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On the equivalence of finite difference and edge element formulations in magnetic field analysis using vector potential

On the equivalence of finite difference and edge element formulations in magnetic field analysis using vector potential
On the equivalence of finite difference and edge element formulations in magnetic field analysis using vector potential
Purpose – Numerical three-dimensional formulations using vector potential A have been examined for magnetic fields, with emphasis on the finite difference (FDM) and edge element (EEM) methods, with the view to establish common features. The paper aims to discuss these issues.

Design/methodology/approach – It has been shown that for hexahedral elements the FDM equations may be presented in the form similar to the EEM equations, providing the products of the nodal potentials and distances between the nodes are used as unknowns in FDM, instead of the usual nodal potentials.

Findings – The analogy between the FDM and the EEM approach has been established.

Originality/value – It has been demonstrated, following from this and previous publications, that analogy exists between all fundamental methods of field solutions relying on space discretisation. This is helpful in terms of classification of the methods and aids the understanding of physical processes involved.
finite difference method, edge element method, finite element methods, magnetic fields
0332-1649
47-55
Demenko, Andrzej
68a3919c-d7b1-435a-b52a-da8701d20dde
Sykulski, Jan K.
d6885caf-aaed-4d12-9ef3-46c4c3bbd7fb
Demenko, Andrzej
68a3919c-d7b1-435a-b52a-da8701d20dde
Sykulski, Jan K.
d6885caf-aaed-4d12-9ef3-46c4c3bbd7fb

Demenko, Andrzej and Sykulski, Jan K. (2014) On the equivalence of finite difference and edge element formulations in magnetic field analysis using vector potential. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 33 (1/2), 47-55. (doi:10.1108/COMPEL-10-2012-0231).

Record type: Article

Abstract

Purpose – Numerical three-dimensional formulations using vector potential A have been examined for magnetic fields, with emphasis on the finite difference (FDM) and edge element (EEM) methods, with the view to establish common features. The paper aims to discuss these issues.

Design/methodology/approach – It has been shown that for hexahedral elements the FDM equations may be presented in the form similar to the EEM equations, providing the products of the nodal potentials and distances between the nodes are used as unknowns in FDM, instead of the usual nodal potentials.

Findings – The analogy between the FDM and the EEM approach has been established.

Originality/value – It has been demonstrated, following from this and previous publications, that analogy exists between all fundamental methods of field solutions relying on space discretisation. This is helpful in terms of classification of the methods and aids the understanding of physical processes involved.

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More information

Published date: February 2014
Keywords: finite difference method, edge element method, finite element methods, magnetic fields
Organisations: EEE

Identifiers

Local EPrints ID: 363049
URI: http://eprints.soton.ac.uk/id/eprint/363049
ISSN: 0332-1649
PURE UUID: acf38372-f1ed-4f48-9189-fa46ec4e985c
ORCID for Jan K. Sykulski: ORCID iD orcid.org/0000-0001-6392-126X

Catalogue record

Date deposited: 12 Mar 2014 11:59
Last modified: 20 Jul 2019 01:28

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