East Asian J. Appl. Math., 15 (2025), pp. 113-137.
Published online: 2025-01
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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} }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.