<div>Recently, researchers have pointed their attention toward Method of Moments (MoM)-based approaches to model low frequency magnetic devices (i.e. transformers and inductors). This has been prompted by the use of population-based design (PBD) methods wherein the performance of large numbers (on the order of millions) of candidate designs must be evaluated. MoM is attractive for such problems due to the fact that only the magnetic material is discretized. In addition, for the case in which the magnetic material is linear, only a surface mesh is required. In this research, point-matching and Galerkin-based MoM formulations are utilized for the design of electric machinery. In the formulations considered, the model inputs are the free currents of machine windings and the bound currents of permanent magnets. The unknowns are the magnetizations within the magnetic material which are used to compute winding inductance, electromagnetic torque, and core loss. </div><div><br></div><div>The proposed Galerkin formulation has been utilized in the PBD of a surface-mount permanent magnet machine with favorable results. Specifically, it is shown that a machine's performance can be evaluated on a time scale expected of a practical design tool. This is achieved in part through judicious exploitation of the periodic structure and excitation of machines to reduce the size of the system matrix. It is shown how the exploitation of periodic structure may be extended to the point-matching formulation for use in nonlinear analyses. Finally, alternative hybrid approaches that combine surface and volume meshing are explored for the analysis of an internal permanent magnet machine. It is shown that such a combination holds promise as a tool for rapid evaluation of machine performance.</div>