Numerical solution method for the electric impedance tomography problem in the case of piecewise constant conductivity and several unknown boundaries

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• 作者：S. V. Gavrilov ; A. M. Denisov
• 刊名：Differential Equations
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：52
• 期：7
• 页码：877-886
• 全文大小：392 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Ordinary Differential Equations
  Partial Differential Equations
  Difference and Functional Equations
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1608-3083
• 卷排序：52

文摘

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.Original Russian Text © S.V. Gavrilov, A.M. Denisov, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 7, pp. 917–926.