An equilibrium finite element method for electrical impedance tomography

We present a new numerical method for the forward problem of electrical impedance tomography with the shunt model. The new method builds on a discretization of the total Joule heat consumed over the region, in terms of the current density. It gives an approximation of the distribution of current density before using it to reconstruct the potential distribution. Simulations on a 2D and a 3D EIT model indicate the new method can produce more accurate approximations than the traditional FEM, based on the same mesh. The new method has the potential to be a competitive alternative of the traditional FEMs and incoporated into some reconstruction algorithms of EIT.