  In magnetized plasma, the magnetic field confines particles around field
lines. The ratio between the intensity of the parallel and perpendicular
viscosity or heat conduction may reach the order of $10^{12}$. When the
magnetic fields have closed field lines and form a "magnetic island", the
convergence order of most known schemes depends on the anisotropy strength. In
this paper, by integration of the original differential equation along each
closed field line, we introduce a simple but very efficient asymptotic
preserving reformulation, which yields uniform convergence with respect to the
anisotropy strength. Only slight modification to the original code is required
and neither change of coordinates nor mesh adaptation is needed. Numerical
examples demonstrating the performance of the new scheme are presented.

Numerical Analysis