TY - JOUR T1 - A Physics-Wise Splitting Preconditioner with Selective Relaxation for the Multi-Group Radiation Diffusion Equations in Three Dimensions AU - Yue , Xiaoqiang AU - Hou , Junbai AU - Yuan , Long AU - Xu , Xiaowen AU - Shu , Shi JO - Communications in Computational Physics VL - 2 SP - 467 EP - 490 PY - 2025 DA - 2025/08 SN - 38 DO - http://doi.org/10.4208/cicp.OA-2023-0147 UR - https://global-sci.org/intro/article_detail/cicp/24304.html KW - Radiation diffusion equations, physics-wise splitting, selective relaxation, algebraic multigrid, parallel and distributed computing. AB -

Designing a good preconditioner for accelerating the iterative solution of the three-dimensional multi-group radiation diffusion equations based on a cell-centered finite volume discretization has been the focus of intensive research efforts over the past 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 implementation as well as the two-level parallelization. Lastly, the new preconditioner is applied to the experimental test cases arising from realistic simulations of the hydrodynamic instability during the deceleration phase of a laser-driven spherical implosion to illustrate the numerical robustness, computational efficiency, parallel strong and weak scalabilities, and its competitiveness with some existing monolithic and block preconditioning approaches.