An accurate formula for the reconstruction of conductivity inhomogeneitis

Habib Ammari; Jin Keun Seo

doi:10.1016/S0196-8858(02)00557-2

An accurate formula for the reconstruction of conductivity inhomogeneitis

Habib Ammari
, Jin Keun Seo

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

43 Citations (Scopus)

Abstract

We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy.

Original language	English
Pages (from-to)	679-705
Number of pages	27
Journal	Advances in Applied Mathematics
Volume	30
Issue number	4
DOIs	https://doi.org/10.1016/S0196-8858(02)00557-2
Publication status	Published - 2003 May

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (H. Ammari), [email protected] (J.K. Seo). 1 The author was partly supported by ACI Jeunes Chercheurs (0693) from the Ministry of Education and Scientific Research, France. 2 The author was partly supported by KOSEF grant 1999-2-103-001-5.

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1016/S0196-8858(02)00557-2

Cite this

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abstract = "We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy.",

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AU - Seo, Jin Keun

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N2 - We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy.

AB - We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy.

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An accurate formula for the reconstruction of conductivity inhomogeneitis

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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