Periodic Boundary Conditions in the Natural Element Method

The purpose of this paper is to introduce periodic and antiperiodic boundary conditions in the natural element method (NEM). It is shown that as the NEM shape functions verify the Kronecker delta property, the imposition of such boundary conditions can be done in an easy way as in the finite-element method (FEM). These boundary conditions are important because they allow exploitation of the inherent symmetry of the electromagnetic devices. Therefore, with these techniques the NEM can now easily take advantage of the symmetry of electrical machines. The proposed approach is evaluated, and its results are compared with those obtained by the traditional FEM.