We present simulations of diffusion-limited transport in an initi ally 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. opintensive residual evaluation, we observe that an analytical Jacobian gives better performance (in terms of the overall execution time to solution) than a Jacobianfree approach.