Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements

In this paper, we propose an original optimization approach for reconstructing interface changes of a conductivity inclusion from measurements of eigenvalues and eigenvectors associated with the transmission problem for the Laplacian. Based on a rigorous asymptotic formalism, 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 estimates 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 discussed. AMS subject classifications. 35R30, 35B34 Key words. shape reconstruction, vibration analysis, asymptotic expansion, reconstruction algorithm, optimization problem

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Habib Ammari, Elena Beretta, Elisa Francini, Hyeonbae Kang, Mikyoung Lim
• Keywords: Asymptotic Formula, MOC 2010, Optimization Problem, Rigorous Asymptotic Formalism, Security Privacy