Mathematical Determination of the Fréchet Derivative with Respect to the Domain for a Fluid-Structure Scattering Problem. Case of Polygonal-Shaped Domains

Abstract : The characterization of the Fréchet derivative of the elasto-acoustic scattered field with respect to Lipschitz continuous polygonal domains is established. The considered class of domains is of practical interest since two-dimensional scatterers are always transformed into polygonal-shaped domains when employing finite element methods for solving direct and inverse scattering problems. The obtained result indicates that the Fréchet derivative with respect to the scatterer of the scattered field is the solution of the same elasto-acoustic scattering problem but with additional right-hand side terms in the transmission conditions across the fluid-structure interface. This characterization has the potential to advance the state-of-the-art of the solution of inverse obstacle problems.
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Submitted on : Tuesday, December 5, 2017 - 3:49:38 PM
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Hélène Barucq, Rabia Djellouli, Elodie Estecahandy, Mohand Moussaoui. Mathematical Determination of the Fréchet Derivative with Respect to the Domain for a Fluid-Structure Scattering Problem. Case of Polygonal-Shaped Domains. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2017, pp.1-29. ⟨hal-01655937⟩

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