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The characterisation of small low conducting inclusions in an otherwiseuniform background from low-frequency electrical field measurements hasimportant applications in medical imaging using electrical impedance tomographyas well as in geological imaging using electrical resistivity tomography. It isknown that such objects can be characterised by a P\'oyla-Szeg\"o(polarizability) tensor. Such characterisations have attracted interest as theycan provide object features in a machine learning classification algorithm andprovide an alternative imaging solution. However, to be able train machinelearning algorithms, large dictionaries are required and it is essential thatthe characterisations are accurate. In this work, we obtain accurate numericalapproximations to the tensor coefficients, by applying an adaptive boundaryelement method. The goal being to provide a sequence of benchmark{computations} for the tensor coefficients to allow other software developerscheck the accuracy of their codes.

Benchmark computations for the polarization tensor of small conducting objects