Special finite element shape functions for axisymmetric magnetic problems

New infinite elements which can be used for a solution of axisymmetric magnetic problems with open boundaries are presented. It is supposed that the new elements are being developed for the vector potential A(r,z) and the modified vector potential rA formulation. The elements can represent any type of decay towards infinity, and the element matrix when the decay function is 1/ρⁿ, n⩾1, ρ²=r ²+z² is given explicity. Standard finite elements for the rA formulation yield very inaccurate results near r =0. The introduction, close to the symmetry axis, of so-called axial elements with special shape functions is proposed. The formulation is so simple that closed-form expressions for the element matrix are obtained. Numerical results are presented for a problem having an analytical solution