Smoothened complete electrode model

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Authors

Hyvönen, Nuutti
Mustonen, Lauri

Date

2017-12

Department

Department of Mathematics and Systems Analysis

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Mcode

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Language

en

Pages

2250–2271

Series

SIAM JOURNAL ON APPLIED MATHEMATICS, Volume 77, issue 6

Abstract

This work reformulates the complete electrode model of electrical impedance tomography in order to enable more efficient numerical solution. The model traditionally assumes constant contact conductances on all electrodes, which leads to a discontinuous Robin boundary condition since the gaps between the electrodes can be described by vanishing conductance. As a consequence, the regularity of the electromagnetic potential is limited to less than two square-integrable weak derivatives, which negatively affects the convergence of, e.g., the finite element method. In this paper, a smoothened model for the boundary conductance is proposed, and the unique solvability and improved regularity of the ensuing boundary value problem are proven. Numerical experiments demonstrate that the proposed model is both computationally feasible and compatible with real-world measurements. In particular, the new model allows faster convergence of the finite element method.

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Keywords

electrical impedance tomography, complete electrode model, inverse elliptic boundary value problems, regularity

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DOI

10.1137/17M1124292

Citation

Hyvönen, N & Mustonen, L 2017, ' Smoothened complete electrode model ', SIAM Journal on Applied Mathematics, vol. 77, no. 6, pp. 2250–2271 . https://doi.org/10.1137/17M1124292

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https://urn.fi/URN:NBN:fi:aalto-201902252103

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[article-cris] Perustieteiden korkeakoulu / SCI