We compare the performance of two alternative algorithms which aim to construct a force-free magnetic field given suitable
boundary conditions. For this comparison, we have implemented both algorithms on the same finite element grid which uses Whitney
forms to describe the fields within the grid cells. The additional use of conjugate gradient and multigrid iterations result
in quite effective codes.
The Grad Rubin and Wheatland Sturrock Roumeliotis algorithms both perform well for the reconstruction of a known analytic
force-free field. For more arbitrary boundary conditions the Wheatland Sturrock Roumeliotis approach has some difficulties
because it requires overdetermined boundary information which may include inconsistencies. The Grad Rubin code on the other
hand loses convergence for strong current densities. For the example we have investigated, however, the maximum possible current
density seems to be not far from the limit beyond which a force-free field cannot exist anymore for a given normal magnetic
field intensity on the boundary.