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OPTIMIZATION ALGORITHM FOR RECONSTRUCTING INTERFACE CHANGES OF A CONDUCTIVITY INCLUSION
 

Summary: OPTIMIZATION ALGORITHM FOR RECONSTRUCTING
INTERFACE CHANGES OF A CONDUCTIVITY INCLUSION
FROM MODAL MEASUREMENTS
HABIB AMMARI, ELENA BERETTA, ELISA FRANCINI, HYEONBAE KANG,
AND MIKYOUNG LIM
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 transmis-
sion 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 gradi-
ent 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 ap-
proach is documented by a variety of numerical results. The resolution limit
of our algorithm is also highlighted.
1. Introduction
Let be a smooth domain and D be an inclusion contained in whose bound-
ary is also assumed to be smooth. Shape deformation of D causes a perturbation
of modal parameters. The aim of this paper is to show how this information can be

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics