We consider the problem of determining the shape of a bounded aperture in an infinite screen from knowledge of the diffracted field on a plane located within the domain where the wave propagates. This is an ill-posed problem. We restore a logarithmic stability in the class of apertures with a priori bounded perimeter. We are also concerned with the numerical reconstruction of the aperture. An approximated reconstruction is obtained as a suitable level set of the minimizing function of a penalized least-square functional. Some examples are given.
An inverse problem for Helmholtz equation / R. MAGNANINI; G. PAPI. - STAMPA. - Rencontre multidiciplinaire sur les problèmes invèrses 31:(1984), pp. 246-254. (Intervento presentato al convegno Rencontre multidiciplinaire sur les problèmes invèrses tenutosi a MONTPELLIER, Francia nel 1983).
An inverse problem for Helmholtz equation
MAGNANINI, ROLANDO;PAPI, GLORIA
1984
Abstract
We consider the problem of determining the shape of a bounded aperture in an infinite screen from knowledge of the diffracted field on a plane located within the domain where the wave propagates. This is an ill-posed problem. We restore a logarithmic stability in the class of apertures with a priori bounded perimeter. We are also concerned with the numerical reconstruction of the aperture. An approximated reconstruction is obtained as a suitable level set of the minimizing function of a penalized least-square functional. Some examples are given.
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