Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer

In this paper, we present a comparison of four preconditioning strategies for Jacobian systems arising in the fully implicit solution of radiation diffusion coupled with material energy transfer. The four preconditioning methods are block Jacobi, Schur complement, and operator splitting approaches that split the preconditioner solve into two steps. One splitting method includes the coupling of the radiation and material fields that appears in the matrix diagonal in the first solve, and the other method puts this coupling into the second solve. All preconditioning approaches use multigrid methods to invert blocks of the matrix formed from the diffusion operator. The Schur complement approach is clearly seen to be the most effective for a large range of weightings between the diffusion and energy coupling terms. In addition, tabulated opacity studies were conducted where, again, the Schur preconditioner performed well. Last, a parallel scaling study was done showing algorithmic scalability of the Schur preconditioner.