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

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.

Citation

Demenko, A. and Sykulski, J. (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, Vol. 33 No. 1/2, pp. 47-55. https://doi.org/10.1108/COMPEL-10-2012-0231