Parallel Implicit Solution of Diffusion-limited Radiation Transport

We present simulations of diffusion-limited transport in an initially cold medium of two different materials subjected to an impulsive radiative load, using a Newton-Krylov-Schwarz solver. The spatial discretization employs Galerkin finite elements with linear piecewise continuous basis functions over simplices in 2D and 3D. Temporal integration is via a solution-adaptive implicit Euler method. The code shows excellent domain-decomposed scalability on the Teragrid, BlueGene, and System X platforms. Comparing implementations for this application with flop-intensive residual evaluation, we observe that an analytical Jacobian gives better performance (in terms of the overall execution time to solution) than a Jacobian-free approach. 1 Diffusion-limited radiation transport Under the assumptions of isotropic radiation with no frequency dependence, transport through a material characterized by spatially varying atomic number Z and thermal conductivity of κ can be modeled by the following coupled nonlinear equations, known as flux-limited radiation diffusion [9]: