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Reconstructing Small Perturbations of an Obstacle for Acoustic Waves from Boundary Measurements on the Perturbed Shape Itself
  • Habib Zribi
Habib Zribi
University of Hafr Al Batin,
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Abstract

We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigourous by using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation). We extend these techniques to derive asymptotic expansions of the Dirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms of the small perturbations of the obstacle as well as relationships between the shape deformation of an obstacle and boundary measurements of DNO or NDO on the perturbed shape itself. All relationships lead us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the obstacle.

Peer review status:ACCEPTED

22 Jul 2020Submitted to Mathematical Methods in the Applied Sciences
26 Jul 2020Submission Checks Completed
26 Jul 2020Assigned to Editor
25 Sep 2020Reviewer(s) Assigned
28 Dec 2020Review(s) Completed, Editorial Evaluation Pending
29 Dec 2020Editorial Decision: Revise Major
13 Jan 20211st Revision Received
13 Jan 2021Submission Checks Completed
13 Jan 2021Assigned to Editor
13 Jan 2021Reviewer(s) Assigned
20 Apr 2021Review(s) Completed, Editorial Evaluation Pending
21 Apr 2021Editorial Decision: Accept