Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity

2013/10/09 by Hyeonbae Kang, Kyoungsun Kim, Kang, Hyeonbae +7
Mathematics · #35J20 #45Q05 #65N21 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J20 #msc:45Q05 #msc:65N21

paper · pdf · doi:10.48550/arxiv.1310.2439

15 pages, 5 figures, 5 tables

arxiv created 2013/10/09 · arxiv updated 2013/10/10

Abstract

The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the body are derived in terms of two pairs of voltage and current data measured on the boundary of the body. These bounds are derived using the translation method. We also provide numerical examples to show that these bounds are quite tight and stable under measurement noise.

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