Volume 1, Issue 4
Determining a Piecewise Conductive Medium Body by a Single Far-Field Measurement

Xinlin Cao, Huaian Diao & Hongyu Liu

CSIAM Trans. Appl. Math., 1 (2020), pp. 740-765.

Published online: 2020-12

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  • Abstract

We are concerned with the inverse problem of recovering a conductive medium body. The conductive medium body arises in several applications of practical importance, including the modelling of an electromagnetic object coated with a thin layer of a highly conducting material and the magnetotellurics in geophysics. We consider the determination of the material parameters inside the body as well as on the conductive interface by the associated electromagnetic far-field measurement. Under the transverse-magnetic polarisation, we derive two novel unique identifiability results in determining a 2D piecewise conductive medium body associated with a polygonal-nest or a polygonal-cell geometry by a single active or passive far-field measurement.

  • Keywords

Electromagnetic scattering, conductive transmission condition, inverse problem, single far-field measurement, polygonal, corner singularity.

  • AMS Subject Headings

35Q60, 78A46, 35P25, 78A05, 81U40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-740, author = {Xinlin and Cao and and 10042 and and Xinlin Cao and Huaian and Diao and and 10043 and and Huaian Diao and Hongyu and Liu and and 10044 and and Hongyu Liu}, title = {Determining a Piecewise Conductive Medium Body by a Single Far-Field Measurement}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {4}, pages = {740--765}, abstract = {

We are concerned with the inverse problem of recovering a conductive medium body. The conductive medium body arises in several applications of practical importance, including the modelling of an electromagnetic object coated with a thin layer of a highly conducting material and the magnetotellurics in geophysics. We consider the determination of the material parameters inside the body as well as on the conductive interface by the associated electromagnetic far-field measurement. Under the transverse-magnetic polarisation, we derive two novel unique identifiability results in determining a 2D piecewise conductive medium body associated with a polygonal-nest or a polygonal-cell geometry by a single active or passive far-field measurement.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0020}, url = {http://global-sci.org/intro/article_detail/csiam-am/18544.html} }
TY - JOUR T1 - Determining a Piecewise Conductive Medium Body by a Single Far-Field Measurement AU - Cao , Xinlin AU - Diao , Huaian AU - Liu , Hongyu JO - CSIAM Transactions on Applied Mathematics VL - 4 SP - 740 EP - 765 PY - 2020 DA - 2020/12 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0020 UR - https://global-sci.org/intro/article_detail/csiam-am/18544.html KW - Electromagnetic scattering, conductive transmission condition, inverse problem, single far-field measurement, polygonal, corner singularity. AB -

We are concerned with the inverse problem of recovering a conductive medium body. The conductive medium body arises in several applications of practical importance, including the modelling of an electromagnetic object coated with a thin layer of a highly conducting material and the magnetotellurics in geophysics. We consider the determination of the material parameters inside the body as well as on the conductive interface by the associated electromagnetic far-field measurement. Under the transverse-magnetic polarisation, we derive two novel unique identifiability results in determining a 2D piecewise conductive medium body associated with a polygonal-nest or a polygonal-cell geometry by a single active or passive far-field measurement.

Xinlin Cao, Huaian Diao & Hongyu Liu. (2020). Determining a Piecewise Conductive Medium Body by a Single Far-Field Measurement. CSIAM Transactions on Applied Mathematics. 1 (4). 740-765. doi:10.4208/csiam-am.2020-0020
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