Surface current reconstruction using magnetic field tomography

The identification of characteristics or shape reconstruction of boundary surfaces are inverse problems arising in industrial applications, e.g., in magnetic fluid dynamics. We have investigated the identification of the interface between two conducting fluids using multichannel magnetic field measurements (magnetic field tomography). We considered a highly simplified model of an aluminum electrolysis cell consisting of a cylinder containing two compartments with different conductivities. Numerical simulations using the finite element method (FEM) have been evaluated. Additionally, magnetic field measurements taken from an experimental setup of this cylindrical object have been used as a reference for comparison. We propose a new test problem for the evaluation of inverse methods which consists in the estimation of the interface shape characteristics based on the current density distribution in the vicinity of the deformed interface using magnetic field measurements.