Dynamic Implicit 3D Adaptive Mesh Refinement for Non-Equilibrium Radiation DiffusionI

The time dependent non-equilibrium radiation diffusion equations are im-portant 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 prob-lems 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 non-linear 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 mini-mize memory and computational costs, Jacobian Free Newton-Krylov meth-ods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver conver-gence