Extensions to the finite element method for the analysis of inverse problems in electromagnetic devices

This thesis is concerned with the development of inverse finite element methods for an electrical impedance tomography system for producing cross-sectional images of the distribution of insulating media embedded in conducting media, and for a numerical design tool for optimal synthesis of nonlinear magnetostatic systems.; The overall imaging system described has the potential of being both fast and cost effective in comparison with alternative methods. Major advances are made in the computational reconstruction of images from electrical excitation and response data with respect to existing capabilities reported in the literature. The methods developed use multiple plate-electrode excitation in conjunction with finite element block decomposition, preconditioned voltage conversion, layer approximation of the third dimension, and post processing of boundary measurements to obtain optimal boundary excitations. Reasonably accurate imaging of single and multiple targets of differing size, geometry, location, and separation is demonstrated and the resulting images are better than any others found in the literature. A demonstration is provided of the imaging of one or more circular objects within the measurement plane with demonstrated linear resolution of six parts in two hundred. Accurate excitation and measurement of boundary voltages and currents appears adequate to obtain reasonable images of the real conductivity distribution within a body and the outlines of insulating targets suspended within a homogeneous conducting medium.; A novel inverse method developed to minimize the computational effort by combining the optimization process with the nonlinear finite element equations is capable of obtaining optimal geometric parameters of a saturable magnetic device to approximate a desired magnetic flux density distribution at certain test points. A second-order approach based on the Lagrange-Newton method is formulated in conjunction with the augmented Lagrange multipliers method to efficiently and reliably solve the constrained optimization problem. The best capabilities to parametrically represent the device geometry and the nonlinear material characteristics are incorporated into the optimization algorithm to calculate derivatives efficiently. A demonstration of test cases arising from optimally designing electrical machinery and electromagnets verified the validity of the overall theory and developments.