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(2015)
Iterative Method for Determining the Shape and Conductivity of Homogeneous Inclusion in the Two-Dimensional Electric Impedance Tomography Problem
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Metody resheniya nekorrektnykh zadach (Methods for Solving Ill-Posed Problems)
H. Eckel, R. Kress (2007)
Nonlinear integral equations for the inverse electrical impedance problemInverse Problems, 23
S. Gavrilov, A. Denisov (2011)
Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace’s equation in a piecewise homogeneous mediumComputational Mathematics and Mathematical Physics, 51
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Stability for an inverse problem in potential theoryTransactions of the American Mathematical Society, 332
G. Alessandrini, V. Isakov (1996)
Analicity and uniqueness for the inverse conductivity problem
K. Astala, L. Päivärinta (2006)
Calderon's inverse conductivity problem in the planeAnnals of Mathematics, 163
A.N. Tikhonov, V.Ya. Arsenin (1979)
Metody resheniya nekorrektnykh zadach
Munkh-Erdene Ts, E. Lee, J. Seo, B. Harrach, Sungwhan Kim (2013)
Projective Electrical Impedance Reconstruction with Two MeasurementsSIAM J. Appl. Math., 73
S.V. Gavrilov, A.M. Denisov (2012)
Iterative Method for Solving a Three-Dimensional Electrical Impedance Tomography Problem in the Case of Piecewise Constant Conductivity and One Measurement on the BoundaryZh. Vychisl. Mat. Mat. Fiz., 52
S. Gavrilov, A. Denisov (2014)
Numerical method for solving a two-dimensional electrical impedance tomography problem in the case of measurements on part of the outer boundaryComputational Mathematics and Mathematical Physics, 54
K. Knudsen, M. Lassas, J. Mueller, S. Siltanen (2009)
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEMInverse Problems and Imaging, 3
(2009)
Numerical Methods for Solving Some Inverse Problems of Heart Electrophysiology
S.V. Gavrilov, A.M. Denisov (2011)
Numerical Methods for Determining the Inhomogeneity Boundary in a Boundary Value Problem for the Laplace Equation in a Piecewise Homogeneous MediumZh. Vychisl. Mat. Mat. Fiz., 51
Hyeonbae Kang, J. Seo, D. Sheen (1997)
Numerical identification of discontinuous conductivity coefficientsInverse Problems, 13
(1999)
Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Moskov
S.V. Gavrilov, A.M. Denisov (2014)
Numerical Method for Solving a Two-Dimensional Electrical Impedance Tomography Problem in the Case of Measurements on Part of the Outer BoundaryZh. Vychisl. Mat. Mat. Fiz., 54
B. Barceló, E. Fabes, J. Seo (1994)
The inverse conductivity problem with one measurement: uniqueness for convex polyhedra, 122
M. Brühl, M. Hanke (2000)
Numerical implementation of two noniterative methods for locating inclusions by impedance tomographyInverse Problems, 16
S. Gavrilov, A. Denisov (2012)
Iterative method for solving a three-dimensional electrical impedance tomography problem in the case of piecewise constant conductivity and one measurement on the boundaryComputational Mathematics and Mathematical Physics, 52
A.A. Samarskii, A.N. Tikhonov (1999)
Uravneniya matematicheskoi fiziki
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.
Differential Equations – Springer Journals
Published: Aug 9, 2016
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