Abstract
A convergence study of the forward problem of electrical impedance tomography is performed using triangular high-order piecewise polynomial finite-element methods (p-FEM) on a square domain. The computation of p-FEM for the complete electrode model (CEM) is outlined and a novel analytic solution to the CEM on a square domain is presented. Errors as a function of mesh-refinement and computational time, as well as convergence rates as a function of contact impedance, are computed numerically for different polynomial approximation orders. It is demonstrated that p-FEM can generate more accurate forward solutions in less computational time, which implies more accurate simulated interior potentials, electrode voltages and conductivity Jacobians.
Highlights
Electrical impedance tomography (EIT) is an emerging imaging modality that aims to reconstruct the interior conductivity distribution of an object from electrical measurements obtained on the periphery
A convergence study of different EIT forward problems was performed on a 2D square domain using polynomial finite-element methods (p-FEM), and a novel semi-analytic solution to the complete electrode model (CEM) on the square domain was derived
For the CEM higher order polynomial approximations resulted in greater convergence rates under uniform h-refinement
Summary
Electrical impedance tomography (EIT) is an emerging imaging modality that aims to reconstruct the interior conductivity distribution of an object from electrical measurements obtained on the periphery. Given a vector of measured voltages U(σT ) ∈ Rm at σT , a typical EIT reconstruction algorithm seeks to find the conductivity as the minimizer of a data misfit and regularization functional σ. Hp-FEM can achieve exponential convergence as a function of the number of degrees of freedom of the approximation (see [14,15] for an application of hp-FEM in 2D EIT for the continuum model and CEM, respectively, as well as [16] for an application of p-FEM in 2D EIT for the CEM) This is the first study to use a novel analytic solution to the CEM as a testbed for p-FEM convergence.
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