  The time dependent non-equilibrium radiation diffusion equations are
important for solving the transport of energy through radiation in optically
thick regimes and find applications in several fields including astrophysics
and inertial confinement fusion. The associated initial boundary value problems
that are encountered often exhibit a wide range of scales in space and time and
are extremely challenging to solve. To efficiently and accurately simulate
these systems we describe our research on combining techniques that will also
find use more broadly for long term time integration of nonlinear multiphysics
systems: implicit time integration for efficient long term time integration of
stiff multiphysics systems, local control theory based step size control to
minimize the required global number of time steps while controlling accuracy,
dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational
costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear
solution, and optimal multilevel preconditioner components that provide level
independent solver convergence.
