... A renormalized Gaussian approximation in the spin-fluctuation theory" . Melnikov N.B. and Paradezhenko G.V. The effect of spin fluctuations on the magnetic phase transition is studied by the functional integral method. ... A characteristic feature of the Gaussian approximation is the first-order phase transition. In this paper a method is proposed for renormalizing the Gaussian approximation by taking into account the fourth-order terms of the free energy expansion in the fluctuating field. ...
... Application of the low-rank approximation technique in the Gauss elimination method for sparse linear systems" . ... The construction of a low-rank approximation is based on using the adaptive cross approximation (ACA) approach, which is more efficient compared to the SVD and QR methods. ... Keywords: three-dimensional problems of mathematical physics, algorithms for sparse linear systems, Gauss elimination method, low-rank approximation, HSS matrix representation, iterative refinement. ...
... Spatial modeling of water foam dynamics with moving Lagrangian grids under shock wave impact" . Bolotnova R.Kh. and Agisheva U.O. The dynamic processes of wave pulse propagation in an aqueous foam and the air shock wave interaction with the foam barrier are numerically modeled and studied. ... Keywords: pressure pulse, gas-liquid foam, two-phase model, spatial problems, numerical simulation, moving Lagrangian grids, two-phase wave flows. ...
... An exponentially convergent method for solving boundary integral equations on polygons" . Arushanyan I.O. The boundary integral equation of the potential theory in the case of the inner Dirichlet problem for the Laplace operator and the system of boundary integral equations of the Dirichlet boundary value problem for the two-dimensional theory of elasticity in domains with a finite number of corner points are considered. ...
... To the inverse heat conduction problem" . Morozov V.A., Markovskiy A.N., and Lezhnev V.G. An algorithm for the regularization of the inverse heat conduction problem is proposed on the basis of the Fourier method. ... Keywords: inverse heat conduction problem, ill-posed problems, regularization, heat conduction, projection algorithm, complete systems of potentials. ... Morozov V.A. тАУ Research Computing Center, Lomonosov Moscow State University; Leninskie Gory, Moscow, 119992, Russia; Dr. Sci., ...
... Optimization of a partitioning algorithm for a hypergraph with arbitrary weights of vertices" . Rusakov A.S. and Sheblaev M.V. One of the methods for the decomposition of a large problem to subproblems is its representation as a graph or hypergraph and partition this graph to approximately equal subgraphs with minimal cuts. ... Keywords: hypergraph partitioning, Fiduccia-Mattheyses algorithm, clustering, distributed computing systems, parallel programming. ...
... A lattice Monte Carlo model for nanostructure formation analysis" . Karpov A.N., Zverev A.V., Nastovjak A.G., Usenkov S.V., and Shwartz N.L. A kinetic lattice Monte Carlo model of semiconductor nanostructures formation with a diamond-like crystal lattice structure is proposed. ... Keywords: simulation, Monte Carlo method, nanostructures, lattice models, gallium arsenide (GaAs), silicon nanocrystals, gallium nanocrystals. PDF (Full text in Russian, References in English) (814KB) . ...
... Numerical analysis of the FitzHugh-Nagumo model in a three-dimensional domain" . Pavel'chak I.A. The FitzHugh-Nagumo mathematical model of heart excitation is considered in the form of the initial boundary value problem for the evolution system of partial differential equations in a three-dimensional domain that corresponds to the actual geometry of the heart and its ventricles. A numerical analysis of excitation caused by a localized source is performed. ...
... A geometric approach to solving the problem of tracking cyclones and anticyclones" . Ivanov B.N. Initial data for tracking cyclones and anticyclones are the isolines of sea-level pressure and geopotential fields at standard heights. ... The proposed scheme of cyclone and anticyclone identification is of the most common character and is applicable to any type of fields if the isolines of such fields are characterized by their nesting and are stable with time. ...
... New a posteriori error estimates for approximate solutions to iregular operator equations" . Bakushinsky A.B. and Leonov A.S. A brief overview of developed up to date a posteriori error estimates for approximate solutions to irregular operator equations is given. ... In this paper a new method for a posteriori estimates of the accuracy of approximate solutions calculated using the iterative procedures for irregular operator equations is proposed. ...
