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

Abstract

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.

arXiv comment15 pages, 12 figures

References in corpus (1)

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

Cited by in corpus (3)

• Identification of cavities and inclusions in linear elasticity with a phase-field approach
• Reconstruction of material losses by perimeter penalization and phase-field methods
• A phase-field approach for detecting cavities via a Kohn-Vogelius type functional