# Smoothened complete electrode model

## TL;DR

This paper introduces a smoothened boundary conductance model for electrical impedance tomography that enhances numerical solution efficiency and convergence by improving the regularity of the electromagnetic potential.

## Contribution

It proposes a novel smoothened boundary conductance model, proving its unique solvability and better regularity, leading to faster finite element method convergence.

## Key findings

- The smoothened model is computationally feasible.
- It improves convergence speed of numerical methods.
- Compatible with real-world measurement data.

## Abstract

This work reformulates the complete electrode model of electrical impedance tomography in order to enable more efficient numerical solution. The model traditionally assumes constant contact conductances on all electrodes, which leads to a discontinuous Robin boundary condition since the gaps between the electrodes can be described by vanishing conductance. As a consequence, the regularity of the electromagnetic potential is limited to less than two square-integrable weak derivatives, which negatively affects the convergence of, e.g., the finite element method. In this paper, a smoothened model for the boundary conductance is proposed, and the unique solvability and improved regularity of the ensuing boundary value problem are proven. Numerical experiments demonstrate that the proposed model is both computationally feasible and also compatible with real-world measurements. In particular, the new model allows faster convergence of the finite element method.