Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy
arXiv:1207.0586 · doi:10.1016/j.jcp.2017.02.007
Abstract
This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we introduce a topological derivative-based electromagnetic imaging function operated at several nonzero frequencies. The properties of the imaging function are carefully analyzed for the configurations of both symmetric and non-symmetric incident field directions. This analysis explains why the application of incident fields with symmetric direction operated at multiple frequencies guarantees a successful reconstruction. Various numerical simulations with noise-corrupted data are conducted to assess the performance, effectiveness, robustness, and limitations of the proposed technique.
17 pages, 27 figures
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- A topology optimisation of acoustic devices based on the frequency response estimation with the Padé approximation
- Topological derivative-based technique for imaging thin inhomogeneities with few incident directions
- Inversion of limited-aperture Fresnel experimental data using orthogonality sampling method with single and multiple sources