Significant Error Propagation in the Finite Difference Solution of Linear and Non-Linear Two dimensional Magnetostatic problems utilizing boundary condition of the third kind

This paper poses a two dimensional magnitostatic problem in cylindrical coordinate in r and thetas directions having various regions with different permeabilities which requires the boundary condition of the third kind at some of the interfaces for obtaining the solution. It solves the problem using the finite element and then the finite difference techniques by employing vector potential formulation. The finite difference results obtained for the problem, by using the linear and non-linear regions of a B-H curve plus the boundary condition of the third kind, show low magnetic vector potential as well as the magnetic flux density when compared to the finite element results. Hence, the paper investigates the reason behind the low magnitostatic flux computation in the 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 flux calculation using the finite difference method. The results obtained by the new technique are in close agreement with the finite element method. Finally, it analyzes the possible source of error in modeling magnitostatic boundary conditions in finite difference formulation of vector Poisson or Laplace equation in cylindrical coordinates.