Smoothened complete electrode model
This work addresses a computational bottleneck in electrical impedance tomography by enabling more efficient numerical solutions for practitioners using finite element methods.
The authors reformulate the complete electrode model for electrical impedance tomography by smoothing the boundary conductance, improving the regularity of the electromagnetic potential and enabling faster convergence of the finite element method. Numerical experiments confirm computational feasibility and compatibility with real-world measurements.
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.