Abstract
We establish an asymptotic representation formula for the steady state current perturbations caused by internal corrosive boundary parts of small surface measure. Based on this formula we design a non-iterative method of MUSIC (multiple signal classification) type for localizing the corrosive parts from voltage-to-current observations. We perform numerical experiments to test the viability of the algorithm and the results clearly demonstrate that the algorithm works well even in the presence of relatively high noise ratios.
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H. Ammari is partially supported by the Brain Pool Korea Program at Seoul National University, H. Kang is partially supported by KOSEF grant R01-2006-000-10002-0, E. Kim is supported by BK21 Math. Division at Seoul National University, and M.S. Vogelius is partially supported by NSF grant DMS-0604999.
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Ammari, H., Kang, H., Kim, E. et al. A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements. Numer. Math. 108, 501–528 (2008). https://doi.org/10.1007/s00211-007-0130-x
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DOI: https://doi.org/10.1007/s00211-007-0130-x