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A highly efficient domain decomposition method, called the dual-primal finite-element tearing and interconnecting (FETI-DP) method, is applied to improve the efficiency of three-dimensional (3-D) finite-element analysis of electromechanical and electric machine problems. The FETI-DP method decomposes an original large-scale 3-D problem into many subdomain problems and then treats the subdomain problems concurrently using parallel computing schemes to reduce the total computation time. Higher order hierarchical basis functions are implemented to improve the accuracy of the simulation and also to facilitate the treatment of the low-frequency breakdown problem, which is encountered by the traditional finite-element method with vector basis functions when solving electromechanical problems. With the separation of higher order basis functions from the lowest order ones offered by hierarchical basis functions, the low-frequency breakdown problem can be handled by applying the tree-cotree splitting method to the lowest order basis functions. The resulting accurate finite-element computation of the magnetic field is then used to calculate force and torque by using the Maxwell stress tensor method.