Reconstruction of discontinuous parameters in a second order impedance boundary operator. (15th August 2016)

• Record Type: Journal Article
• Authors: Chaabane, S; Charfi, B; Haddar, H
• Is Part Of: Inverse problems. Volume 32:Number 10(2016:Oct.)
• Publication Date: 2016-08-15
• Subjects: discontinuous parameters -- generalized boundary conditions -- identifiability -- identification -- gradient algorithm; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/10/105004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Kohn–Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of an unknown number of discontinuity points.