New BEM/BEM and BEM/FEM scalar potential formulations for magnetostatic problems

The majority of the numerical methods applied so far for the simulation of a magnetostatic problem is based either on reduced and total scalar or vector potential formulations. The first one suffers from cancellation errors, the second one from the difficulty of defining the jump condition for potential on the surface of a magnet. Furthermore, the vector potential introduces three Degrees of Freedom per node increasing the computational effort for the solution of a three dimensional problem. Mayergoyz et al. (1987) proposed an alternative formulation, which is based on scalar potentials and is free of the aforementioned problems. The present work implements this formulation for the solution of magnetostatic problems by utilizing either Boundary Element Method (BEM) or its combination with Finite Element Method (FEM). Both numerical schemes are explained for two dimensional and linear problems. Two representative magnetostatic problems are solved and their solutions are compared to the corresponding ones taken by well-known commercial package.