Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

LeeKoKim

Virtual resistive network and conductivity reconstruction with Faradayʼs law

M-G. Lee, M-S. Ko,  Y-J. Kim, Virtual resistive network and conductivity reconstruction with Faradayʼs law, Inverse Problems, 30(12):125009,  2014
M-G. Lee, M-S. Ko, Y-J. Kim,
MREIT, virtual resistive network, mimetic discretization, isotropic conductivity
2014
A network-based conductivity reconstruction method is introduced using the third Maxwell equation, or Faradayʼs law, for a static case. The usual choice in electrical impedance tomography is the divergence-free equation for the electrical current density. However, if the electrical current density is given, the curl-free equation for the electrical field gives a direct relation between the current and the conductivity and this relation is used in this paper. Mimetic discretization is applied to the equation, which gives the virtual resistive network system. Properties of the numerical schemes introduced are investigated and their advantages over other conductivity reconstruction methods are discussed. Numerically simulated results, with an analysis of noise propagation, are presented.​