A new coordinate transform for the finite element solution of axisymmetric problems in magnetostatics

It is pointed out that, although field computation in two-dimensional (2-D) axial symmetric problems has a longstanding history and its software has acquired the status of robustness and reliability, problems with singularities in the neighborhood of r=0 still remain a point of concern. A simple example is shown which exhibits a disturbing lack of accuracy and seems to mock all ideas of reasonability of finite-element solutions. A simple solution to the problem is presented, consisting of transforming the vector potential into a form which is better adapted to the bilinear interpolation used in first-order finite elements. For one-dimensional problems with piecewise linear materials this approach yields exact solutions; an increase in accuracy was obtained for other problems also.>