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arXiv · 0909.5139

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

Luca Rondi
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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.

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Luca Rondi. 2009-09-28. Reconstruction of material losses by perimeter penalization and phase-field methods. https://doi.org/10.1016/j.jde.2011.03.014

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