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A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements. (English) Zbl 1149.78005
The authors establish an asymptotic representation formula for the steady state current perturbations caused by internal corrosive boundary parts of small surface measure. Here the corrosive boundary parts are a subset of the boundary of an inaccessible simply connected 2D region whose closure is a subset of a larger simply connected 2D region whose boundary is accessible and to which a voltage is applied. Based on this formula, the authors design a noniterative method of MUSIC (multiple signal classification) type to localize the corrosive parts from voltage-to-current observations. Numerical experiments are performed to test the viability of the algorithm. The algorithm is shown to perform well in the presence of relatively high noise ratios, provided the corrosion coefficients are sufficiently large.

MSC:
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35R30 Inverse problems for PDEs
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