This article is cited in 6 papers

Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s 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: A boundary value problem for Laplace’s equation in a bounded 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 and the solution of the equation given the solution and its normal derivative on the boundary of the domain is discussed. Numerical methods are proposed for solving the inverse problem, and the results of numerical experiments are presented.

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

UDC: 519.624.2

Received: 17.02.2011

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:8, 1377–1390

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