Numerical modelling and analysis of the forward and inverse problems in electrical capacitance tomography, Int

This paper is dedicated to my loving parents Abstract. Electrical capacitance tomography (ECT) attempts to reconstruct the internal permittivity distribution of an object. Data for the image re-construction are capacitance measurements taken at the periphery. There are potential applications for ECT in monitoring multi-phase flow in industrial processes. The image reconstruction of ECT remains a challenging problem. Linear and nonlinear reconstruction methods are studied in this paper. In this paper two-dimensional image reconstruction programs based on standard reg-ularized Gauss Newton (GN) and Broyden Quasi-Newton (BQN) methods are implemented. The forward problem is solved via using finite element method (FEM). In GN the forward problem and the Jacobian matrices are recalculated in each iteration. In BQN an approximated inverse of the Jacobian matrix can be calculated directly. This paper studies a combined GN and BQN algorithm, in which for first few iterations GN is used and then BQN iterations are used for the last few iterations close to the solution. This combined GN and BQN technique is demonstrated by using simulated and experimental ECT data. Key Words. Electrical capacitance tomography, inverse problems, linear and nonlinear methods, finite element method. 1