATORS
Кл.слова (ненормированные):
силовые конструкции -- load-bearing structures -- Numerical solutions -- stress concentration -- Numerical convergence -- technical stability -- численные решения -- концентрация напряжений -- численная сходимость -- техническая устойчивость
Аннотация: Практическая деятельность по решению задач анализа напряженного состояния силовых конструкций с концентраторами напряжений требует развития численных методов моделирования элементов конструкций в области зон высоких градиентов напряжений, обусловленных, в частности, конструктивными концентраторами. Показано, что для геометрически сложных элементов конструкций широко применяемые подходы к реализации метода конечных элементов не гарантируют сходимости численного решения. В статье рассматриваются задачи, связанные с вопросами надежности вычислений с помощью метода конечных элементов. Они зависят как от надежности математической постановки задачи, так и от точности численного решения поставленной задачи. Рассматриваются практические приемы оценки погрешности вычислений. В качестве перспективных путей обеспечения сходимости и достоверности результатов моделирования предлагаются подходы теории технической устойчивости дифференциальных уравнений, специальные вычислительные процедуры, применяемые на стадиях пре- и постпроцессинга.
Practical activity for solving problems of analysis of stress state of load-bearing structures with stress concentrators demands developing numerical methods for simulating high gradient stress zones of structural elements due to structural concentrators. It is shown that widely used approaches to finite element method realization do not make sure convergence for numerical solution for geometrically complex structural elements. The paper is dedicated to problems associated with reliability of calculations by means of finite element method. They depend on validity of mathematical problem definition and adequacy of numerical solution of given problem. Practical techniques for calculating errors assessment are discussed. In the capacity of perspective path to guaranteeing convergence and validity of simulation results approaches of theory for differential equations technical stability and special computational procedures on pre and post processing stages are proposed.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
СКТБ «Наука» КНЦ СО РАН
Доп.точки доступа:
Доронин, Сергей Владимирович; Rogalev A.N.
Перевод заглавия: ISSUES OF CONVERGENCE OF THE FINITE ELEMENT ESTIMATIONS OF STRESS STATE OF LOAD-BEARING STRUCTURES WITH STRESS CONCENTRATORS
Кл.слова (ненормированные):
силовые конструкции -- load-bearing structures -- Numerical solutions -- stress concentration -- Numerical convergence -- technical stability -- численные решения -- концентрация напряжений -- численная сходимость -- техническая устойчивость
Аннотация: Практическая деятельность по решению задач анализа напряженного состояния силовых конструкций с концентраторами напряжений требует развития численных методов моделирования элементов конструкций в области зон высоких градиентов напряжений, обусловленных, в частности, конструктивными концентраторами. Показано, что для геометрически сложных элементов конструкций широко применяемые подходы к реализации метода конечных элементов не гарантируют сходимости численного решения. В статье рассматриваются задачи, связанные с вопросами надежности вычислений с помощью метода конечных элементов. Они зависят как от надежности математической постановки задачи, так и от точности численного решения поставленной задачи. Рассматриваются практические приемы оценки погрешности вычислений. В качестве перспективных путей обеспечения сходимости и достоверности результатов моделирования предлагаются подходы теории технической устойчивости дифференциальных уравнений, специальные вычислительные процедуры, применяемые на стадиях пре- и постпроцессинга.
Practical activity for solving problems of analysis of stress state of load-bearing structures with stress concentrators demands developing numerical methods for simulating high gradient stress zones of structural elements due to structural concentrators. It is shown that widely used approaches to finite element method realization do not make sure convergence for numerical solution for geometrically complex structural elements. The paper is dedicated to problems associated with reliability of calculations by means of finite element method. They depend on validity of mathematical problem definition and adequacy of numerical solution of given problem. Practical techniques for calculating errors assessment are discussed. In the capacity of perspective path to guaranteeing convergence and validity of simulation results approaches of theory for differential equations technical stability and special computational procedures on pre and post processing stages are proposed.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
СКТБ «Наука» КНЦ СО РАН
Доп.точки доступа:
Доронин, Сергей Владимирович; Rogalev A.N.
