2-D method of moments formulations for nonlinear low-frequency electromagnetics

In this research, point-matching, Galerkin, and a hybrid point-matching/Galerkin approach are derived for modeling nonlinear materials in a 2-D method of moments formulation intended for the analysis of low-frequency magnetic components. Analytical expressions are derived for all terms of the Jacobian needed within a Newton–Raphson solver. All approaches are found to have strong convergence properties, wherein they are relatively insensitive to initial guess and achieve convergence within a low number of iterations without the need for a relaxation factor. The tradeoffs between accuracy and numerical efficiency of the approaches are evaluated by comparing the predicted flux linkage of a rectangular core inductor over a wide range of input current.