TY - JOUR
T1 - Smoothened complete electrode model
AU - Hyvönen, Nuutti
AU - Mustonen, Lauri
PY - 2017/12
Y1 - 2017/12
N2 - 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 compatible with real-world measurements. In particular, the new model allows faster convergence of the finite element method.
AB - 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 compatible with real-world measurements. In particular, the new model allows faster convergence of the finite element method.
KW - electrical impedance tomography
KW - complete electrode model
KW - inverse elliptic boundary value problems
KW - regularity
UR - https://arxiv.org/abs/1703.08022
U2 - 10.1137/17M1124292
DO - 10.1137/17M1124292
M3 - Article
VL - 77
SP - 2250
EP - 2271
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 6
ER -