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# Scattering in a partially open waveguide: The inverse problem

• * Corresponding author: Laurent Bourgeois
• In this paper we consider an inverse scattering problem which consists in retrieving obstacles in a partially embedded waveguide in the acoustic case, the measurements being located on the accessible part of the structure. Such accessible part can be considered as a closed waveguide (with a finite cross section), while the embedded part can be considered as an open waveguide (with an infinite cross section). We propose an approximate model of the open waveguide by using Perfectly Matched Layers in order to simplify the resolution of the inverse problem, which is based on a modal formulation of the Linear Sampling Method. Some numerical results show the efficiency of our approach. This paper can be viewed as a continuation of the article , which was focused on the forward problem.

Mathematics Subject Classification: Primary: 35J05, 35R25, 35R30, 35R35, 47G10.

 Citation: • • Figure 1.  Original configuration

Figure 2.  Configuration with PMLs

Figure 3.  Choice of the near-field equation. Top left: near-field equation (46). Top right: near-field equation (47). Bottom: wrong near-field equation associated with the uniform closed waveguide

Figure 4.  Restriction to $N$ terms in the right-hand side of the near-field equation (46), with $N \neq \tilde{N}$. Left: $N = \tilde{N} + 1$. Right: $N = \tilde{N} - 1$

Figure 5.  Influence of the distance between the defects and the interface. Left: one obstacle. Right: two obstacles

Figure 6.  Impact of the amplitude of noise. Top left: 1% noise. Top right: 10% noise. Bottom: 20% noise

Figure 7.  Impact of the frequency. Top left: $N = 7$. Top right: $N = 13$. Bottom: $N = 26$

Figure 8.  One obstacle at least is located in the sheath

Figure 9.  Contour $C_R$ for the residue theorem

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