Error analysis in finite difference solution of linear and non-linear cylindrical magnetostatic problems

This paper poses a magnitostatic problem in cylindrical coordinate with different permeabilities for each region. In this problem the boundary condition of the third kind is utilized. This problem is solved using the finite element and finite difference methods and also the analytical solutions for the linear case. The finite difference results of the finite difference method show low magnetic vector potential as well as the magnetic flux density when compared to the finite element results and in the linear case, to the analytical solution. This paper investigates the cause and the dependency of error production to the number of mesh points (grid size) selected and the permeability of the medium when using the finite difference method in conjunction with boundary condition of the third kind. It then, presents a complete error analysis for different material permeability and grid size selections used for the core in the linear and non-linear cases. It also shows a technique to overcome the problem of low magnetic flux density calculation using the finite difference method. The results obtained by the new technique shows close agreement with the finite element method as well as the analytical solution.