Magnetostatic analysis by BEM for multiply connected problem

Purpose: The purpose of this study is to demonstrate the novel approach in treating multiply connected problems in magnetostatic. Design/methodology/approach: The new double layer approach (DLA) to be proposed is based on the use of the exciting double layer on the cut-surface. Applying Ampere’s circuital law to the circuital path along a toroidal core of M–C model, this paper derives unified exciting potential (UEP) from the common exciting potential. The UEP is applicable to the simply or M–C analysis. To check the effectiveness of the UEP, this paper analyze typical M–C problems and compares the results with those of other benchmark problems and also those obtained by surface charge method (SCM). Because the SCM encounters a cancellation error, this paper overcomes this problem by using the concept of direct boundary element method (BEM). Findings: Using the improved DLA, this paper analyzed a typical multiply connected model and compared the results with those of the SCM, which has been improved to overcome cancellation errors. This paper has confirmed that the results obtained by the improved DLA are the same as those obtained by the improved SCM and Steklov–Poincaré operator formulation, tested at the well-known benchmark problems given in Andjelic et al. (2010). From these results, this paper concluded that the Improved DLA works well and that the improved SCM becomes available for analyzing both the simply and multiply connected problems. Originality/value: Expanding a concept of the exciting double layer on the cut-surface, this paper improve the DLA to analyze the M–C problems. Applying Ampere’s circuital law to the full circuital path along the toroidal core of M–C problem, this paper derive UEP from the original exciting potential to get the governing BIE. The BIE is applicable to either simply or multiply connected analysis.