A three dimensional magnetic field analysis by a novel finite element method using magnetic flux density directly as an unknown variable

A rigorous formulation for the analysis of three-dimensional magnetic field problems based on a novel finite-element method is presented in which the magnetic flux density is used directly as an unknown variable. Unlike solutions obtained by using scalar or vector potential, the results ensure continuity of the magnitude of the magnetic flux density vector between adjacent elements in a medium, and the accuracy of the magnetic flux density is much higher than with the traditional method. Furthermore, a subdivision coarser than that of traditional method can be used to obtain the same accuracy in the calculation of magnetic flux density, so that the memory required can be reduced. Some simple examples are provided