Parallel sweep-based preconditioner for the solution of the linear Boltzmann transport equation

The Boltzmann transport equation is solved in the context of radiative heat transfer, for an isotropically scattering medium with reflecting boundaries. Under these circumstances, the different ordinates of the angular flux are mutually coupled. We explore here the use of a parallel sweep-based block diagonal preconditioner as a complement of the GMRES solver on the solution of the discretization matrix (which includes all the inter-ordinate couplings). The validity of this approach, when compared to the standard source iteration scheme, is successfully assessed for a significant range of the coupling parameters.