On the Fréchet derivative in elastic obstacle scattering

Frédérique Le Louër (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

In this paper, we investigate the existence and characterizations of the Fréchet derivative of solutions to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique - the factorization of the difference of the far-field pattern for two different scatterers - introduced by Kress and Päivärinta to establish Fréchet differentiability in acoustic scattering. For the Dirichlet boundary condition an alternative proof of a differentiability result due to Charalambopoulos is provided and new results are proven for the Neumann and impedance exterior boundary value problems.

Mots clés: Navier equation; Fréchet derivative; far-field pattern; Dirichlet condition; Neumann condition; impedance condition; inverse scattering; Elastic scattering

Domaines: Analyse numérique [math.NA]

Frédérique Le Louër. On the Fréchet derivative in elastic obstacle scattering. SIAM Journal on Applied Mathematics, 2012, 72 (5), http://dx.doi.org/10.1137/110834160. ⟨10.1137/110834160⟩. ⟨hal-00692029⟩