Reconstruction of small interface changes of an inclusion from modal measurements II: The elastic case

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

Research output: Contribution to journalArticle

Abstract

In order to reconstruct small changes in the interface of an elastic inclusion from modal measurements, we rigorously derive an asymptotic formula which is in some sense dual to the leading-order term in the asymptotic expansion of the perturbations in the eigenvalues due to interface changes of the inclusion. Based on this (dual) formula we propose an algorithm to reconstruct the interface perturbation. We also consider an optimal way of representing the interface change and the reconstruction problem using incomplete data. A discussion on resolution is included. Proposed algorithms are implemented numerically to show their viability.

Original languageEnglish (US)
Pages (from-to)322-339
Number of pages18
JournalJournal des Mathematiques Pures et Appliquees
Volume94
Issue number3
DOIs
StatePublished - Sep 1 2010

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Inclusion
Perturbation
Incomplete Data
Viability
Asymptotic Formula
Asymptotic Expansion
Eigenvalue
Term

Keywords

  • Eigenvalue problem
  • Elastic inclusion
  • Interface changes
  • Modal measurements
  • Reconstruction

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Reconstruction of small interface changes of an inclusion from modal measurements II : The elastic case. / Ammari, Habib; Beretta, Elena; Francini, Elisa; Kang, Hyeonbae; Lim, Mikyoung.

In: Journal des Mathematiques Pures et Appliquees, Vol. 94, No. 3, 01.09.2010, p. 322-339.

Research output: Contribution to journalArticle

Ammari, Habib ; Beretta, Elena ; Francini, Elisa ; Kang, Hyeonbae ; Lim, Mikyoung. / Reconstruction of small interface changes of an inclusion from modal measurements II : The elastic case. In: Journal des Mathematiques Pures et Appliquees. 2010 ; Vol. 94, No. 3. pp. 322-339.
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