APPLICABILITY OF VECTOR POTENTIALS IN THE FINITE-ELEMENT SOLUTION OF 3-DIMENSIONAL EDDY-CURRENT PROBLEMS

The accuracy and the efficiency of different magnetic and electric vector potential formulations in the solution of three-dimensional eddy current problems is investigated. The finite element method with nodal finite elements is applied to space discretization. Depending on the problem, the time dependence of field variables is modelled either by the time stepping method or by the time harmonic approximation. Various methods for modelling the multiply connectivity and current or voltage forced conditions are examined. The efficiency of direct and iterative solution methods is investigated in the solution of matrix equations. The calculation methods are applied to three eddy current problems of different types. Two of the problems have been proposed by international Eddy Current Workshops (the Bath Cube and the Asymmetrical Conductor with a Hole). The third problem consists of a racetrack shaped conductor which is supplied either from a current or from a voltage source. If the accuracy of the field solution is considered, the magnetic and electric vector potentials are in most cases equally applicable. The electric vector potential results in lower computational costs in problems where the magnetic vector potential cannot be used alone but also the electric scalar potential must be involved in the conducting regions. If the electric scalar potential is not required the magnetic vector potential is usually preferred. In the multiply connected problems the hole element cutting method turned out to be most efficient. This method can also be used to model the current and voltage forced conditions. In the current forced cases it is, however, required that the rate of the time variation is significant enough, If this is not the case, then the methods based on the electric scalar potential are more reliable.