Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
IMPACT FACTOR 2017: 0.941
5-year IMPACT FACTOR: 0.953
CiteScore 2017: 0.91
SCImago Journal Rank (SJR) 2017: 0.461
Source Normalized Impact per Paper (SNIP) 2017: 1.022
Mathematical Citation Quotient (MCQ) 2017: 0.49
Iterative methods for planar crack reconstruction in semi-infinite domains
We consider the problem of determining the shape and location of cracks from Cauchy data on the boundary of semi-infinite domains modeling the reconstruction of cracks within a heat conducting medium from temperature and heat flux measurements. Our reconstructions are based on a pair of nonlinear integral equations for the unknown crack and the unknown flux jump on the crack that are linear with respect to the flux and nonlinear with respect to the crack. We propose two different iteration methods employing the following idea: Given an approximate reconstruction for the crack we first solve one of the equations for the flux and subsequently linearize the other equation for updating the crack. The foundations for this approach for solving the inverse problem in semi-infinite domains are provided and numerical experiments exhibit the feasibility of both methods and their stability with respect to noisy data.
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