| Abstract: |
| In this talk, we investigate the inverse scattering problem of an obstacle
embedded in a thin plate using near-field measurements of flexural waves. The
forward scattering problem is reduced to a coupled system of boundary value
problems for the propagating and evanescent waves. Assuming the obstacle is a
small perturbation of a circle, we employ the method of transformed field
expansions to express the solution as a power series, obtaining closed-form
expressions for the zeroth and first-order terms. These expressions are then
used to derive an approximate reconstruction formula for the inverse
scattering problem. We explore different types of incident fields, some of
which lead to simplified and more efficient reconstruction methods. Numerical
experiments demonstrate the effectiveness and efficiency of the proposed
approach. |
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