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

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...