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Mathematics > Numerical Analysis

arXiv:2211.05623 (math)
[Submitted on 10 Nov 2022 (v1), last revised 31 May 2023 (this version, v2)]

Title:A high order discontinuous Galerkin method for the recovery of the conductivity in Electrical Impedance Tomography

Authors:Xiaosheng Li, Wei Wang
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Abstract:In this work, we develop an efficient high order discontinuous Galerkin (DG) method for solving the Electrical Impedance Tomography (EIT). EIT is a highly nonlinear ill-posed inverse problem where the interior conductivity of an object is recovered from the surface measurements of voltage and current flux. We first propose a new optimization problem based on the recovery of the conductivity from the Dirichlet-to-Neumann map to minimize the mismatch between the predicted current and the measured current on the boundary. And we further prove the existence of the minimizer. Numerically the optimization problem is solved by a third order DG method with quadratic polynomials. Numerical results for several two-dimensional problems with both single and multiple inclusions are demonstrated to show the high {accuracy and efficiency} of the proposed high order DG method. Analysis and computation for discontinuous conductivities are also studied in this work.
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
Cite as: arXiv:2211.05623 [math.NA]
  (or arXiv:2211.05623v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.05623

Submission history

From: Wei Wang [view email]
[v1] Thu, 10 Nov 2022 14:54:37 UTC (1,183 KB)
[v2] Wed, 31 May 2023 15:41:26 UTC (913 KB)
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