  This work presents efficient solution techniques for radiative transfer in
the smoothed particle hydrodynamics discretization. Two choices that impact
efficiency are how the material and radiation energy are coupled, which
determines the number of iterations needed to converge the emission source, and
how the radiation diffusion equation is solved, which must be done in each
iteration. The coupled material and radiation energy equations are solved using
an inexact Newton iteration scheme based on nonlinear elimination, which
reduces the number of Newton iterations needed to converge within each time
step. During each Newton iteration, the radiation diffusion equation is solved
using Krylov iterative methods with a multigrid preconditioner, which abstracts
and optimizes much of the communication when running in parallel. The code is
verified for an infinite medium problem, a one-dimensional Marshak wave, and a
two and three-dimensional manufactured problem, and exhibits first-order
convergence in time and second-order convergence in space. For these problems,
the number of iterations needed to converge the inexact Newton scheme and the
diffusion equation are independent of the number of spatial points and the
number of processors.
