FRITSCH, Mr Jean-François (2019) Identification of a defect in an acoustic waveguide with an abrupt change of properties PFE - Project Graduation, ENSTA.

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We are interested in the identification of obstacles in an acoustic waveguide from scattering data. Among the inverse identification methods, the sampling methods have proven their effi- ciency. The goal of this work is to adapt the modal formulation of the Linear Sampling Method initially proposed in [Bourgeois and Lunéville,2008] to waveguides with an abrupt change of properties. We show that for a waveguide with a jump of wavenumber, the analytically known Green function enables us to derive this formulation easily. In the case of a guide with an abrupt change of section, we show that despite the lack of analytical expression for the Green function, the mode-matching method enables us to expand the Green function with respect to reference fields that we introduce. From that, we propose a modal formulation of the method. The Linear Sampling Method is imple- mented from scratch using the library XLIFE++, and we investigate with numerical experiments the quality of the recovery of obstacles in both configurations. Finally, we adapt the multiple scattering method to waveguides in order to synthesize efficiently scattering data when the ob- stacle is far from the transition surface. The performances of the method are studied and the well-posedness of the reduced problem shown following [Koyama, 2010].

Item Type:Thesis (PFE - Project Graduation)
Uncontrolled Keywords:Inverse problem, Linear Sampling Method, acoustic waveguide, XLIFE++
Subjects:Mathematics and Applications
ID Code:7954
Deposited By:Jean-François Fritsch
Deposited On:04 mars 2020 13:35
Dernière modification:04 mars 2020 13:35

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