  In magnetized plasma, the magnetic field confines the particles around the
field lines. The anisotropy intensity in the viscosity and heat conduction may
reach the order of $10^{12}$. When the boundary conditions are periodic or
Neumann, the strong diffusion leads to an ill-posed limiting problem. To remove
the ill-conditionedness in the highly anisotropic diffusion equations, we
introduce a simple but very efficient asymptotic preserving reformulation in
this paper. The key idea is that, instead of discretizing the Neumann boundary
conditions locally, we replace one of the Neumann boundary condition by the
integration of the original problem along the field line, the singular
$1/\epsilon$ terms can be replaced by $O(1)$ terms after the integration, so
that yields a well-posed problem. Small modifications to the original code are
required and no change of coordinates nor mesh adaptation are needed.
  Uniform convergence with respect to the anisotropy strength $1/\epsilon$ can
be observed numerically and the condition number does not scale with the
anisotropy.
