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

Title
OPTIMIZATION ALGORITHM FOR RECONSTRUCTING INTERFACE CHANGES OF A CONDUCTIVITY INCLUSION FROM MODAL MEASUREMENTS
Authors
Ammari, H.; Beretta, E.; Francini, E.; Kang, H.; Lim, M.
Keywords
reconstruction algorithm, Shape reconstruction
Issue Date
2010-07
Publisher
AMER MATHEMATICAL SOC
Abstract
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.
URI
http://dspace.inha.ac.kr/handle/10505/20111
ISSN
0025-5718
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Journal Papers, Reports(수학 논문, 보고서)
Files in This Item:
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