Significant Error Propagation in the Finite Difference Solution of Non-Linear Magnetostatic Problems Utilizing Boundary Condition of the Third Kind

Abstract

This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite difference method show low magnetic vector potential as well as the magnetic field density when compared to the finite element results and in the linear case, to the analytical solution. This paper investigates the reason behind the low magnetostatic field computation in cylindrical coordinates using the finite difference method when boundary condition of the third kind is used. It then, presents a technique to overcome the problem of low magnetic field calculation using the finite difference method. The results obtained by the new technique are in close agreement with the finite element method as well as the analytical solution. Finally, it analyzes the possible source of error in modeling magnetostatic boundary conditions in finite difference formulation of vector Poisson or Laplace’s equation in cylindrical coordinates.