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Modern electrical plant and machinery have to be designed to operate at high power densities at minimum cost and optimal efficiency with a high degree of reliability during operation. These stringent requirements necessitate accurate performance prediction at the design stage. As a first and important step in this process, the magnetic field distribution must be evaluated taking full account of the geometrical complexity of the field region, magnetic saturation of the iron parts, and circulating currents in conducting media. The advent of digital computers has spurred the development of sophisticated numerical techniques to accomplish this task with a high degree of precision. In this paper, three-dimensional vector potential solution methods for linear and nonlinear diffusion and magnetostatic field problems are presented. The methods are illustrated by numerical examples where feasible. This research has been partially funded by the Electric Power Research Institute, Palo Alto, California under EPRI contract RP 1288-1.