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Volume 32, Issue 3
Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

Xiaoqiang Yue, Jianmeng He, Xiaowen Xu, Shi Shu & Libo Wang

DOI: 10.4208/cicp.OA-2021-0223

Commun. Comput. Phys., 32 (2022), pp. 829-849.

Published online: 2022-09

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  • Abstract

We concentrate on the parallel, fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetry-preserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high dimensions. In this article, motivated by [M. J. Gander, S. Loisel, D. B. Szyld, SIAM J. Matrix Anal. Appl. 33 (2012) 653–680] and [S. Nardean, M. Ferronato, A. S. Abushaikha, J. Comput. Phys. 442 (2021) 110513], we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain, and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear systems. Robustness, computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

  • Keywords

Radiation diffusion equations, Schwarz methods, algebraic multigrid, parallel and distributed computing.

  • AMS Subject Headings

65F10, 65N55, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-829, author = {Yue , XiaoqiangHe , JianmengXu , XiaowenShu , Shi and Wang , Libo}, title = {Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {3}, pages = {829--849}, abstract = {

We concentrate on the parallel, fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetry-preserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high dimensions. In this article, motivated by [M. J. Gander, S. Loisel, D. B. Szyld, SIAM J. Matrix Anal. Appl. 33 (2012) 653–680] and [S. Nardean, M. Ferronato, A. S. Abushaikha, J. Comput. Phys. 442 (2021) 110513], we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain, and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear systems. Robustness, computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0223}, url = {http://global-sci.org/intro/article_detail/cicp/21047.html} }
TY - JOUR T1 - Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions AU - Yue , Xiaoqiang AU - He , Jianmeng AU - Xu , Xiaowen AU - Shu , Shi AU - Wang , Libo JO - Communications in Computational Physics VL - 3 SP - 829 EP - 849 PY - 2022 DA - 2022/09 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2021-0223 UR - https://global-sci.org/intro/article_detail/cicp/21047.html KW - Radiation diffusion equations, Schwarz methods, algebraic multigrid, parallel and distributed computing. AB -

We concentrate on the parallel, fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetry-preserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high dimensions. In this article, motivated by [M. J. Gander, S. Loisel, D. B. Szyld, SIAM J. Matrix Anal. Appl. 33 (2012) 653–680] and [S. Nardean, M. Ferronato, A. S. Abushaikha, J. Comput. Phys. 442 (2021) 110513], we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain, and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear systems. Robustness, computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

Yue , XiaoqiangHe , JianmengXu , XiaowenShu , Shi and Wang , Libo. (2022). Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions. Communications in Computational Physics. 32 (3). 829-849. doi:10.4208/cicp.OA-2021-0223
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