Geodesic
Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results
Wolfgang Ring1 ; Luca Rondi2
1Universität Graz, Austria
2Università degli Studi di Trieste, Italy
Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 353-371

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DOI

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.
DOI : 10.4171/ifb/262
Classification : 35-XX, 62-XX, 65-XX, 00-XX
Mots-clés : Inverse problems; cracks; cavities; phase-field; perimeter penalization; optimality system

Wolfgang Ring  1   ; Luca Rondi  2

1 Universität Graz, Austria
2 Università degli Studi di Trieste, Italy 
Wolfgang Ring; Luca Rondi. Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results. Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 353-371. doi: 10.4171/ifb/262
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     title = {Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/262/}
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