  We present a new method for evolving the equations of magnetohydrodynamics
(both Newtonian and relativistic) that is capable of maintaining a
divergence-free magnetic field ($\nabla \cdot \mathbf{B} = 0$) on adaptively
refined, conformally moving meshes. The method relies on evolving the magnetic
vector potential and then using it to reconstruct the magnetic fields. The
advantage of this approach is that the vector potential is not subject to a
constraint equation in the same way the magnetic field is, and so can be
refined and moved in a straightforward way. We test this new method against a
wide array of problems from simple Alfven waves on a uniform grid to general
relativistic MHD simulations of black hole accretion on a nested,
spherical-polar grid. We find that the code produces accurate results and in
all cases maintains a divergence-free magnetic field to machine precision.
