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We compare the performance of two alternative algorithms which aim toconstruct a force-free magnetic field given suitable boundary conditions. Forthis comparison, we have implemented both algorithms on the same finite elementgrid which uses Whitney forms to describe the fields within the grid cells. Theadditional use of conjugate gradient and multigrid iterations result in quiteeffective codes. The Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithmsboth perform well for the reconstruction of a known analytic force-free field.For more arbitrary boundary conditions the Wheatland-Sturrock-Roumeliotisapproach has some difficulties because it requires overdetermined boundaryinformation which may include inconsistencies. The Grad-Rubin code on the otherhand loses convergence for strong current densities. For the example we haveinvestigated, however, the maximum possible current density seems to be not farfrom the limit beyond which a force free field cannot exist anymore for a givennormal magnetic field intensity on the boundary.

Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm