Abstract
The Dirichlet problem for Laplace’s equation in a two-dimensional domain filled with a piecewise homogeneous medium is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem of determining the inhomogeneity boundary from additional information on the solution of the Dirichlet problem is considered. A numerical method based on the linearization of the nonlinear operator equation for the unknown boundary is proposed for solving the inverse problem. The results of numerical experiments are presented.
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Original Russian Text © S.V. Gavrilov, A.M. Denisov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 8, pp. 1462–1470.
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Gavrilov, S.V., Denisov, A.M. Numerical method for determining the inhomogeneity boundary in the Dirichlet problem for Laplace’s equation in a piecewise homogeneous medium. Comput. Math. and Math. Phys. 50, 1391–1398 (2010). https://doi.org/10.1134/S0965542510080099
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DOI: https://doi.org/10.1134/S0965542510080099