Two-Dimensional Galerkin Magnetostatic Method of Moments

In this paper, method of moments (MoM) solutions for 2-D magnetostatic problems are considered. An initial focus is on the detailed derivations for point matching and Galerkin formulations. As part of its derivation, it is shown that analytical solutions exist for all of the integrals; one must evaluate. This eliminates differences in the computational requirements between the two formulations. A second focus is to compare the accuracy of the methods. To do so, the solutions obtained in modeling an E-I core are compared with a finite-element solution. It is shown that the point matching solution is prone to significant error as the permeability of the core increases. In contrast, it is shown that the error for a Galerkin formulation remains small for arbitrary permeability and a surprisingly low number of elements.