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

Habib Ammari, Elena Beretta, Elisa Francini, Hyeonbae Kang, Mikyoung Lim

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1757-1777
Number of pages21
JournalMathematics of Computation
Volume79
Issue number271
DOIs
StatePublished - Jul 1 2010

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Keywords

  • Asymptotic expansion
  • Optimization problem
  • Reconstruction algorithm
  • Shape reconstruction
  • Vibration analysis

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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