We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the unknown material loss by a single boundary measurement of current and voltage type. The method is based on the use of phase-field functions to model the material losses and on a perimeter-like penalization to regularize the otherwise ill-posed problem. We justify the proposed approach by a convergence result, as the error on the measurement goes to zero.

Reconstruction of material losses by perimeter penalization and phase-field methods / L. Rondi. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 251:1(2011), pp. 150-175.

Reconstruction of material losses by perimeter penalization and phase-field methods

L. Rondi
2011

Abstract

We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the unknown material loss by a single boundary measurement of current and voltage type. The method is based on the use of phase-field functions to model the material losses and on a perimeter-like penalization to regularize the otherwise ill-posed problem. We justify the proposed approach by a convergence result, as the error on the measurement goes to zero.
inverse problems; cavities; phase-field functions; perimeter penalization
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/597866
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