Novel finite element analysis method using magnetic flux density directly as an unknown variable

In magnetic field analysis, designers are interested in the magnitude of magnetic flux density. It is common practice to use vector potential as an unknown variable and then differentiate it to obtain the magnetic flux density. This paper uses the magnetic flux density directly as an unknown variable. The formulation of this new method and its application to two-dimensional and axisymmetrical magnetic fields are explained and illustrated. The calculated error of the magnetic flux density by the new technique is compared with that obtained by the traditional finite element method for a model of known solution. The comparison shows that the new method is capable of producing better results than the traditional one in terms of computation time and accuracy. Furthermore, the proposed technique will be useful for the calculation of three-dimensional fields and eddy-current problems.