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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 1, Pages 63–70 (Mi zvmmf10817)  

Numerical method for solving an inverse problem for Laplace's equation in a domain with an unknown inner boundary

S. V. Gavrilov

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, 119991 Russia

Abstract: An inverse problem for Laplace's equation in a doubly connected two-dimensional domain is considered. Given Dirichlet and Neumann data specified on the known outer boundary of the domain, the task is to determine an unknown inner boundary on which the function takes a constant value. The uniqueness of the solution to this inverse problem is proved. An iterative numerical method for determining the unknown boundary is proposed. Numerical results are presented.

Key words: Laplace's equation, unknown boundary, numerical method.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation AAAA-A16-116021510092-2
This work was supported by the Faculty of Computational Mathematics and Cybernetics of Moscow State University, state register no. AAAA-A16-116021510092-2.


DOI: https://doi.org/10.1134/S0044466919010095


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:1, 59–65

Bibliographic databases:

UDC: 519.624.2
Received: 27.03.2018

Citation: S. V. Gavrilov, “Numerical method for solving an inverse problem for Laplace's equation in a domain with an unknown inner boundary”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 63–70; Comput. Math. Math. Phys., 59:1 (2019), 59–65

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