Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results

Details Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results

2010-05-20

arxiv.org/abs/1005.3704v1

Mathematics

Analysis of PDEs

15 pages, 12 figures

Scientific paper

We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the use of phase-field functions to describe the defects to be reconstructed and the use of perimeter-like penalizations to regularize the ill-posed problem. The numerical implementation is based on the solution of the corresponding optimality system by a gradient method. Numerical simulations are presented to show the validity of the method.

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