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Level-set function approach to an inverse interface problem. (English) Zbl 0986.35130
Summary: A model problem in electrical impedance tomography for the identification of unknown shapes from data in a narrow strip along the boundary of a domain is investigated. The representation of the shape of the boundary and its evolution during an iterative reconstruction process is achieved by the level set method. The shape derivatives of this problem involve the normal derivative of the potential along the unknown boundary. Hence an accurate resolution of its derivatives along the unknown interface is essential. It is obtained by the immersed interface method.

MSC:
35R30Inverse problems for PDE
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
49Q10Optimization of shapes other than minimal surfaces