Geodesic
An approximate analytical solution to the forward inhomogeneous EIT problem on the 2D disk with allowance for the electrode contact impedance
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 19-29

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An approximate analytical solution of the potential distribution in a two-dimensional circle with a radially inhomogeneous conductivity is obtained for the boundary conditions of the full electrode model, which takes into account the contact resistance of the electrodes at a given current strength. The solution is obtained by separating variables and using Fourier series, for the coefficients of which it is necessary to solve a system of linear equations. The obtained solution was compared with an approximate analytical solution of a similar problem for a homogeneous disk and with the Neumann-Robin boundary conditions. A good agreement was obtained, the quality of which improved with an increase in the number of terms taken into account in the series.
Keywords: elliptic equation in a circle, complete electrode model with integro-differential boundary condition, Fourier series.
Mots-clés : piecewise constant coefficients 
@article{VTGU_2021_74_a2,
     author = {A. V. Starchenko and M. A. Sednev and S. V. Pan'ko},
     title = {An approximate analytical solution to the forward inhomogeneous {EIT} problem on the {2D} disk with allowance for the electrode contact impedance},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {19--29},
     publisher = {mathdoc},
     number = {74},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2021_74_a2/}
}
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A. V. Starchenko; M. A. Sednev; S. V. Pan'ko. An approximate analytical solution to the forward inhomogeneous EIT problem on the 2D disk with allowance for the electrode contact impedance. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 19-29. http://geodesic.mathdoc.fr/item/VTGU_2021_74_a2/