Geodesic
Numerical solution of the inverse problem of electrical impedance tomography using the iteration method
Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 4, pp. 5-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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A computational algorithm has been developed for solving the inverse problem of electrical impedance tomography in a complete electrode model, which is an inverse coefficient problem for a difference scheme built on unstructured grids for an elliptic equation with integro-differential boundary conditions. The iteration algorithm is based on the iterative regularized Gauss—Newton method in which the inverse matrix of the main matrix of the system of linear equations is calculated; the derivatives of the main matrix whose coefficients depend linearly on conductivity are found analytically. The implementation of the computational algorithm is performed for the two-dimensional case of a 16-electrode disk model with one insert. The influence of the choice of the initial approximation and the error in the input data on the convergence of the iteration process has been studied.
Mots-clés : coefficient inverse problem
Keywords: elliptic equation with piecewise constant coefficients, integro-differential boundary condition, finite volume method, unstructured grid, complete electrode model, conductivity reconstruction, iteratively regularized Gauss—Newton method. 
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A. A. Afanasyeva; A. V. Starchenko. Numerical solution of the inverse problem of electrical impedance tomography using the iteration method. Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 4, pp. 5-19. http://geodesic.mathdoc.fr/item/SJIM_2024_27_4_a0/

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