Accurate Benchmark Computations of the Polarizability Tensor for Characterising Small Conducting Inclusions

The characterisation of small conducting inclusions with low conductivities in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in geological imaging using electrical resistivity tomography. It is known that such objects can be characterised by a P\'oyla-Szeg\"o polarizability tensor. The coefficients of this tensor for different shapes and contrasts involves the solution of a transmission problem, which in general must be done numerically. With a dictionary classification algorithm in mind, we provide a series of accurate tensor characterisations of objects that can be used as benchmarks for developers of software tools for solving the transmission problem. To this end, we apply adaptive the boundary element method to achieve our accurate solutions.