Near-field imaging of obstacles with the factorization method: Fluid-solid interaction
- Yin, Tao
- Hu, Guanghui
- Xu, Liwei
- Zhang, Bo
2010 Mathematics Subject Classification
- 35R30 74B05 78A46
- inverse scattering, fluid-solid interaction problem, factorization method, Helmholtz equation, Navier equation, near-field imaging, outgoing-to-incoming operator
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.
- Inverse Problems, 32 (2016) pp. 015003/1--015003/29.