An inverse coordinate multigrid method for free boundary magnetohydrostatics

The equations of 2D magnetohydrostatic equilibrium with free (pressure) boundary conditions are expressed in inverse (i.e., flux) coordinates for both cartesian and axisymmetric geometries. The resulting quasi-linear elliptic system is solved using FAS full multigrid with line relaxation as the smoothing procedure. If field line connectivity is specified in the ignorable coordinate (i.e., field shear or twist is given), the system is governed by integrodifferential equations, which are solved in the same way. Convergence rates are generally excellent, though an expanding fluxtube model, which provides a particularly difficult test, results in somewhat slower, though still acceptable, convergence.