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Geometric formulation of edge and nodal finite element equations in electromagnetics

Geometric formulation of edge and nodal finite element equations in electromagnetics
Geometric formulation of edge and nodal finite element equations in electromagnetics
Purpose – The purpose of this paper is to emphasise the analogies between variational and network formulations using geometrical forms, with the purpose of developing alternative but otherwise equivalent derivations of the finite element (FE) method.
Design/methodology/approach – FEequations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation.
Findings – It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods, employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi-branch circuit models.
Originality/value – The approach proposed in the paper explores the analogy of the FE formulation to loop or nodal magnetic or electric networks and has been shown to be very beneficial in teaching, especially to students well familiar with circuit methods. The presented methods are also helpful when formulating classical network models. Finally, for the first time, the geometrical forms of edge and facet element functions have been demonstrated.
0332-1649
1347-1357
Demenko, A.
4f2e9586-6a46-44e6-8573-ce6613cc3032
Sykulski, J.K.
d6885caf-aaed-4d12-9ef3-46c4c3bbd7fb
Demenko, A.
4f2e9586-6a46-44e6-8573-ce6613cc3032
Sykulski, J.K.
d6885caf-aaed-4d12-9ef3-46c4c3bbd7fb

Demenko, A. and Sykulski, J.K. (2012) Geometric formulation of edge and nodal finite element equations in electromagnetics. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 31 (5), 1347-1357. (doi:10.1108/03321641211246392).

Record type: Article

Abstract

Purpose – The purpose of this paper is to emphasise the analogies between variational and network formulations using geometrical forms, with the purpose of developing alternative but otherwise equivalent derivations of the finite element (FE) method.
Design/methodology/approach – FEequations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation.
Findings – It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods, employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi-branch circuit models.
Originality/value – The approach proposed in the paper explores the analogy of the FE formulation to loop or nodal magnetic or electric networks and has been shown to be very beneficial in teaching, especially to students well familiar with circuit methods. The presented methods are also helpful when formulating classical network models. Finally, for the first time, the geometrical forms of edge and facet element functions have been demonstrated.

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Published date: September 2012
Organisations: EEE

Identifiers

Local EPrints ID: 342608
URI: http://eprints.soton.ac.uk/id/eprint/342608
ISSN: 0332-1649
PURE UUID: 4dfaf42f-cec8-4fc0-b5dc-e53b1fc3316d
ORCID for J.K. Sykulski: ORCID iD orcid.org/0000-0001-6392-126X

Catalogue record

Date deposited: 10 Sep 2012 08:28
Last modified: 20 Jul 2019 01:28

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