Beside magnetic equivalent circuit and finite element methods, sub-domain analysis (SDA) is an alternative method, which can be used to evaluate electrical machines behavior. It has a reasonable accuracy, and its parametric nature is allowed to apply to optimization or sensitivity analysis. Commonly, this method is based on variables separation technique of Maxwell equations and Fourier series. Eigenvalues and eigen-functions are so important for obtaining accurate results. In this paper, Maxwell equations are solved for two adjacent regions, i.e., copper (Cu) and permanent magnet (PM). It was paid less attention before, and it introduces supplementary eigenvalue and eigen-function for asymmetry conditions in Cu or PM magnetic field regions.