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Volume 15, Issue 1
A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions

Xiaoqiang Yue, Chenxi Zhang, Chunyan Chen, Xiaowen Xu & Shi Shu

East Asian J. Appl. Math., 15 (2025), pp. 113-137.

Published online: 2025-01

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  • Abstract

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.

  • AMS Subject Headings

65F10, 65N55, 65Y05, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-15-113, author = {Yue , XiaoqiangZhang , ChenxiChen , ChunyanXu , Xiaowen and Shu , Shi}, title = {A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions}, journal = {East Asian Journal on Applied Mathematics}, year = {2025}, volume = {15}, number = {1}, pages = {113--137}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-185.301023}, url = {http://global-sci.org/intro/article_detail/eajam/23743.html} }
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 -

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.

Yue , XiaoqiangZhang , ChenxiChen , ChunyanXu , Xiaowen and Shu , Shi. (2025). A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions. East Asian Journal on Applied Mathematics. 15 (1). 113-137. doi:10.4208/eajam.2023-185.301023
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