TY - JOUR
T1 - A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions
AU - Yue , Xiaoqiang
AU - Zhang , Chenxi
AU - Chen , Chunyan
AU - Xu , Xiaowen
AU - Shu , Shi
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 113
EP - 137
PY - 2025
DA - 2025/01
SN - 15
DO - http://doi.org/10.4208/eajam.2023-185.301023
UR - https://global-sci.org/intro/article_detail/eajam/23743.html
KW - Radiation diffusion equation, matrix splitting preconditioner, selective relaxation, algebraic multigrid, parallel computing.
AB - <p style="text-align: justify;">This article is concerned with a matrix splitting preconditioning technique
with two selective relaxations and algebraic multigrid subsolves for $(G + 2) \times (G + 2)$ block-structured sparse linear systems derived from the three-dimensional flux-limited
multi-group radiation diffusion equations, where $G$ is the number of photon energy
groups. We introduce an easy-to-implement algebraic selection strategy for the sole
contributing parameter, report a spectral analysis and investigate the degree of the minimal polynomial of its left and right preconditioned matrices, and discuss its sequential
practical implementation together with the two-level parallelization. Experiments are
run with the representative real-world unstructured capsule implosion test cases and
it is found that the numerical robustness, computational efficiency and parallel scalability of the proposed preconditioner evaluated on the Tianhe-2A supercomputer with
up to 2,816 processor cores are superior to some existing popular monolithic and block
preconditioning approaches.</p>