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Author: Hu, Guanghui × Author: Yin, Tao × End date: 2019 × Start date: 2010 × Type: Text × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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Now showing 1 - 3 of 3
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    Direct and inverse elastic scattering from anisotropic media
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Bao, Gang; Hu, Guanghui; Yin, Tao; Sun, Jiguang
    Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show uniqueness and existence of weak solutions by applying the Fredholm alternative and using properties of the Dirichlet-to-Neumann map in both two and three dimensions. The Fréchet derivative of the near-field solution operator with respect to the scattering interface is derived. As an application, we design a descent algorithm for recovering the interface from the near-field data of one or several incident directions and frequencies. Numerical examples in 2D are demonstrated to show the validity and accuracy of our methods.
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    Finite element method to fluid-solid interaction problems with unbounded periodic interfaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Hu, Guanghui; Rathsfeld, Andreas; Yin, Tao
    Consider a time-harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid fluid of constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by its Lamé constants. This paper is concerned with a variational approach to the fluid-solid interaction problems with unbounded biperiodic Lipschitz interfaces between the domains of the acoustic and elastic waves. The existence of quasi-periodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. A finite element scheme coupled with Dirichlet-to-Neumann mappings is proposed. The Dirichlet-to-Neumann mappings are approximated by truncated Rayleigh series expansions, and, finally, numerical tests in 2D are performed.
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    Near-field imaging of scattering obstacles with the factorization method: Fluid-solid interaction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Yin, Tao; Hu, Guanghui; Xu, Liwei; Zhang, Bo
    Consider a time-harmonic acoustic point source incident on a bounded isotropic linearly elastic body immersed in a homogeneous compressible inviscid fluid. This paper is concerned with the inverse fluid-solid interaction (FSI) problem of recovering the elastic body from near-field data generated by infinitely many incident point source waves at a fixed energy. The incident point sources and the receivers for recording scattered signals are both located on a non-spherical closed surface, on which an outgoing-to-incoming (OtI) operator is appropriately defined. We provide a theoretical justification of the factorization method for precisely characterizing the scatterer by utilizing the spectrum of the near-field operator. This generalizes the imaging scheme developed in [G. Hu, J. Yang, B. Zhang, H. Zhang, Inverse Problems 30 (2014): 095005] to the case when near-field data are measured on non-spherical surfaces. Numerical examples in 2D are demonstrated to show the validity and accuracy of the inversion algorithm, even if limited aperture data are available on one or several line segments.