Convexification for a 1D Hyperbolic Coefficient Inverse Problem with Single Measurement Data

2020/02/04 by Smirnov, Alexey V., Klibanov, Michael V., Nguyen, Loc H.
#35L10 #35R30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2002.01074

Abstract

A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most important element of the construction is the presence of the Carleman Weight Function in a weighted Tikhonov-like functional. This functional is strictly convex on a certain bounded set in a Hilbert space, and the diameter of this set is an arbitrary positive number. The global convergence of the gradient projection method is established. Computational results demonstrate a good performance of the numerical method for noisy data.

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