Treatment of singularities in the computation of magnetic fields with periodic boundary conditions by the boundary element method

It is shown that under periodic conditions the singularities in the BEM (boundary equation method) caused by geometric corners, subdomains, and discontinuous boundary conditions can be effectively and accurately treated by the double node-method, where the compatible equation is not needed. The application of the double-node method is considered in connection with Dirichlet´s problem, Neumann´s problem, and an interface problem together with periodic boundary conditions. Finally, an airgap magnetic field of an asynchronous machine with a discontinuous boundary current sheet distribution is calculated by means of this method. The numerical results obtained agree very well with the analytical results. It is concluded that, compared to the finite-element method, the BEM is better suited to calculate an airgap magnetic field with the discontinuous boundary conditions