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A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions

A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions

Year:    2025

Author:    Xiaoqiang Yue, Chenxi Zhang, Chunyan Chen, Xiaowen Xu, Shi Shu

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2023-185.301023

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 1 : pp. 113–137

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Radiation diffusion equation matrix splitting preconditioner selective relaxation algebraic multigrid parallel computing.

Author Details

Xiaoqiang Yue

Chenxi Zhang

Chunyan Chen

Xiaowen Xu

Shi Shu