Theoretical and numerical comparisons between Laplace's solution and Poisson's solution to the forward problem for a finite right circular cylinder [EIT image reconstruction]

Abstract

This paper shows that the full analytical solution derived by the mode matching technique for a finite right circular cylinder using Laplace's equation with inhomogeneous boundary conditions reduces to the full analytical solution derived by the Green's function technique for Poisson's equation using homogeneous boundary conditions when two identical rectangular electrodes are arbitrarily placed on the curved surface of the cylinder. Numerical comparisons between the full solution to Laplace's equation and a reduced form in terms of computed potentials on some points and reconstruction of equipotentials for a polar drive configuration are also presented.