Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives

Electrical resistance tomography is a novel non-intrusive technique to image the electrical conductivity distribution. The technique is characterized as a nonlinear, ill-posed inverse problem with many unknowns. A numerical method based on boundary element method is presented in this paper, aiming to obtain the boundary of inclusions with a constant conductivity. The forward problem employs the complete electrode model and the size of system matrix is reduced. The Jacobian matrix is established through the partial derivatives of element integrals and linearization of the system. The analytical integrations for quadratic elements are presented, where higher-order integrals are expressed by lower-order ones for rapid calculation. The iterative Levenberg–Marquardt method is adopted to solve the inverse problem.