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End date: 2019 × Start date: 2019 × Type: Report × Subject: Dirichlet boundary condition × Subject: uniqueness ×

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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.
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    Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Elschner, Johannes; Hu, Guanghui; Yamamoto, Masahiro
    Consider the two-dimensional inverse elastic scattering problem of recovering a piecewise linear rigid rough or periodic surface of rectangular type for which the neighboring line segments are always perpendicular.We prove the global uniqueness with at most two incident elastic plane waves by using near-field data. If the Lamé constants satisfy a certain condition, then the data of a single plane wave is sufficient to imply the uniqueness. Our proof is based on a transcendental equation for the Navier equation, which is derived from the expansion of analytic solutions to the Helmholtz equation. The uniqueness results apply also to an inverse scattering problem for non-convex bounded rigid bodies of rectangular type.