Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of cracks and material losses by perimeter-like
  penalizations and phase-field methods: numerical results   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.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol