Self-Check Function of Double-Layer Approach in Multiply-Connected Problem

The Double-Layer Approach possesses superior features for the analysis of static magnetic problems. In this paper, as a novelty, we introduce the Self-Check Function, an inherent feature in the double-layer BEM, which enables proof of the correctness of the solutions of the governing BIE. Thanks to the Self-Check Function, we can easily prove the solution of BIE by tracking the magnetic field. When analyzing the multiply-connected problem in magnetostatic, it is obligatory to use the cut-surface. There appear two kinds of double-layers: one on the surface of magnetic body and the other on the cut-surface within the exciting current loop. Utilizing the Ampere's circuital integral law, we introduce the novel, unified exciting double-layer on the cut-surface, controlled by the Self-Check Function. Using the Self-Check Function, we solve a typical multiply-connected problem and demonstrate that the unified exciting double-layer works well.