Numerical Method for Solving an Inverse Problem for Laplace’s Equation in a Domain with an Unknown Inner Boundary

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 59; no. 1; pp. 59 - 65
Main Author: Gavrilov, S. V.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.01.2019
Springer Nature B.V
Subjects:
Computational Mathematics and Numerical Analysis
Dirichlet problem
Inverse problems
Iterative methods
Laplace equation
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical methods
Laplace’s equation
numerical method
unknown boundary
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary: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.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542519010093