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

Fingerprint

Asymptotic Formula
Conductivity
Optimization Algorithm
Inclusion
Gradient Estimate
Transmission Problem
Asymptotic analysis
Eigenvalues and Eigenfunctions
Error term
Viability
Asymptotic Analysis
Eigenvalues and eigenfunctions
Optimization Problem
Perturbation
Numerical Results
Optimization
Formulation
Estimate

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements. / Ammari, Habib; Beretta, Elena; Francini, Elisa; Kang, Hyeonbae; Lim, Mikyoung.

In: Mathematics of Computation, Vol. 79, No. 271, 01.07.2010, p. 1757-1777.

Research output: Contribution to journalArticle

Ammari, Habib ; Beretta, Elena ; Francini, Elisa ; Kang, Hyeonbae ; Lim, Mikyoung. / Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements. In: Mathematics of Computation. 2010 ; Vol. 79, No. 271. pp. 1757-1777.
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