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End date: 2019 × Start date: 2010 × DDC: 510 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: factorization method × Subject: uniqueness ×

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    Some inverse problems arising from elastic scattering by rigid obstacles
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Kirsch, Andreas; Sini, Mourad
    In the first part, it is proved that a C2-regular rigid scatterer in R3 can be uniquely identified by the shear part (i.e. S-part) of the far-field pattern corresponding to all incident shear waves at any fixed frequency. The proof is short and it is based on a kind of decoupling of the S-part of scattered wave from its pressure part (i.e. P-part) on the boundary of the scatterer. Moreover, uniqueness using the S-part of the far-field pattern corresponding to only one incident plane shear wave holds for a ball or a convex Lipschitz polyhedron. In the second part, we adapt the factorization method to recover the shape of a rigid body from the scattered S-waves (resp. P-waves) corresponding to all incident plane shear (resp. pressure) waves. Numerical examples illustrate the accuracy of our reconstruction in R2. In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set.
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    The factorization method for inverse elastic scattering from periodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hu, Guanghui; Lu, Yulong; Zhang, Bo
    This paper is concerned with the inverse scattering of time-harmonic elastic waves from rigid periodic structures. We establish the factorization method to identify an unknown grating surface from knowledge of the scattered compressional or shear waves measured on a line above the scattering surface. Near-field operators are factorized by selecting appropriate incident waves derived from quasi-periodic half-space Green’s tensor to the Navier equation. The factorization method gives rise to a uniqueness result for the inverse scattering problem by utilizing only the compressional or shear components of the scattered field corresponding to all quasi-periodic incident plane waves with a common phase-shift. A number of computational examples are provided to show the accuracy of the inversion algorithms, with an emphasis placed on comparing reconstructions from the scattered near-field and those from its compressional and shear components.