519.63+539.313
А 64
А 64
Анализ конечно-элементных оценок напряженного состояния силовых конструкций с концентраторами напряжений
[Текст] : статья / С. В. Доронин, А. Н. Рогалев, Е. М. Рейзмунт // Современные технологии. Системный анализ. Моделирование. - 2015. - № 2. - С. 26-31
. - ISSN 1813-9108
Перевод заглавия: ANALYSIS OF THE FINITE ELEMENT ESTIMATIONS OF STRESS STATE OF LOAD-BEARING STRUCTURES WITH STRESS CONCENTRATORS
Кл.слова (ненормированные):
силовые конструкции -- load-bearing structures -- Numerical solutions -- stress concentration -- Numerical convergence -- численные решения -- концентрация напряжений -- численная сходимость
Аннотация: Концентрация напряжения в элементах силовых конструкций является одним из основных факторов их прочности, живучести, техногенной безопасности. Несмотря на значительные успехи в области исследования природы и влияния концентрации напряжений на конструкционную прочность, накопленные аналитические, численные, экспериментальные данные не могут охватить все многообразие конструктивных форм и условий нагружения конструкций. Наиболее распространенным в настоящее время является численный подход к анализу концентрации напряжений, реализуемый чаще всего с использованием коммерческих пакетов конечно-элементного анализа. В этом случае принципиальное значение имеет удовлетворение требованиям точности и достоверности результатов моделирования. Опыт численного исследования напряженного состояния в области концентраторов напряжений свидетельствует о многочисленных случаях нарушения этих требований, возникающих вследствие проблем со сходимостью и устойчивостью численных решений. В настоящей работе рассматриваются конечно-элементные решения ряда элементов конструкций с концентраторами напряжений, не удовлетворяющие требованиям сходимости, и анализируются возможные причины возникающих ошибок.
Stress concentration in load-bearing structures elements is one of the main factors of their strength, survivability, safety. In spite of considerable advances of investigations for nature of stress concentration and its influence on structural strength accumulated analytic, numerical, experimental data can’t cover all diversity of structural forms and loading conditions. The numerical approach for analysing stress concentration with the help of commercial finite-element software is the most widely-spread at present. In this case meeting requirements of accuracy and reliability of simulation data is of fundamental importance. The experience of numerical investigation for stress state of structural elements with stress concentrators demonstrates numerous cases of violation of these requirements due to difficulties with convergence and stability of numerical solutions. In this paper finite-element solutions for stress concentrators which are not meeting requirements of convergence are discussed and possible reasons of errors are analysed.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
СКТБ «Наука» КНЦ СО РАН
Доп.точки доступа:
Рогалев, Алексей Николаевич; Rogalev A.N.; Рейзмунт, Елена Михайловна; Reizmunt E.M.
Перевод заглавия: ANALYSIS OF THE FINITE ELEMENT ESTIMATIONS OF STRESS STATE OF LOAD-BEARING STRUCTURES WITH STRESS CONCENTRATORS
| УДК |
Кл.слова (ненормированные):
силовые конструкции -- load-bearing structures -- Numerical solutions -- stress concentration -- Numerical convergence -- численные решения -- концентрация напряжений -- численная сходимость
Аннотация: Концентрация напряжения в элементах силовых конструкций является одним из основных факторов их прочности, живучести, техногенной безопасности. Несмотря на значительные успехи в области исследования природы и влияния концентрации напряжений на конструкционную прочность, накопленные аналитические, численные, экспериментальные данные не могут охватить все многообразие конструктивных форм и условий нагружения конструкций. Наиболее распространенным в настоящее время является численный подход к анализу концентрации напряжений, реализуемый чаще всего с использованием коммерческих пакетов конечно-элементного анализа. В этом случае принципиальное значение имеет удовлетворение требованиям точности и достоверности результатов моделирования. Опыт численного исследования напряженного состояния в области концентраторов напряжений свидетельствует о многочисленных случаях нарушения этих требований, возникающих вследствие проблем со сходимостью и устойчивостью численных решений. В настоящей работе рассматриваются конечно-элементные решения ряда элементов конструкций с концентраторами напряжений, не удовлетворяющие требованиям сходимости, и анализируются возможные причины возникающих ошибок.
Stress concentration in load-bearing structures elements is one of the main factors of their strength, survivability, safety. In spite of considerable advances of investigations for nature of stress concentration and its influence on structural strength accumulated analytic, numerical, experimental data can’t cover all diversity of structural forms and loading conditions. The numerical approach for analysing stress concentration with the help of commercial finite-element software is the most widely-spread at present. In this case meeting requirements of accuracy and reliability of simulation data is of fundamental importance. The experience of numerical investigation for stress state of structural elements with stress concentrators demonstrates numerous cases of violation of these requirements due to difficulties with convergence and stability of numerical solutions. In this paper finite-element solutions for stress concentrators which are not meeting requirements of convergence are discussed and possible reasons of errors are analysed.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
СКТБ «Наука» КНЦ СО РАН
Доп.точки доступа:
Рогалев, Алексей Николаевич; Rogalev A.N.; Рейзмунт, Елена Михайловна; Reizmunt E.M.
539.3
К 65
К 65
Контроль точности решения при анализе напряженно-деформированного состояния высокоответственных технических объектов
[Текст] : статья / А. Н. Рогалев, С. В. Доронин, А. А. Рогалев // Системы. Методы. Технологии. - 2015. - № 3. - С. 32-38
. - ISSN 2077-5415
Перевод заглавия: Solution accuracy control for analysis of stress-strain state of critical technical objects
Кл.слова (ненормированные):
вычислительная ошибка -- матрица жесткости -- моделирование -- система линейных алгебраических уравнений -- контроль точности -- Numerical error -- Stiffness matrix -- modeling -- System of linear equations -- accuracy control
Аннотация: В статье рассматриваются подходы к оценке вычислительной ошибки при решении системы линейных алгебраических уравнений, в качестве матрицы коэффициентов которой рассматривается матрица жесткости конечно-элементной модели технического объекта. Предлагаемый подход предполагает, что уровень вычислительной ошибки определяется структурой и значениями матрицы коэффициентов, и заключается в численном решении системы линейных уравнений с матрицей жесткости и такой специально подобранной правой частью, для которой известно точное решение. Сравнение численного и точного решений позволяет получить оценку вычислительной ошибки, позволяющую судить о приемлемости построенной конечно-элементной модели. Получение указанной оценки является дополнительной процедурой контроля точности численного решения при анализе его сходимости путем последовательного уменьшения шага конечных элементов. Развиваемый подход весьма актуален для конструкций ответственных технических объектов, где цена ошибки при проектных расчетах оказывается неприемлемо высокой. Для реализации предлагаемого подхода организован интерфейс между пакетом конечно-элементного моделирования ANSYS и вычислительным пакетом компьютерной алгебры Wolfram Mathematica. В качестве примера приводится получение оценки вычислительной ошибки численного решения системы линейных алгебраических уравнений с матрицей жесткости силовой конструкции бака высокого давления для перспективных электрореактивных двигателей космических аппаратов. Силовая конструкция представляет собой оболочку давления, подвешенную на системе вантов с регулируемым уровнем натяжения, закрепленных, в свою очередь, на пространственной стержневой системе - силовой структуре корпуса космического аппарата. Для рассматриваемой конструкции найден уровень конечно-элементной дискретизации, обеспечивающий сходимость численного решения.
The paper is devoted to approaches to a problem of numerical error evaluation when solving the system of linear equations. The stiffness matrix of a finite-element model of a technical object is a coefficient matrix of the system of linear equations. The approach proposed supposes that the level of numerical error is determined by a structure and magnitude of coefficient matrix. The approach consists of numerical solving system of linear equations with stiffness matrix and special right-hand member with exact solution known. Comparison of numerical and exact solutions allows evaluating numerical error and making decision on the quality of finite-element model. Evaluation numerical error is a supplementary procedure for checking accuracy of numerical solution within solution convergence analysis by means of cascade reduction mesh spacing. The approach is of great actuality for structures of critical technical objects with great worth of design calculations error. To implement the approach, data interface between the finite-element analysis package ANSYS and computer algebra package Wolfram Mathematica has been created. Evaluated numerical error has been given as an example for numerical solution system of linear equations with stiffness matrix for load-bearing unit of high pressure tank for perspective spacecraft electrojet engines. The load-bearing unit consists of pressure shell suspended by means of cable system with controlled tension. The cable system is attached to spatial bar system - load-bearing frame structure of spacecraft. For the structures considered the level of finite-element discretization has been determined to provide numerical solution convergence.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Институт космических и информационных технологий Сибирского федерального университета
Специальное конструкторско-технологическое бюро «Наука» Красноярского научного центра СО РАН
Доп.точки доступа:
Доронин, С.В.; Doronin S.V.; Рогалев, А.А.; Rogalyov A.A.; Rogalyov A.N.
Перевод заглавия: Solution accuracy control for analysis of stress-strain state of critical technical objects
| УДК |
Кл.слова (ненормированные):
вычислительная ошибка -- матрица жесткости -- моделирование -- система линейных алгебраических уравнений -- контроль точности -- Numerical error -- Stiffness matrix -- modeling -- System of linear equations -- accuracy control
Аннотация: В статье рассматриваются подходы к оценке вычислительной ошибки при решении системы линейных алгебраических уравнений, в качестве матрицы коэффициентов которой рассматривается матрица жесткости конечно-элементной модели технического объекта. Предлагаемый подход предполагает, что уровень вычислительной ошибки определяется структурой и значениями матрицы коэффициентов, и заключается в численном решении системы линейных уравнений с матрицей жесткости и такой специально подобранной правой частью, для которой известно точное решение. Сравнение численного и точного решений позволяет получить оценку вычислительной ошибки, позволяющую судить о приемлемости построенной конечно-элементной модели. Получение указанной оценки является дополнительной процедурой контроля точности численного решения при анализе его сходимости путем последовательного уменьшения шага конечных элементов. Развиваемый подход весьма актуален для конструкций ответственных технических объектов, где цена ошибки при проектных расчетах оказывается неприемлемо высокой. Для реализации предлагаемого подхода организован интерфейс между пакетом конечно-элементного моделирования ANSYS и вычислительным пакетом компьютерной алгебры Wolfram Mathematica. В качестве примера приводится получение оценки вычислительной ошибки численного решения системы линейных алгебраических уравнений с матрицей жесткости силовой конструкции бака высокого давления для перспективных электрореактивных двигателей космических аппаратов. Силовая конструкция представляет собой оболочку давления, подвешенную на системе вантов с регулируемым уровнем натяжения, закрепленных, в свою очередь, на пространственной стержневой системе - силовой структуре корпуса космического аппарата. Для рассматриваемой конструкции найден уровень конечно-элементной дискретизации, обеспечивающий сходимость численного решения.
The paper is devoted to approaches to a problem of numerical error evaluation when solving the system of linear equations. The stiffness matrix of a finite-element model of a technical object is a coefficient matrix of the system of linear equations. The approach proposed supposes that the level of numerical error is determined by a structure and magnitude of coefficient matrix. The approach consists of numerical solving system of linear equations with stiffness matrix and special right-hand member with exact solution known. Comparison of numerical and exact solutions allows evaluating numerical error and making decision on the quality of finite-element model. Evaluation numerical error is a supplementary procedure for checking accuracy of numerical solution within solution convergence analysis by means of cascade reduction mesh spacing. The approach is of great actuality for structures of critical technical objects with great worth of design calculations error. To implement the approach, data interface between the finite-element analysis package ANSYS and computer algebra package Wolfram Mathematica has been created. Evaluated numerical error has been given as an example for numerical solution system of linear equations with stiffness matrix for load-bearing unit of high pressure tank for perspective spacecraft electrojet engines. The load-bearing unit consists of pressure shell suspended by means of cable system with controlled tension. The cable system is attached to spatial bar system - load-bearing frame structure of spacecraft. For the structures considered the level of finite-element discretization has been determined to provide numerical solution convergence.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Институт космических и информационных технологий Сибирского федерального университета
Специальное конструкторско-технологическое бюро «Наука» Красноярского научного центра СО РАН
Доп.точки доступа:
Доронин, С.В.; Doronin S.V.; Рогалев, А.А.; Rogalyov A.A.; Rogalyov A.N.
The joint creeping motion of three viscid liquids in a plane layer: A priori estimates and convergence to steady flow
/ V. K. Andreev, N. Cheremnykh // J. Appl. Ind. Math. - 2016. - Vol. 10, Is. 1. - P7-20, DOI 10.1134/S1990478916010026
. - ISSN 1990-4789
Кл.слова (ненормированные):
a priori estimates -- asymptotic behavior -- conjugate initial-boundary value problem -- thermocapillarity -- Boundary value problems -- Estimation -- Heat conduction -- Initial value problems -- Liquids -- Nonlinear equations -- A-priori estimates -- Asymptotic behaviors -- Conducting liquid -- Immiscible liquids -- Initial-boundary value problems -- Invariant solutions -- Non-linear inverse problem -- Thermocapillarity -- Inverse problems
Аннотация: We study a partially invariant solution of rank 2 and defect 3 of the equations of a viscid heat-conducting liquid. It is interpreted as a two-dimensional motion of three immiscible liquids in a flat channel bounded by fixed solid walls, the temperature distribution on which is known. From a mathematical point of view, the resulting initial-boundary value problem is a nonlinear inverse problem. Under some assumptions (often valid in practical applications), the problem can be replaced by a linear problem. For the latter we obtain some a priori estimates, find an exact steady solution, and prove that the solution approaches the steady regime as time increases, provided that the temperature on the walls stabilizes. © 2016, Pleiades Publishing, Ltd.
Scopus
Держатели документа:
Institute of Computational Modelling, Akademgorodok 50, bld. 44, Krasnoyarsk, Russian Federation
Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Cheremnykh, N.
Кл.слова (ненормированные):
a priori estimates -- asymptotic behavior -- conjugate initial-boundary value problem -- thermocapillarity -- Boundary value problems -- Estimation -- Heat conduction -- Initial value problems -- Liquids -- Nonlinear equations -- A-priori estimates -- Asymptotic behaviors -- Conducting liquid -- Immiscible liquids -- Initial-boundary value problems -- Invariant solutions -- Non-linear inverse problem -- Thermocapillarity -- Inverse problems
Аннотация: We study a partially invariant solution of rank 2 and defect 3 of the equations of a viscid heat-conducting liquid. It is interpreted as a two-dimensional motion of three immiscible liquids in a flat channel bounded by fixed solid walls, the temperature distribution on which is known. From a mathematical point of view, the resulting initial-boundary value problem is a nonlinear inverse problem. Under some assumptions (often valid in practical applications), the problem can be replaced by a linear problem. For the latter we obtain some a priori estimates, find an exact steady solution, and prove that the solution approaches the steady regime as time increases, provided that the temperature on the walls stabilizes. © 2016, Pleiades Publishing, Ltd.
Scopus
Держатели документа:
Institute of Computational Modelling, Akademgorodok 50, bld. 44, Krasnoyarsk, Russian Federation
Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Cheremnykh, N.
Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density
/ I. I. Ryzhkov, A. V. Minakov // J. Membr. Sci. - 2016. - Vol. 520. - P515-628, DOI 10.1016/j.memsci.2016.08.004
. - ISSN 0376-7388
Кл.слова (ненормированные):
Charged membranes -- Electrolyte transport -- Interfacial effects -- Nanofiltration -- Numerical modeling -- Aspect ratio -- Charge density -- Diffusion -- Electrolytes -- Ions -- Nanofiltration -- Nanopores -- Navier Stokes equations -- Numerical models -- Surface potential -- Charged membranes -- Diffusion and migration -- Electrolyte transport -- Interfacial effects -- Ion concentrations -- Membrane potentials -- Smooth approximation -- Volume charge density -- Nanofiltration membranes
Аннотация: The pressure–driven electrolyte transport through nanofiltration membrane pores with constant surface potential or charge density is investigated theoretically. Two approaches are employed in the study. The first one is based on one–dimensional Nernst–Planck equation coupled with electroneutrality, zero current, and Donnan equilibrium conditions. This model is extended to account for interfacial effects by using a smooth approximation of step function for the volume charge density. The second approach is based on two–dimensional Nernst–Planck, Poisson, and Navier–Stokes equations, which are solved in a high aspect ratio nanopore connecting two reservoirs with much larger diameter. The modification of equations on the basis of Slotboom transformation is employed to speed up the convergence rate. The distributions of potential, pressure, ion concentrations and fluxes due to convection, diffusion, and migration in the nanopore and reservoirs are discussed and analyzed. It is found that for constant surface charge density, the convective flux of counter–ions in the nanopore is almost completely balanced by the opposite migration flux, while for constant surface potential, the convective flux is balanced by the opposite diffusion and migration fluxes. The co–ions in the nanopore are mainly transported by diffusion. A particular attention is focused on describing the interfacial effects at the nanopore entrance/exit. Detailed comparison between one– and two–dimensional models is performed in terms of rejection, pressure drop, and membrane potential dependence on the surface potential/charge density, volume flux, ion concentration, and pore radius. A good agreement between these models is found when the Debye length is smaller than the pore radius and the surface potential or charge density are sufficiently low. © 2016 Elsevier B.V.
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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Siberian Federal University, Svobodny 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Minakov, A. V.; Рыжков, Илья Игоревич
Кл.слова (ненормированные):
Charged membranes -- Electrolyte transport -- Interfacial effects -- Nanofiltration -- Numerical modeling -- Aspect ratio -- Charge density -- Diffusion -- Electrolytes -- Ions -- Nanofiltration -- Nanopores -- Navier Stokes equations -- Numerical models -- Surface potential -- Charged membranes -- Diffusion and migration -- Electrolyte transport -- Interfacial effects -- Ion concentrations -- Membrane potentials -- Smooth approximation -- Volume charge density -- Nanofiltration membranes
Аннотация: The pressure–driven electrolyte transport through nanofiltration membrane pores with constant surface potential or charge density is investigated theoretically. Two approaches are employed in the study. The first one is based on one–dimensional Nernst–Planck equation coupled with electroneutrality, zero current, and Donnan equilibrium conditions. This model is extended to account for interfacial effects by using a smooth approximation of step function for the volume charge density. The second approach is based on two–dimensional Nernst–Planck, Poisson, and Navier–Stokes equations, which are solved in a high aspect ratio nanopore connecting two reservoirs with much larger diameter. The modification of equations on the basis of Slotboom transformation is employed to speed up the convergence rate. The distributions of potential, pressure, ion concentrations and fluxes due to convection, diffusion, and migration in the nanopore and reservoirs are discussed and analyzed. It is found that for constant surface charge density, the convective flux of counter–ions in the nanopore is almost completely balanced by the opposite migration flux, while for constant surface potential, the convective flux is balanced by the opposite diffusion and migration fluxes. The co–ions in the nanopore are mainly transported by diffusion. A particular attention is focused on describing the interfacial effects at the nanopore entrance/exit. Detailed comparison between one– and two–dimensional models is performed in terms of rejection, pressure drop, and membrane potential dependence on the surface potential/charge density, volume flux, ion concentration, and pore radius. A good agreement between these models is found when the Debye length is smaller than the pore radius and the surface potential or charge density are sufficiently low. © 2016 Elsevier B.V.
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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Siberian Federal University, Svobodny 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Minakov, A. V.; Рыжков, Илья Игоревич
New Hermite finite elements on rectangles
/ 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
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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Полный текст (доступен только в ЛВС)
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
Inexact Uzawa conjugate gradient method for the Stokes problem for incompressible fluid
/ E. Dementyeva, E. Karepova, I. Kireev // 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 10.1063/1.4964996
. -
Аннотация: In this paper, the two-dimensional Stokes equations are considered for a viscous incompressible fluid in a channel. To construct a discrete problem, the Taylor-Hood finite elements are used. The obtained system of linear algebraic equations is of the saddle point type and is solved by a modified inexact Uzawa conjugate gradient method. Usually the Uzawa methods are considered for velocity-pressure unknowns. In our version, the problem is formulated in terms of velocity-pressure deviations from the desired saddle point of the discrete problem. This allows one to improve considerably the numerical efficiency of the method. The convergence of the method is studied numerically as well as theoretically. © 2016 Author(s).
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Держатели документа:
Institute of Computational Modelling, SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Kireev, I.; Дементьева, Екатерина Васильевна
Аннотация: In this paper, the two-dimensional Stokes equations are considered for a viscous incompressible fluid in a channel. To construct a discrete problem, the Taylor-Hood finite elements are used. The obtained system of linear algebraic equations is of the saddle point type and is solved by a modified inexact Uzawa conjugate gradient method. Usually the Uzawa methods are considered for velocity-pressure unknowns. In our version, the problem is formulated in terms of velocity-pressure deviations from the desired saddle point of the discrete problem. This allows one to improve considerably the numerical efficiency of the method. The convergence of the method is studied numerically as well as theoretically. © 2016 Author(s).
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Полный текст (доступен только в ЛВС)
Держатели документа:
Institute of Computational Modelling, SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Kireev, I.; Дементьева, Екатерина Васильевна
519.614
О-118
О-118
Ортогонально-степенной метод решения частичной проблемы собственных значений и векторов для симметричной неотрицательно определенной матрицы
[Текст] : статья / И. В. Киреев // Вычислительные методы и программирование: новые вычислительные технологии. - 2016. - Т. 17, № 1. - С. 44-54
. - ISSN 1726-3522
Перевод заглавия: An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
Кл.слова (ненормированные):
собственный вектор -- eigenvector -- eigenvalue -- Conjugate direction method -- Krylov subspaces -- собственное значение -- метод сопряженных направлений -- подпространства Крылова
Аннотация: Предложена и обоснована экономичная версия метода сопряженных направлений для построения нетривиального решения однородной системы линейных алгебраических уравнений с вырожденной симметричной неотрицательно определенной квадратной матрицей. Предложено однопараметрическое семейство одношаговых нелинейных итерационных процессов вычисления собственного вектора, отвечающего наибольшему собственному значению симметричной неотрицательно определенной квадратной матрицы. Это семейство включает в себя степенной метод как частный случай. Доказана сходимость возникающих последовательностей векторов к собственному вектору, ассоциированному с наибольшим характеристическим числом матрицы. Предложена двухшаговая процедура ускорения сходимости итераций этих процессов, в основе которой лежит ортогонализация в подпространстве Крылова. Приведены результаты численных экспериментов.
An efficient version of the conjugate direction method to find a nontrivial solution of a homogeneous system of linear algebraic equations with a singular symmetric nonnegative definite square matrix is proposed and substantiated. A one-parameter family of one-step nonlinear iterative processes to determine the eigenvector corresponding to the largest eigenvalue of a symmetric nonnegative definite square matrix is also proposed. This family includes the power method as a special case. The convergence of corresponding vector sequences to the eigenvector associated with the largest eigenvalue of the matrix is proved. A two-step procedure is formulated to accelerate the convergence of iterations for these processes. This procedure is based on the orthogonalization in Krylov subspaces. A number of numerial results are discussed.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Kireev I.V.
Перевод заглавия: An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
| УДК |
Кл.слова (ненормированные):
собственный вектор -- eigenvector -- eigenvalue -- Conjugate direction method -- Krylov subspaces -- собственное значение -- метод сопряженных направлений -- подпространства Крылова
Аннотация: Предложена и обоснована экономичная версия метода сопряженных направлений для построения нетривиального решения однородной системы линейных алгебраических уравнений с вырожденной симметричной неотрицательно определенной квадратной матрицей. Предложено однопараметрическое семейство одношаговых нелинейных итерационных процессов вычисления собственного вектора, отвечающего наибольшему собственному значению симметричной неотрицательно определенной квадратной матрицы. Это семейство включает в себя степенной метод как частный случай. Доказана сходимость возникающих последовательностей векторов к собственному вектору, ассоциированному с наибольшим характеристическим числом матрицы. Предложена двухшаговая процедура ускорения сходимости итераций этих процессов, в основе которой лежит ортогонализация в подпространстве Крылова. Приведены результаты численных экспериментов.
An efficient version of the conjugate direction method to find a nontrivial solution of a homogeneous system of linear algebraic equations with a singular symmetric nonnegative definite square matrix is proposed and substantiated. A one-parameter family of one-step nonlinear iterative processes to determine the eigenvector corresponding to the largest eigenvalue of a symmetric nonnegative definite square matrix is also proposed. This family includes the power method as a special case. The convergence of corresponding vector sequences to the eigenvector associated with the largest eigenvalue of the matrix is proved. A two-step procedure is formulated to accelerate the convergence of iterations for these processes. This procedure is based on the orthogonalization in Krylov subspaces. A number of numerial results are discussed.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Kireev I.V.