The scalar potential formulation by the boundary integral equation approach is attractive for numerical analysis but has fatal drawbacks due to a multi-valued function in current excitation. We derive an all-purpose boundary integral equation with double layer charges as the state variable and apply it to nonlinear magnetostatic problems by regarding the nonlinear magnetization as fictitious volume charges. We investigate two approaches how to treat the fictitious charges. In discretization by the constant volume element, a surface loop current is introduced for the volume charge. By the linear volume element, the fictitious charges are evaluated on the condition that the divergence of the magnetic flux density is zero. We give a comparative study of these two approaches.
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