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

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

2009-09-28

arxiv.org/abs/0909.5139v2

Mathematics

Analysis of PDEs

28 pages

Scientific paper

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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