An improved boundary distributed source method for electrical resistance tomography forward problem

This paper presents a meshless method called the improved boundary distributed source (IBDS) method to obtain the numerical solution of an electrical resistance tomography (ERT) forward problem. The ERT forward problem contains solving the Laplace equation on piece-wise homogeneous domain subjected to the mixed boundary conditions with constraints of integral form. The IBDS method is mesh-free and does not require a fictitious boundary for source points as in the case of a conventional method of fundamental solution (MFS) approach. Therefore, it can be used for a wide variety of applications involving complex shaped objects that are difficult to mesh. Also, in the IBDS method, the diagonal elements for Neumann boundary conditions are computed analytically unlike the original BDS method. Therefore, the IBDS method is computationally efficient and stable compared to the BDS method. The ERT forward problem to compute the boundary voltages is formulated using a meshless IBDS method. Several numerical examples are tested to demonstrate the feasibility and accuracy of the new formulation. The results are compared with that of standard numerical forward solvers for ERT such as the boundary element method (BEM) and the finite element method (FEM).