Magnetostatic analysis by BEM with magnetic double layer as unknown utilizing volume magnetic charge

The volume integral equation approach replaces magnetic materials with the magnetization in magnetostatic analysis. The concept of magnetic shell relates the magnetization with loop currents. The loop current is equivalent to the magnetic double layer, which gives an integral form of the scalar potential. The nonlinear magnetic field is formulated by regarding the nonlinear magnetization as volume magnetic charges. This paper presents how to utilize the volume charge to solve nonlinear problems. In the case of constant volume element we replace the volume charges with the surface loop currents to derive the nonlinear boundary integral equations having the line and surface loop currents as unknowns. The boundary integral equation is solved iteratively while improving alternately the loop and surface currents.