Characterisation of hidden objects in electrical impedance tomography using adaptive boundary elements

Electromagnetic inverse problems involve determining the location and identifying the shape and parameters of hidden conducting objects. Low-frequency, low-conductivity applications, range from geophysical applications, such as electric resistivity imaging (ERI), including groundwater detection or minerals and oil identification, to medical imaging problems using electrical impedance tomography (EIT). EIT consists of finding the conductivity contrast between an anomaly and a healthy tissue from voltage measurements around the patient body. For EIT, the perturbed electrical potential field (which is related to the voltage measurements) can be described by an asymptotic expansion as the size of an isolated inclusion goes to 0, which the leading order term separating into the gradient of a free-space Green's function, the gradient of the background potential field at the position of the object and the polarization tensor. In this work, we present an adaptive boundary element mesh algorithm to compute the polarization tensor accurately using BEM++. Moreover, the relationship of the computational discretisation of the object is investigated through a series of numerical experiments.