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- Title
Numerical solution method for the electric impedance tomography problem in the case of piecewise constant conductivity and several unknown boundaries.
- Authors
Gavrilov, S.; Denisov, A.
- Abstract
We study the electrical impedance tomography problem with piecewise constant electric conductivity coefficient, whose values are assumed to be known. The problem is to find the unknown boundaries of domains with distinct conductivities. The input information for the solution of this problem includes several pairs of Dirichlet and Neumann data on the known external boundary of the domain, i.e., several cases of specification of the potential and its normal derivative. We suggest a numerical solution method for this problem on the basis of the derivation of a nonlinear operator equation for the functions that define the unknown boundaries and an iterative solution method for this equation with the use of the Tikhonov regularization method. The results of numerical experiments are presented.
- Subjects
ELECTRIC impedance; TOMOGRAPHY; PIECEWISE constant approximation; ELECTRIC conductivity; NONLINEAR operator equations; MATHEMATICAL domains; DERIVATIVES (Mathematics)
- Publication
Differential Equations, 2016, Vol 52, Issue 7, p877
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266116070077