A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

• Published in: Numerische Mathematik Vol. 108; no. 4; pp. 501 - 528
• Main Authors: Ammari, Habib, Kang, Hyeonbae, Kim, Eunjoo, Louati, Kaouthar, Vogelius, Michael S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.02.2008; Springer; Springer Verlag
• Subjects: Classical Analysis and ODEs; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; General Mathematics; Global analysis, analysis on manifolds; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical analysis. Scientific computation; Numerical and Computational Physics; Sciences and techniques of general use; Simulation; Theoretical; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; 35R30; Iterative method; Numerical analysis; Algorithm; Steady state; Classification; Surface; reconstruction; corrosion; asymptotic representation formula; layer potentials
• ISSN: 0029-599X; 0945-3245
• DOI: 10.1007/s00211-007-0130-x

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.