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

  • Rondi L
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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. © 2011 Elsevier Inc.

Author-supplied keywords

  • Cavities
  • Inverse problems
  • Perimeter penalization
  • Phase-field functions
  • Primary
  • Secondary

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Authors

  • Luca Rondi

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