A new version of the convexification method for a 1D coefficient inverse problem with experimental data. (21st September 2018)

• Record Type: Journal Article
• Authors: Klibanov, Michael V; Kolesov, Aleksandr E; Sullivan, Anders; Nguyen, Lam
• Is Part Of: Inverse problems. Volume 34:Number 11(2018:Nov.)
• Publication Date: 2018-09-21
• Subjects: experimental data -- coefficient inverse problem -- convexification -- Carleman weight function -- numerical method -- global convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aadbc6
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A new version of the convexification method is developed analytically and tested numerically for a 1D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called 'tail function', which is a complement of a certain truncated integral with respect to the wave number. Globally strictly convex cost functional is constructed with the Carleman weight function. Global convergence of the gradient projection method to the correct solution is proved. Numerical tests are conducted for both computationally simulated and experimental data.