  We solve the anisotropic diffusion equation in 2D, where the dominant
direction of diffusion is defined by a vector field which does not conform to a
Cartesian grid. Our method uses operator splitting to separate the diffusion
perpendicular and parallel to the vector field. The slow time scale is solved
using a provably stable finite difference formulation in the perpendicular to
the vector field, and an integral operator for the diffusion parallel to it.
Energy estimates are shown to for the continuous and semi-discrete cases.
Numerical experiments are performed showing convergence of the method, and
examples is given to demonstrate the capabilities of the method.