... Mikhailov E.A. and Modyaev I.I. A problem connected with magnetic fields of galaxies is considered. ... These phenomena are characterized by dimensionless coefficients of the dynamo equations. ... The growth rates of statistical moments of the magnetic field are evaluated. ... The problem that has only a time dependence and the problem that has a spatial dependence are also considered. ... Keywords: galaxy magnetic fields, equations with random coefficients, dynamo theory, intermittency. ...
... Numerical conditioning analysis of two-dimensional problems in electrical impedance tomography" . Gavrilov S.V. A two-dimensional problem of electrical impedance tomography with a piecewise constant electrical conductivity with two known values is considered. ... The numerical conditioning analysis of this problem is performed with a respect to the type and number of electrical potential excitations at the outer boundary. ...
... Modeling of thermal flows in a medium with phase transitions using the lattice Boltzmann method" . Kupershtokh A.L., Medvedev D.A., and Gribanov I.I. A new method is proposed for the computation of heat and mass transfer for the modeling of flow of a medium with liquid-vapor phase transitions using the lattice Boltzmann equations (LBE). ... Keywords: lattice Boltzmann method, phase transitions, dynamics of multiphase fluids, heat and mass transfer, mesoscopic methods, computer simulations. ...
... Application of the duality principle in inverse problems for parabolic equations with unknown right-hand sides" . ... Application of this principle makes it possible to study the uniqueness problem for ill-posed inverse problems in their original formulations in the context of the theory of parabolic equations. Keywords: parabolic equations, inverse problems, adjoint problems, control problems, duality principle, uniqueness theorems, H lder spaces. ...
... Bi-Newton's method for computing spectral projectors" . Demyanko K.V. and Nechepurenko Yu.M. An efficient Newton-like method for computing the spectral projector associated with a separated group of eigenvalues near a specified shift of a large sparse matrix is proposed and justified. ... Keywords: Newton's method, inverse iterations, tuning, invariant subspace, spectral projector. PDF (Full text in Russian, References in English) (246KB) . ...
... Transferring the boundary conditions to the middle surface for the numerical solution of a boundary value problem in the linear wing theory" . ... For the numerical solution of this problem, an approach based on the method of potentials and boundary integral equations is used. The thickness of the wing is taken into account in the formulation of the boundary value problem at the middle surface with transferring the boundary conditions to this surface. ...
... A numerical algorithm for the analysis of viscoelastic waves in the Kelvin-Voigt medium" . Sadovskii V.M. and Sadovskaya O.V. A numerical algorithm for solving dynamic problems in the theory of the viscoelastic Kelvin-Voigt medium is proposed on the basis of Ivanov's method of constructing difference schemes with prescribed dissipative properties. ... The algorithm is tested by solving the problem of traveling surface waves. ... PDF (Full text in Russian, References in English) (753KB) . ...
... Overall supercomputer performance analysis based on system monitoring data" . ... An approach to overall performance analysis, including peculiarities of application runs, assignment of jobs to queues, and total resource utilization of supercomputer systems is proposed. This approach is based on the analysis of system monitoring data and is aimed at providing a number of means for the qualitative behavior evaluation of supercomputer applications and HPC systems as a whole. ...
... A method of iterative regularization for solving inverse problems of forming structural components" . ... The springback is determined by solving the direct forming problem with a finite element method and is used in an iterative method for solving the inverse problem. ... The developed methods are realized in the MSC.Marc system. ... Keywords: inverse forming problems, variational inequalities, uniqueness, stability, iterative regularization methods, finite element method. ...
... A probabilistic error estimate of quadrature formulas accurate for Haar polynomials" . Kirillov K.A. Quadrature formulas possessing the Haar d -property (i.e., the formulas that are accurate for Haar functions of groups with the numbers not exceeding a given number d ) are studied. ... In this paper we obtain a probabilistic error estimate on the classes S p for the quadrature formulas possessing the Haar d -property. ...