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We consider the numerical approximation of the radiative transfer equationusing discontinuous angular and continuous spatial approximations for the evenparts of the solution. The even-parity equations are solved using a diffusionsynthetic accelerated source iteration. We provide a convergence analysis forthe infinite-dimensional iteration as well as for its discretized counterpart.The diffusion correction is computed by a subspace correction, which leads to aconvergence behavior that is robust with respect to the discretization. Theproven theoretical contraction rate deteriorates for scattering dominatedproblems. We show numerically that the preconditioned iteration is in practicerobust in the diffusion limit. Moreover, computations for the lattice problemindicate that the presented discretization does not suffer from the ray effect.The theoretical methodology is presented for plane-parallel geometries withisotropic scattering, but the approach and proofs generalize tomulti-dimensional problems and more general scattering operators verbatim.

On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer