Open Repository of Keldysh Institute of Applied Mathematics of RAS
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MPI+OpenMP implementation of BiCGStab method with factorized explicit preconditioner
No full textAbstract:
A preconditioner for large sparse nonsymmetric positive definite coefficient matrix is considered based on its approximate inverse in the form of product of a lower triangular sparse matrix by an upper triangular matrix. For the class of matrices considered, a new preconditioning based on approximate block Jacobi with incomplete inverse LU-factorization preconditioning is proposed. For parallel implementation of the corresponding preconditioned BiCGStab algorithm, the MPI+OpenMP techniques were used. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning and the Jacobi preconditioning used with the BiCGStab for several test problems from the University of Florida sparse matrix collection are presented.Note:
Research direction:Programming, parallel computing, multimedi
On expansions in Papkovich–Fadle functions in the problem of plate bending
No full textAbstract:
On the example of the boundary value problem of bending of a thin elastic semi-infinite plate in which the long sides are free, while a self-balanced bending moment and a generalized shearing force are specified at its end, the main stages of constructing exact solutions to the boundary value problems of bending of thin elastic rectangular plates are considered. The solution is constructed in the form of series in Papkovich–Fadle eigenfunctions. The unknown expansion coefficients are determined in the same way as in classical periodic solutions in trigonometric series, and have the same structure, i.e. are expressed in terms of the Fourier integrals of the boundary functions given at the end of the half-strip. Herewith the systems of functions that are constructed in the work and that are biorthogonal to the Papkovich–Fadle eigenfunctions are used. The exact solutions have properties that are not inherent in any of the known solutions of plate bending theory. Some of them are discussed in the article. The final formulas describing the exact solution to the boundary value problem are simple and can easily be used in engineering practice. The work is based on the results obtained by the authors earlier in solving boundary value problems of the plane theory of elasticity in a rectangular domain.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Numerical and analytical methods in the problem of marine electrical prospecting in a plane-layered medium
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This paper is of survey and methodological nature. A brief overview of the most common methods of active marine electrical prospecting is given. The problems of effective numerical and analytical solution of Maxwell's equations in the frequency domain are considered for the electrical prospecting on the basis of the classical 1D multilayer model of the medium. The electromagnetic field response in the form of Hankel integrals is received using the approach proposed by K. Key. The effective numerical calculation of integrals by extraction of exponential asymptotics, and separate calculation of terms with different speed of convergence is considered. In this case, the approach of the 'additive scheme' developed by the author is used, in which the solution for a multilayer medium is represented as a sum of solutions for 2-, 3-layer, etc. media. This not only speeds up calculations and improves their accuracy, but is also convenient for parallelization. The analytical solution for the most poorly convergent case of two-layer air-water medium including 'air wave' is constructed. As an example, the results of calculations for the different frequencies, depths of the hydrocarbon layer and thicknesses of the water layer are presented.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Investigation of steady-state motions of Earth artificial satellite in single axis magnetic orientation mode
No full textAbstract:
We investigate the angular motion of an axially symmetric artificial satellite with a permanent magnet in the Earth's magnetic field (EMF). The satellite orbital motion is considered taking into account the influence of the non-centrality of the Earth's gravitational field and the atmosphere drag, IGRF is used as the model of the EMF, the satellite's own magnetic moment is parallel to the axis of symmetry. Steady-state satellite motions are constructed in which this axis forms a small angle with the EMF vector. We approximate such a motion by a sequence of periodic solutions of modified motion equations. These solutions have the orbital period, but the sequence as a whole reproduces almost full spectrum of a steady-state motion including the frequencies relating to the Earth rotation.Note:
Research direction:Theoretical and applied problems of mechanic
Numerical modeling of the characteristic problems of dissociation of gas hydrates in a porous medium. One-dimensional formulation
No full textAbstract:
In the paper some characteristic problems of dissociation of gas hydrates in a porous medium, which in the first approximation can be reduced to one-dimensional, are considered. These tasks include the study of the mutual influence of gas hydrates and climate, as well as important technological and ecological problems of the flow in the well or fault. Calculations using a mathematical model for the joint description of the gas hydrate zone and the zone with no gas hydrates are carried out. The calculation results showed the applicability of the developed methods to solving such problems.Note:
Research direction:Mathematical modelling in actual problems of science and technic
The Works and Party with Dimitry Evgenievich Okhozimsky
No full textAbstract:
Ten years have passed since Dimitry Evgenievich Okhozimsky is no longer with us. About his works and accomplishments are written a lot [1-6]. This paper is about another side of his activity: the initiative of the artistic reflection of the success in the 5th Division Keldysh Institute of Applied Mathematics, the head of which he was. Illustrating short story is about the works of Dimitry Evgenievich and achievements of the 5th Department, posters and drawings are created over the years due to anniversaries and other events of the Department and the Institute. They are made often with the instructions of Dimitry Evgenievich, with his support, active interest and participation. It is the memory of him and communion with him.Note:
Research direction:Theoretical and applied problems of mechanic
Examples of exact solutions for problems of bending plate with free face planes
No full textAbstract:
The paper discusses examples of exact solutions of the boundary problem on the bending of a thin elastic semi-infinite plate, in which the long sides are free, and at the end are self-balanced bending moment and generalized shear force are specified. The solutions are obtained in the form of the series in Papkovich–Fadle eigenfunctions. The unknown expansions coefficients are determined by formulas and are expressed via the Fourier integrals of the boundary functions specified at the plate side.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Towards calculating turbulent flows with the Spalart-Allmaras model by using the LU-SGS-GMRES algorithm
No full textAbstract:
A numerical model for turbulent three-dimensional flows at high Reynolds numbers is considered. The RANS approach based on the turbulence model of Spalart and Allmaras (SA) is used. The method of wall functions for modeling surface friction is implemented. Specifics of the numerical algorithm based on the LU-SGS–GMRES solver, and program implementation of the present numerical model are discussed. Numerical solutions of the compressible viscous gas flow over a flat plate and in an asymmetric diffuser, and also mathematical modeling of the turbulent mixture layer of two compressible flows are carried out to perform verification and validation of the RANS equations with the SA model for turbulence and the method of wall functions for modeling boundary conditions of the “law of wall” type.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Superconducting properties of a nonideal bipolaron gas
No full textAbstract:
The properties of a Bose gas of translation-invariant (TI) bipolarons analogous to Cooper pairs are considered. As in the BCS theory, the description of a TI-bipolaron gas is based on the electron-phonon interaction and Froehlich Hamiltonian. As distinct from the BCS theory, when the correlation length greatly exceeds the mean distance between the pairs, here we deal with the opposite case when the correlation length is much less than the distance between the pairs. We calculate the critical temperature of the transition of a TI-bipolaron Bose-gas into the superconducting state, its energy, heat capacity and heat of the transition. The results obtained are used to explain the experiments on high-temperature superconductors. Possible ways of raising the critical temperature of high-temperature superconductors are discussed.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Simulation of antagonistic conflicts in the third-order cybernetics paradigm
No full textAbstract:
The article presents a new approach to the research of conflict interaction in conditions of high uncertainty of the situation, based on modeling the behavior of intellectual agents. The conflict space is represented in the form of a discrete description of the participants' states and the possibilities of transition between these states when agents perform actions. The principles and examples of a quantitative assessment of the comparative significance of states, as well as the development on their basis of a rational strategy of behavior in the conflict, are presentedNote:
Research direction:Mathematical modelling in actual problems of science and technic