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Nonlinear magnetostatic BEM formulation using one unknown double layer charge

Kazuhisa Ishibashi (Corporate Research, ABB Switzerland Ltd, Baden, Switzerland)
Zoran Andjelic (Corporate Research, ABB Switzerland Ltd, Baden, Switzerland)



The purpose of this paper is to solve generic magnetostatic problems by BEM, by studying how to use a boundary integral equation (BIE) with the double layer charge as unknown derived from the scalar potential.


Since the double layer charge produces only the potential gap without disturbing the normal magnetic flux density, the field is accurately formulated even by one BIE with one unknown. Once the double layer charge is determined, Biot‐Savart's law gives easily the magnetic flux density.


The BIE using double layer charge is capable of treating robustly geometrical singularities at edges and corners. It is also capable of solving the problems with extremely high magnetic permeability.


The proposed BIE contains only the double layer charge while the conventional equations derived from the scalar potential contain the single and double layer charges as unknowns. In the multiply connected problems, the excitation potential in the material is derived from the magnetomotive force to represent the circulating fields due to multiply connected exciting currents.



Ishibashi, K. and Andjelic, Z. (2011), "Nonlinear magnetostatic BEM formulation using one unknown double layer charge", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 6, pp. 1870-1884.



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Copyright © 2011, Emerald Group Publishing Limited

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