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Your search keyword '"Reutskiy, S.Y."' showing total 2 results
Start Over Author "Reutskiy, S.Y." Topic anisotropy
2 results on '"Reutskiy, S.Y."'

1. A novel meshless method for fully nonlinear advection–diffusion-reaction problems to model transfer in anisotropic media.

Author

Lin, Ji, Reutskiy, S.Y., and Lu, Jun

Subjects
*MESHFREE methods, *REACTION-diffusion equations, *ANISOTROPY, *RADIAL basis functions, *BOUNDARY value problems
Abstract

Abstract This article presents the new version of the backward substitution method (BSM) for simulating transfer in anisotropic and inhomogeneous media governed by linear and fully nonlinear advection–diffusion-reaction equations (ADREs). The key idea of the method is to formulate a general analytical expression of the solution in the form of the series over a basis system which satisfies the boundary conditions with any choice of the free parameters. The radial basis functions (RBFs) of the different types are used to generate the basis system for expressing the solution. Then the expression is substituted into the ADRE under consideration and the free parameters are determined by the collocation inside the solution domain. As a result we separate the approximation of the boundary conditions and the approximation of the PDE inside the solution domain. This approach leads to an important improvement of the accuracy of the approximate solution and can be easily extended onto irregular domain problems. Furthermore, the proposed method is extended to general fully nonlinear ADREs in combination with the quasilinearization technique. Some numerical results and comparisons are provided to justify the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Published
2018
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2. A meshless radial basis function method for 2D steady-state heat conduction problems in anisotropic and inhomogeneous media.

Author

Reutskiy, S.Y.

Subjects
*MESHFREE methods, *RADIAL basis functions, *STEADY state conduction, *ANISOTROPY, *INHOMOGENEOUS materials, *PARTIAL differential equations, *OPERATOR theory
Abstract

The paper presents a new meshless numerical method for solving 2D steady-state heat conduction problems in anisotropic and inhomogeneous media. The coefficients of the governing PDEs are spatially dependent functions including the main operator part. The boundary conditions of a most general form for the temperature and the heat flux are considered. The key idea of the method is the use of the basis functions which satisfy the homogeneous boundary conditions of the problem. Each basis function used in the algorithm is a sum of a RBF and a special correcting function which is chosen to satisfy the homogeneous BC of the problem. The conical radial basis functions, the Duchon splines and the multiquadric RBFs are used in approximation of the PDE. This allows us to seek an approximate solution in the form which satisfies the boundary conditions of the initial problem with any choice of the free parameters. As a result we separate the approximation of the boundary conditions and the approximation of the PDE inside the solution domain. The numerical experiments are carried out for accuracy and convergence investigations. The comparison of the numerical results obtained in the paper with the exact solutions and with the data obtained with the use of other numerical techniques is performed. The numerical examples demonstrate that the present method is accurate, convergent, stable, and computationally efficient in solving this kind of problems. [ABSTRACT FROM AUTHOR]

Published
2016
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