A Physics-Wise Splitting Preconditioner with Selective Relaxation for the Multi-Group Radiation Diffusion Equations in Three Dimensions (Communications in Computational Physics, 2025)
Designing a good preconditioner for accelerating the iterative solution of thethree-dimensional multi-group radiation diffusion equations based on a cell-centeredfinite volume discretization has been the focus of intensive research efforts over thepast few decades. In the present paper, we develop a physics-wise splitting preconditioning algorithm with selective relaxation and algebraic multigrid subsolves.The spectral distribution and the degree of the minimal polynomial of its right-preconditioned matrix together with the conditional convergence property of its iteration method are analyzed. Subsequently, we discuss its sequential implementationas well as the two-level parallelization. Lastly, the new preconditioner is applied to theexperimental test cases arising from realistic simulations of the hydrodynamic instability during the deceleration phase of a laser-driven spherical implosion to illustratethe numerical robustness, computational efficiency, parallel strong and weak scalabilities, and its competitiveness with some existing monolithic and block preconditioningapproaches.