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

TL;DR

This paper presents a numerical implementation of a variational phase-field method with perimeter penalizations for reconstructing cracks and cavities, demonstrating its effectiveness through simulations.

Contribution

It introduces a novel numerical approach combining phase-field functions and perimeter-like penalizations for inverse crack and cavity reconstruction.

Findings

Successful numerical reconstruction of cracks and cavities.

Effective regularization of ill-posed inverse problems.

Validation through numerical simulations.

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.