A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
New physics-based preconditioning of implicit methods for non-equilibrium radiation diffusion
Journal of Computational Physics
Analyzing radiation diffusion using time-dependent sensitivity-based techniques
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
Studies of the accuracy of time integration methods for reaction-diffusion equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Numerical analysis of time integration errors for nonequilibrium radiation diffusion
Journal of Computational Physics
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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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.