Newton-Raphson finite element programs for axisymmetric vector fields

A new direct formulation for finite element Jacobian matrices has been implemented in computer programs for axisymmetric vector potential fields. Computational tests show that the method has the expected quadratic convergence, and that numerical quadratures of relatively low degree suffice to provide high result accuracy without convergence degradation. The programs, which form part of the MagNet Eleven analysis system, generally require very little more computing time than comparable x-y plane problems, for which Jacobian matrices are analytically known.