  We present a method for accelerating discrete ordinates radiative transfer
calculations for radiative transfer. Our method works with nonlinear positivity
fixes, in contrast to most acceleration schemes. The method is based on the
dynamic mode decomposition (DMD) and using a sequence of rank-one updates to
compute the singular value decomposition needed for DMD. Using a sequential
method allows us to automatically determine the number of solution vectors to
include in the DMD acceleration. We present results for slab geometry discrete
ordinates calculations with the standard temperature linearization. Compared
with positive source iteration, our results demonstrate that our acceleration
method reduces the number of transport sweeps required to solve the problem by
a factor of about 3 on a standard diffusive Marshak wave problem, a factor of
several thousand on a cooling problem where the effective scattering ratio
approaches unity, and a factor of 20 improvement in a realistic, multimaterial
radiating shock problem.
