This article is cited in 2 papers

A numerical method for determining the inhomogeneity boundary in the Dirichlet problem for the Laplace equation in a piecewise-homogeneous medium

S. V. Gavrilov, A. M. Denisov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992 Russia

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.

Key words: Dirichlet problem for Laplace's equation, piecewise homogeneous medium, unknown boundary, inverse problem, numerical method.

UDC: 519.632.4

Received: 26.02.2010

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:8, 1391–1398

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