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Coupling finite elements and magnetic networks in magnetostatics
Author(s) -
Philips Dirk Alexander
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620351005
Subject(s) - finite element method , magnetostatics , coupling (piping) , magnetic potential , interpolation (computer graphics) , extended finite element method , mixed finite element method , mathematical analysis , computation , matrix (chemical analysis) , mathematics , boundary value problem , magnetic field , physics , classical mechanics , algorithm , engineering , mechanical engineering , materials science , motion (physics) , quantum mechanics , composite material , thermodynamics
In this paper a new method for computing non‐linear magnetostatic fields is introduced, which allows the simultaneous coupling of a finite element structure with a magnetic network. Combining the advantages of both methods while avoiding their drawbacks, this coupling yields both an accurate and time‐efficient computation. The traditional method of the unknown mesh fluxes is applied for the solution of the magnetic network. The finite element solution, on the other hand, is based on a classical first‐order interpolation of the unknown vector potential. The coupling is established by a proper organization of the unknowns on the boundary common to the finite element and network regions. In this way, a single system of non‐linear equations is obtained. Moreover, it is shown that the coupled system of equations is equivalent to a single finite element system if generalized base functions are allowed. Consequently, various results from finite element theory may be applied. For instance, the matrix governing the iteratively linearized system of equations can directly be shown symmetrical and positive definite. Finally, the field inside a permanent magnet motor is calculated with the coupled method. Although the number of unknowns is dramatically reduced compared to a full FE calculation, the same level of accuracy is achieved. Hereby, the benefit of the coupled method is clearly proved.