We deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements goes to zero. We further notice that we use the Gamma-convergence approximation of the Mumford–Shah functional due to Ambrosio and Tortorelli as the required regularization term.

Reconstruction in the inverse crack problem by variational methods

RONDI, LUCA
2008-01-01

Abstract

We deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements goes to zero. We further notice that we use the Gamma-convergence approximation of the Mumford–Shah functional due to Ambrosio and Tortorelli as the required regularization term.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/1876292
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