Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model

Hintermüller, Michael; Laurain, Antoine; Yousept, Irwin

doi:10.1088/0266-5611/31/6/065006

Article / Chapter Fri May 3 2019 CC BY-NC-ND 3.0

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Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model

Hintermüller, Michael ; Laurain, Antoine ; Yousept, Irwin

In this paper the shape derivative of an objective depending on the solution of an eddy current approximation of Maxwell’s equations is obtained. Using a Lagrangian approach in the spirit of Delfour and Zolésio, the computation of the shape derivative of the solution of the state equation is bypassed. This theoretical result is applied to magnetic impedance tomography, which is an imaging modality aiming at the contactless mapping (identification) of the unknown electrical conductivities inside an object given measurements recorded by receiver coils.

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Date Issued:: 03.05.2019
URN:: urn:nbn:de:hbz:464-20190503-131106-9
DOI:: 10.1088/0266-5611/31/6/065006
Language:: English
Type of Resource:: Text
Keywords:: magnetic induction tomography; shape optimization; shape derivative
Collection:: E-Publications
Dewey Decimal Classification:: 510 Mathematics
Subject categories of the Deutsche Nationalbibliografie:: 510 Mathematics
Apple podcast categories:: Arts
Hosting institution:: Faculty of Mathematics
Info on primary publication:: This is an author-created, un-copyedited version of an article published in: Inverse Problems 31 (2015) 065006. IOP Publishing Ltd. is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/0266-5611/31/6/065006
restriction:: This Accepted Manuscript is © 2015 IOP Publishing Ltd. - Everyone is permitted to use copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License
version identification:: Accepted Manuscript