Analysis of Three-Dimensional Electromagnetic Fields Using Edge Elements

Dual formulation of the three-dimensional magnetostatic and eddy current problems in terms of two-component vector potentials are described. Cancellation errors and interface problems are avoided by means of a numerical procedure based on the adoption of edge elements. The numerical approaches are characterised by a unified treatment magnetostatic and eddy current problems. Each of the two formulations enforces one of the two canonical field equations exactly. In this way, taking the solution (E, B) which results from the electric formulation and the solution (H, J) coming out from the magnetic one, the numerical error is concentrated on the constitutive equations. This allows for an estimation of the global error and provides a useful indication for the mesh refinements. The possibility of determining upper and lower bounds for power/energy related parameters, well known in the magnetostatic case, is also discussed for the eddy current problem.