Abstract

On the use of the reciprocity gap functional in inverse scattering from planar cracks

Amel Ben Abda
Enit-Lamsin, Tunisia

Joint work with Fabrice Delbary, Houssem Haddar

We are concerned with the reconstruction of planar cracks from over
determined
data on the boundary of a domain that contains these cracks. Both
acoustic and
electromagnetic cases will be
considered. We shall explain in each case how the reciprocity gap
functional allows us to recover the Fourier transform
of the jump of the solution across the crack. Under suitable assumptions
the
crack can be seen as the support of this jump, which leads in that cases
to an
explicit reconstruction. We shall address then some numerical issues
related to
this inverse algorithm with special emphasize on the numerical
instability of
evaluating the Fourier transform. This instability is of course inherent
to our
problem. Some three dimensional numerical reconstructions will be
presented.