A numerical reconstruction method in inverse elastic scattering. (English) Zbl 1390.74030
Summary: In this paper a new numerical method for the shape reconstruction of obstacles in elastic scattering is proposed. Initially, the direct scattering problem for a rigid body and the mathematical setting for the corresponding inverse one are presented. Inverse uniqueness issues for the general case of mixed boundary conditions on the boundary of our obstacle, which are valid for a rigid body as well are established. The inversion algorithm based on the factorization method is presented into a suitable form and a new numerical scheme for the reconstruction of the shape of the scatterer, using far-field measurements, is given. In particular, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) and its linchpin within the framework of the factorization method is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples involving a kite, an acorn, and a peanut-shaped object.
MSC:
| 74B05 | Classical linear elasticity |
| 35J57 | Boundary value problems for second-order elliptic systems |
| 35P25 | Scattering theory for PDEs |
| 35R30 | Inverse problems for PDEs |
| 45A05 | Linear integral equations |
| 65F22 | Ill-posedness and regularization problems in numerical linear algebra |
Keywords:
inverse elastic scattering problems; reciprocity gap functional (RGF); factorization method; improved maximum product criterion (IMPC)References:
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