A numerical comparison of different qualitative algorithms for solving 2D inverse elastic scattering problems. (English) Zbl 1476.65353
Summary: In this paper, we numerically compare several well-established and recent qualitative algorithms for the shape reconstruction of obstacles in elastic scattering based on the measured noisy full far-field data. The compared algorithms include linear sampling method, factorization method and its variant (i.e., \(F_\sharp\) method), direct sampling method, and direct factorization method. To regularize the ill-conditioned far-field integral operator used in linear sampling method and factorization method, the Tikhonov regularization is used, where we compared two different regularization parameter choice technique: the generalized discrepancy principle (GDP) and the improved maximum product criterion (IMPC). The GDP requires a priori knowledge of the noise level in the far-field data, while the IMPC does not have such an impractical requirement. Extensive numerical examples are provided to illustrate the difference, similarity, advantage, and disadvantage of the tested qualitative methods under various settings. The direct sampling method and direct factorization method outperform the others in computational efficiency while achieving comparable reconstruction accuracy. We find the \(F_\sharp\) method is numerically less sensitive to noise.
MSC:
| 65R32 | Numerical methods for inverse problems for integral equations |
| 35P25 | Scattering theory for PDEs |
| 74B05 | Classical linear elasticity |
Keywords:
direct factorization method; direct sampling method; inverse elastic scattering; linear sampling method; factorization method; Tikhonov regularizationReferences:
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