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.
Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results / W. Ring, L. Rondi. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - 13:3(2011), pp. 353-371.
|Titolo:||Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results|
RONDI, LUCA (Corresponding)
|Parole Chiave:||inverse problems; cracks; cavities; phase-field; perimeter penalization; optimality system|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2011|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4171/IFB/262|
|Appare nelle tipologie:||01 - Articolo su periodico|