We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
A SPECTRAL TARGET SIGNATURE FOR THIN SURFACES WITH HIGHER ORDER JUMP CONDITIONS.
- Authors
CAKONI, FIORALBA; HEEJIN LEE; MONK, PETER; Yangwen Zhang
- Abstract
In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in Rm, m = 2; 3 from scattering data. In the asymptotic limit as the thickness goes to zero, the thin inhomogeneity is modeled by an open m-1 dimensional manifold (here referred to as screen), and the field inside is replaced by jump conditions on the total field involving a second order surface differential operator. We show that all the surface coeffcients (possibly matrix valued and complex) are uniquely determined from far field patterns of the scattered fields due to infinitely many incident plane waves at a fixed frequency. Then we introduce a target signature characterized by a novel eigenvalue problem such that the eigenvalues can be determined from measured scattering data, adapting the approach in [20]. Changes in the measured eigenvalues are used to identified changes in the coeffcients without making use of the governing equations that model the healthy screen. In our investigation the shape of the screen is known, since it represents the object being evaluated. We present some preliminary numerical results indicating the validity of our inversion approach.
- Subjects
INVERSE problems; DIFFERENTIAL operators; PLANE wavefronts; COMPLEX matrices; INVERSE scattering transform; EIGENVALUES
- Publication
Inverse Problems & Imaging, 2022, Vol 16, Issue 6, p1473
- ISSN
1930-8337
- Publication type
Article
- DOI
10.3934/ipi.2022020