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| The determination of the shape of an elastic obstacle immersed in water from some measurements of the scattered field is an important problem in many technologies such as sonar, geophysical exploration, and medical imaging. This inverse obstacle problem (IOP) is very difficult to solve, especially from a numerical viewpoint, because of its non-linear and ill-posedness characters. We present a work pertaining to the mathematical and numerical analysis of the elasto-acoustic IOP. We have developed an efficient numerical simulation code for wave propagation based on a DG-type method using higher-order finite elements and curved edges at the interface and we have applied it to the reconstruction of objects with the implementation of a regularized Newton method involving a Jacobian matrix which must be evaluated at each iteration. The Fr\'echet derivative of the elasto-acoustic scattered field with respect to the shape of the obstacle is characterized as the solution to the initial direct elasto-acoustic problem except a change in the transmission conditions set on the fluid-structure interface. We therefore show that the evaluation of the Jacobian matrix requires the solution of the direct problem with multiple right-hand sides. We have performed a set of experiments that illustrate the interest of our approach. |
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