Geometric formulation of edge and nodal finite element equations in electromagnetics

• Published in: Compel Vol. 31; no. 5; pp. 1347 - 1357
• Main Authors: Demenko, Andrzej, Sykulski, Jan. K.
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Group Publishing Limited 01.01.2012
• Subjects: Analogies; Circuits; Electric fields; Equivalence; Finite element analysis; Finite element method; Magnetic fields; Mathematical analysis; Mathematical models; Methods; Networks; Studies; Vector potentials; Finite element method; Finite integration technique; Electromagnetic fields; Eddy currents; Magnetic circuits; Electrical engineering education
• ISSN: 0332-1649; 2054-5606
• DOI: 10.1108/03321641211246392

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 - FE equations 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.