Computation of axisymmetric open-boundary eddy-current field problems

Based on the idea of region division a technique known as the hybrid finite-element analytical approach is developed for treating axisymmetric open-boundary eddy-current field problems. The general principle of the technique first introduces a spherical fictitious surface boundary called a coupling boundary to enclose the complex-shaped devices in the presence of an inhomogeneous, anisotropic or even nonlinear medium. In the interior of the spherical fictitious surface boundary the field is formulated by the finite-element method (FEM). Meanwhile, in the exterior region the field is presented by an eigenfunction expression (in Legendre functions). Taking the exterior region as a macroelement, it requires consideration of only the potential continuity at the fictitious boundary nodes with interior finite elements, so the FEM is extended to solve open-boundary problems. The results were compared with both the analytical solution and experimental cases, showing good agreement. The new hybrid scheme combining an analytical solution with the finite-element method offers several advantages: symmetrical matrices; much fewer elements and nodes for the same level at accuracy; and an easy means for calculating the external region field.