A single scalar potential method for 3D magnetostatics using edge elements

It is demonstrated that it is possible to use a single, continuous, scalar potential to solve magnetostatic problems in three dimensions without the loss of accuracy associated with the reduced potential. This method makes use of tetrahedral edge elements and does not require the initial calculation of the field of the currents in the absence of magnetic materials. The method requires no numerical integration, has no restrictions on the current flow or the iron topology, and needs the solution of only one matrix problem. Results obtained by the method for translational and axisymmetric problems agree well with those computed by two-dimensional analysis with a vector potential. The method can be used to obtain accurate flux densities in both air and iron regions of three-dimensional problems