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The reduced scalar potential in regions with permeable materials: Reasons for loss of accuracy and cancellation
Author(s) -
Balac S.,
Caloz G.
Publication year - 2007
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.638
Subject(s) - discretization , scalar (mathematics) , scalar potential , magnetic potential , vector potential , magnetic field , permeability (electromagnetism) , scalar field , mathematics , physics , mathematical analysis , chemistry , mathematical physics , geometry , quantum mechanics , biochemistry , membrane
Practical three‐dimensional magnetic field problems usually involve regions containing current sources as well as regions with magnetic materials. For computational purposes, the use of the reduced scalar potential (RSP) as unknown has the advantage to transform a problem for a vector field throughout the space into a problem for a scalar function, thus reducing the number of degrees of freedom in the discretization. However, in regions with high magnetic permeability the use of the RSP alone usually results in severe loss in accuracy and it is recommended to use both the RSP and the total scalar potential. Using an asymptotic expansion, we investigate theoretically the underlying reasons for this lack of accuracy in permeable regions when using the RSP as a unique potential. Moreover, this investigation leads to an efficient numerical method to compute the magnetic field in regions with high magnetic permeability. Copyright © 2007 John Wiley & Sons, Ltd.