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 / L. Rondi. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 19:6(2008), pp. 635-660.
Reconstruction in the inverse crack problem by variational methods
L. Rondi
2008
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.File | Dimensione | Formato | |
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