OPTIMIZATION ALGORITHM FOR RECONSTRUCTING INTERFACE CHANGES OF A CONDUCTIVITY INCLUSION FROM MODAL MEASUREMENTS

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In this paper, we propose an original and promising optimization approach for reconstructing interface changes of a conductivity inclusion from measurements of eigenvalues and eigenfunctions associated with the transmission problem for the Laplacian. Based on a rigorous asymptotic analysis, we derive an asymptotic formula for the perturbations in the modal measurements that are due to small changes in the interface of the inclusion. Using fine gradient estimates, we carefully estimate the error term in this asymptotic formula. We then provide a key dual identity which naturally yields to the formulation of the proposed optimization problem. The viability of our reconstruction approach is documented by a variety of numerical results. The resolution limit of our algorithm is also highlighted.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2010-07
Language
English
Article Type
Article
Keywords

EIGENVALUES; OPERATORS; DOMAINS; FORMS

Citation

MATHEMATICS OF COMPUTATION, v.79, pp.1757 - 1777

ISSN
0025-5718
DOI
10.1090/S0025-5718-10-02344-6
URI
http://hdl.handle.net/10203/174458
Appears in Collection
MA-Journal Papers(저널논문)
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