Comparison of First-Order Finite Difference and Finite Element Algorithms for the Analysis of Magnetic Fields. Part II. Numerical Results

Numerical results obtained by first- order finite difference and finite element algorithms are compared with closed-form solutions to the finite- depth-slot problem and to the section of an annulus of magnetic and nonmagnetic material, the magnetic field of which is caused by a current-carrying conductor of circular section. Magnitude and boundary condition errors are calculated with respect to these exact solutions, and both methods are compared numerically as applied to a finite slot pitch where a uniform current density region covers the slot area. The simultaneous difference equations resulting from the finite difference and finite element method are solved by Gaussian elimination. Both methods are compared with regard to computing time, storage requirements and errors for Laplace's and Poisson's equations in two dimensions on a numerical basis.