A Selectively Relaxed Alternating Positive Semidefinite Splitting Preconditioner for the Flux-Limited Multi-Group Radiation Diffusion Equations
Year: 2025
Author: Xiaoqiang Yue, Rong Zhou, Chunyan Chen, Xiaowen Xu, Shi Shu
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 3 : pp. 361–383
Abstract
In this article, we concentrate on the fast numerical computation of the radiation energy densities together with electron and ion temperatures of three-dimensional multi-group radiation diffusion equations, which is temporally discretized with the adaptive backward Eulerian scheme, linearized iteratively via the method of frozen coefficients and spatially approximated through a cell-centered finite volume discretization on the adaptive unstructured computational meshes. We present, analyze and implement an alternating positive semidefinite splitting preconditioning technique with two selective relaxations and algebraic multigrid subsolves, and provide an algebraic quasi-optimal selection approach to determine the involved parameters. Our parallel implementation is based on the software package jxpamg and the preconditioned flexible restarted generalized minimal residual solver has been examined by running realistic simulations of hydrodynamic instability on the Tianhe-2A supercomputer to demonstrate its numerical robustness, computational efficiency, parallel strong and weak scalabilities, and the competitiveness with some existing popular monolithic and block preconditioning strategies.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1016
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 3 : pp. 361–383
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Radiation diffusion equations alternating positive semidefinite splitting selective relaxation algebraic multigrid parallel and distributed computing.
Author Details
Xiaoqiang Yue Email
Rong Zhou Email
Chunyan Chen Email
Xiaowen Xu Email
Shi Shu Email