  Many codes have been developed to study highly relativistic, magnetized flows
around and inside compact objects. Depending on the adopted formalism, some of
these codes evolve the vector potential $\mathbf{A}$, and others evolve the
magnetic field $\mathbf{B}=\nabla\times\mathbf{A}$ directly. Given that these
codes possess unique strengths, sometimes it is desirable to start a simulation
using a code that evolves $\mathbf{B}$ and complete it using a code that
evolves $\mathbf{A}$. Thus transferring the data from one code to another would
require an inverse curl algorithm. This paper describes two new inverse curl
techniques in the context of Cartesian numerical grids: a cell-by-cell method,
which scales approximately linearly with the numerical grid, and a global
linear algebra approach, which has worse scaling properties but is generally
more robust (e.g., in the context of a magnetic field possessing some nonzero
divergence). We demonstrate these algorithms successfully generate smooth
vector potential configurations in challenging special and general relativistic
contexts.
