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Author: Zhang, Bo × Subject: Helmholtz equation ×

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    Near-field imaging of scattering obstacles with the factorization method
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Hu, Guanghui; Yang, Jiaqing; Zhang, Bo; Zhang, Haiwen
    In this paper we establish a factorization method for recovering the location and shape of an acoustic bounded obstacle with using the near-field data, corresponding to infinitely many incident point sources. The obstacle is allowed to be an impenetrable scatterer of sound-soft, sound-hard or impedance type or a penetrable scatterer. An outgoing-to-incoming operator is constructed for facilitating the factorization of the near-field operator, which can be easily implemented numerically. Numerical examples are presented to demonstrate the feasibility and effectiveness of our inversion algorithm, including the case where limited aperture near-field data are available only.
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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.