A consideration on thecomputational error of the boundary integral equation method for magnetostatic field problems

The computational error has been investigated for three mathematically equivalent methods: (1) the magnetic vector potential method based on the scalar Green´s theorem, (2) the magnetic vector potential method based on the vector Green´s theorem, and (3) the surface magnetization current method. The application is the magnetostatic field problem of a gapless magnetic circuit like in a transformer in which a large computational error is anticipated. It is found that the numerical error varies from method to method even when the same number and type of boundary elements and the same numerical integration method are used, and is generated mainly by the imperfect cancellation of the permeability-free terms in the boundary integral equation. Two methods for reducing the computational error are presented