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.
1984
Problèmes inverses: rencontre R.C.P.264
Rencontre multidiciplinaire sur les problèmes invèrses
MONTPELLIER, Francia
R. MAGNANINI; G. PAPI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/332530
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