Geodesic
A numerical method for determining the inhomogeneity boundary in the Dirichlet problem for the Laplace equation in a piecewise-homogeneous medium
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1462-1470

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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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     author = {S. V. Gavrilov and A. M. Denisov},
     title = {A numerical method for determining the inhomogeneity boundary in the {Dirichlet} problem for the {Laplace} equation in a piecewise-homogeneous medium},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1462--1470},
     publisher = {mathdoc},
     volume = {50},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a8/}
}
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S. V. Gavrilov; A. M. Denisov. A numerical method for determining the inhomogeneity boundary in the Dirichlet problem for the Laplace equation in a piecewise-homogeneous medium. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1462-1470. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a8/