A High-order Finite Element Method for Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a non-invasive imaging technique where a conductivity distribution in a domain is reconstructed from boundary voltage measurements. The voltage data are generated by injecting currents into the domain. This is an ill-conditioned non-linear inverse problem. Small measurement or forward modeling errors can lead to unbounded fluctuations in the reconstructions. A forward model describes the dependence of the noiseless voltage data on the conductivity distribution. The present work focuses on applying the high-order finite element method (p-FEM) for forward modeling. In the traditional version of the finite element method (h-FEM), the polynomial degree of the element shape functions is relatively low and the discretization error is reduced by increasing the number of elements. In the p-version, in contrast, the polynomial degree is increased and the mesh size is kept constant. In many applications of the finite element method the performance of the p-version is better than that of the h-version. In this work, it is proposed that the p-version provides more efficient tool for EIT forward modeling. Numerical results are presented.