Nonlinear BEM/FEM scalar potential formulation for magnetostatic analysis in superconducting accelerator magnets

Abstract

Hybrid schemes that combine the Finite Element Method (FEM) and the Boundary Element Method (BEM) have been extensively used for the solution of nonlinear magnetostatic problems. The majority of those schemes rely either on reduced and total scalar or vector potential formulations. One main issue regarding the scalar potential formulations is the cancelation errors and difficulties on the definition of potential jump condition on the surface of a magnet, while in the case of vector potential formulations, the size of the simulated problem increases drastically especially in three dimensions. An alternative formulation has been proposed by Mayergoyz et al. (1987), which is based on scalar potentials and provides assistance in ameliorating the aforementioned problems. In the present work that formulation is implemented by employing a BEM/FEM scheme, for the solution of nonlinear magnetostatic problems. The proposed BEM/FEM formulation is employed for the solution of representative magnetostatic problems dealing with different types of superconducting accelerator magnets, while the provided accuracy is assessed through comparisons made with corresponding results obtained by a well-known commercial FEM package.