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The Linear Sampling Method for Kirchhoff-Love infinite plates

  • * Corresponding author: Laurent Bourgeois

    * Corresponding author: Laurent Bourgeois 
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  • This paper addresses the problem of identifying impenetrable obstacles in a Kirchhoff-Love infinite plate from multistatic near-field data. The Linear Sampling Method is introduced in this context. We firstly prove a uniqueness result for such an inverse problem. We secondly provide the classical theoretical foundation of the Linear Sampling Method. We lastly show the feasibility of the method with the help of numerical experiments.

    Mathematics Subject Classification: Primary: 35R25, 35R30, 35R35, 74J15, 74K20.


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  • Figure 1.  Validation of the artificial boundary condition. Left: scattering solution computed in $ \Omega_1 $. Right: scattering solution computed in $ \Omega_2 $

    Figure 2.  Function $ \Psi $ given by (32) for a Dirichlet obstacle, exact data and various wave numbers $ k $. Top left: $ k = 10 $. Top right: $ k = 20 $. Bottom: $ k = 30 $

    Figure 3.  Function $ \Psi $ for a Neumann obstacle, exact data and various wave numbers $ k $. Top left: $ k = 10 $. Top right: $ k = 20 $. Bottom: $ k = 30 $

    Figure 4.  Left: Function $ \Psi $ for a Dirichlet obstacle formed by 3 circles, $ k = 30 $ and exact data. Right: Function $ \Psi $ for a Neumann kite-shaped obstacle, $ k = 20 $ and exact data

    Figure 5.  Function $ \Psi $ for a Dirichlet obstacle, $ k = 20 $ and noisy data. Left: noise of amplitude $ 5\% $. Right: noise of amplitude $ 10\% $

    Figure 6.  Function $ \Psi $ for a Dirichlet obstacle with less (exact) data, $ k = 30 $. Left: two circles. Right: three circles

    Figure 7.  Function $ \Psi $ for a Dirichlet obstacle with less data in the presence of noise, $ k = 20 $. Left: noise of amplitude $ 5\% $. Right: noise of amplitude $ 10\% $

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