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Analogies between finite difference and finite element methods for scalar and vector potential formulations in magnetic field calculations

Analogies between finite difference and finite element methods for scalar and vector potential formulations in magnetic field calculations
Analogies between finite difference and finite element methods for scalar and vector potential formulations in magnetic field calculations
Numerical 3D formulations using scalar ? and vector A potentials are examined for magnetic fields, with emphasis on the finite difference (FDM) and finite element (FEM) methods using nodal and facet elements. It is shown that for hexahedral elements the FDM equations may be presented in a form similar to the FEM equations; to accomplish this the coefficients defining volume integrals in FEM need to be expressed in an approximate manner, while the nodes in FDM require supplementary association with middle points of edges, facets and volumes. The analogy between a description of magnetic field sources arising from the classical mmf distribution approach and when expressed in terms of edge values of vector potential T0 is emphasized. Comparisons are made between results obtained using FDM and FEM for both scalar and vector potential formulations. Forces in systems containing permanent magnets and torques in permanent magnet machines are calculated and compared using both approaches for scalar and vector formulations. A unified form of the stress tensor has been applied to FDM and FEM.
0018-9464
1-6
Demenko, Andrzej
68a3919c-d7b1-435a-b52a-da8701d20dde
Sykulski, Jan
d6885caf-aaed-4d12-9ef3-46c4c3bbd7fb
Demenko, Andrzej
68a3919c-d7b1-435a-b52a-da8701d20dde
Sykulski, Jan
d6885caf-aaed-4d12-9ef3-46c4c3bbd7fb

Demenko, Andrzej and Sykulski, Jan (2016) Analogies between finite difference and finite element methods for scalar and vector potential formulations in magnetic field calculations. IEEE Transactions on Magnetics, 52 (6), 1-6. (doi:10.1109/TMAG.2016.2521345).

Record type: Article

Abstract

Numerical 3D formulations using scalar ? and vector A potentials are examined for magnetic fields, with emphasis on the finite difference (FDM) and finite element (FEM) methods using nodal and facet elements. It is shown that for hexahedral elements the FDM equations may be presented in a form similar to the FEM equations; to accomplish this the coefficients defining volume integrals in FEM need to be expressed in an approximate manner, while the nodes in FDM require supplementary association with middle points of edges, facets and volumes. The analogy between a description of magnetic field sources arising from the classical mmf distribution approach and when expressed in terms of edge values of vector potential T0 is emphasized. Comparisons are made between results obtained using FDM and FEM for both scalar and vector potential formulations. Forces in systems containing permanent magnets and torques in permanent magnet machines are calculated and compared using both approaches for scalar and vector formulations. A unified form of the stress tensor has been applied to FDM and FEM.

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Accepted/In Press date: 10 January 2016
e-pub ahead of print date: 25 January 2016
Published date: June 2016
Organisations: EEE

Identifiers

Local EPrints ID: 393159
URI: http://eprints.soton.ac.uk/id/eprint/393159
ISSN: 0018-9464
PURE UUID: f4527498-69e0-42f4-9285-fe3516f86372
ORCID for Jan Sykulski: ORCID iD orcid.org/0000-0001-6392-126X

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Date deposited: 21 Apr 2016 06:45
Last modified: 07 Oct 2020 02:30

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Contributors

Author: Andrzej Demenko
Author: Jan Sykulski ORCID iD

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