Some treatments of fictitious volume charges in nonlinear magnetostatic analysis by BIE

K. Ishibashi*, Z. Andjelic, Y. Takahashi, T. Takamatsu, K. Tsuzaki, S. Wakao, K. Fujiwara, Y. Ishihara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Article number6136647
Pages (from-to)463-466
Number of pages4
JournalIEEE Transactions on Magnetics
Issue number2
Publication statusPublished - 2012 Feb


  • Boundary integral equation
  • double layer charge
  • fictitious volume charges
  • iterative solutions
  • multi-valued function

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering


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