  A description is given of the algorithms implemented in the AstroBEAR
adaptive mesh refinement code for ideal magnetohydrodynamics. The code provides
several high resolution, shock capturing schemes which are constructed to
maintain conserved quantities of the flow in a finite volume sense. Divergence
free magnetic field topologies are maintained to machine precision by collating
the components of the magnetic field on a cell-interface staggered grid and
utilizing the constrained transport approach for integrating the induction
equations. The maintenance of magnetic field topologies on adaptive grids is
achieved using prolongation and restriction operators which preserve the
divergence and curl of the magnetic field across co-located grids of different
resolution. The robustness and correctness of the code is demonstrated by
comparing the numerical solution of various tests with analytical solutions or
previously published numerical solutions obtained by other codes.
