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

doi:10.1016/j.matpur.2010.02.001

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	322-339
Number of pages	18
Journal	Journal des Mathematiques Pures et Appliquees
Volume	94
Issue number	3
DOIs	https://doi.org/10.1016/j.matpur.2010.02.001
State	Published - Sep 2010

Keywords

Eigenvalue problem
Elastic inclusion
Interface changes
Modal measurements
Reconstruction

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1016/j.matpur.2010.02.001

Cite this

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title = "Reconstruction of small interface changes of an inclusion from modal measurements II: The elastic case",

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.",

keywords = "Eigenvalue problem, Elastic inclusion, Interface changes, Modal measurements, Reconstruction",

author = "Habib Ammari and Elena Beretta and Elisa Francini and Hyeonbae Kang and Mikyoung Lim",

note = "Funding Information: This work was partially supported by the ANR project EchoScan (AN-06-Blan-0089), the STAR project 190117RD, the KICOS project K20803000001-08B1200-00110, and research grants at the Inha University.",

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T1 - Reconstruction of small interface changes of an inclusion from modal measurements II

T2 - The elastic case

AU - Ammari, Habib

AU - Beretta, Elena

AU - Francini, Elisa

AU - Kang, Hyeonbae

AU - Lim, Mikyoung

N1 - Funding Information: This work was partially supported by the ANR project EchoScan (AN-06-Blan-0089), the STAR project 190117RD, the KICOS project K20803000001-08B1200-00110, and research grants at the Inha University.

PY - 2010/9

Y1 - 2010/9

N2 - 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.

AB - 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.

KW - Eigenvalue problem

KW - Elastic inclusion

KW - Interface changes

KW - Modal measurements

KW - Reconstruction

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M3 - Article

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 3

ER -

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

Abstract

Keywords

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