Iterative methods for planar crack reconstruction in semi-infinite domains
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R. Kress
Abstract
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.
© de Gruyter 2008
Articles in the same Issue
- EIT and the average conductivity
- The mappings and inverse problems for evolutionary equations
- Iterative methods for planar crack reconstruction in semi-infinite domains
- A globally accelerated numerical method for optical tomography with continuous wave source
- Complex geometrical optics solutions for anisotropic equations and applications
- Solution of ill-posed problems on sets of functions convex along all lines parallel to coordinate axes
Articles in the same Issue
- EIT and the average conductivity
- The mappings and inverse problems for evolutionary equations
- Iterative methods for planar crack reconstruction in semi-infinite domains
- A globally accelerated numerical method for optical tomography with continuous wave source
- Complex geometrical optics solutions for anisotropic equations and applications
- Solution of ill-posed problems on sets of functions convex along all lines parallel to coordinate axes
