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Screened harmonic system with Dirichlet and Neumann boundary conditions in analysis in the three-dimensional case

https://doi.org/10.25587/2411-9326-2025-4-66-80

Abstract

A screened harmonic system with Dirichlet and Neumann boundary conditions is analyzed in the three-dimensional case. This system is continued through boundaries with Dirichlet and Neumann conditions. The system of linear algebraic equations obtained after discretization of the continued system is considered. An asymptotically optimal analysis is given for the discrete continued system. The method for analyzing the discrete continued system is implemented in the algorithm.

About the Authors

M. P. Eremchuk
South Ural State University
Russian Federation

Maksim P. Eremchuk

76 Lenin Avenue, Chelyabinsk 454080



A. L. Ushakov
South Ural State University
Russian Federation

Andrey L. Ushakov

76 Lenin Avenue, Chelyabinsk 454080



References

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4. Matsokin A. M. and Nepomnyaschikh S. V., “The fictitious-domain method and explicit continuation operators [in Russian],” Comput. Math. Math. Phys., 33, No. 1, 52–68 (1993).

5. Ushakov A. L., “Analysis of the mixed boundary value problem for the Poisson’s equation [in Russian],” Vestn. Yuzhn.-Ural. Gos. Univ., Ser. Mat., Mekh., Fiz., 13, No. 1, 29–40 (2021).

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7. Eremchuk M. P., “Analysis of a screened harmonic system under Dirichlet and Neumann boundary conditions,” Bull. South Ural State Univ., Ser. Math. Mech. Phys., 17, No. 2, 13–22 (2025).

8. Aubin J.-P., Approximation of Elliptic Boundary-Value Problems, Wiley-Intersci., New York (1972)


Review

For citations:


Eremchuk M.P., Ushakov A.L. Screened harmonic system with Dirichlet and Neumann boundary conditions in analysis in the three-dimensional case. Mathematical notes of NEFU. 2025;32(4):66-80. (In Russ.) https://doi.org/10.25587/2411-9326-2025-4-66-80

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ISSN 2411-9326 (Print)
ISSN 2587-876X (Online)