Volume 23, Issue 2
Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations

Xiaoqiang Yue, Shi Shu, Junxian Wang & Zhiyang Zhou

Commun. Comput. Phys., 23 (2018), pp. 540-560.

Published online: 2018-02

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  • Abstract

Inspired by [Q. Y. Hu, S. Shu and J. X. Wang, Math. Comput., 79 (272) (2010): 2059-2078], we firstly present two nonoverlapping domain decomposition (DD) preconditioners B a h and B sm h about the preserving-symmetry finite volume element (SFVE) scheme for solving two-dimensional three-temperature radiation diffusion equations with strongly discontinuous coefficients. It’s worth mentioning that both B a h and B sm h involve a SFVE sub-system with respect to a simple coarse space and SFVE sub-systems which are self-similar to the original SFVE system but embarrassingly parallel. Next, the nearly optimal estimation O((1+log d h ) 3 ) on condition numbers is proved for the resulting preconditioned systems, where d and h respectively denote the maximum diameters in coarse and fine grids. Moreover, we present algebraic and parallel implementations of B a h and B sm h , develop parallel PCG solvers, and provide the numerical results validating the aforementioned theoretical estimations and stating the good algorithmic and parallel scalabilities.

  • Keywords

2-D 3-T radiation diffusion equations, nonoverlapping domain decomposition, simple coarse space, condition number, parallel scalability.

  • AMS Subject Headings

65F10, 65F15, 65N55, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-540, author = {}, title = {Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {2}, pages = {540--560}, abstract = {

Inspired by [Q. Y. Hu, S. Shu and J. X. Wang, Math. Comput., 79 (272) (2010): 2059-2078], we firstly present two nonoverlapping domain decomposition (DD) preconditioners B a h and B sm h about the preserving-symmetry finite volume element (SFVE) scheme for solving two-dimensional three-temperature radiation diffusion equations with strongly discontinuous coefficients. It’s worth mentioning that both B a h and B sm h involve a SFVE sub-system with respect to a simple coarse space and SFVE sub-systems which are self-similar to the original SFVE system but embarrassingly parallel. Next, the nearly optimal estimation O((1+log d h ) 3 ) on condition numbers is proved for the resulting preconditioned systems, where d and h respectively denote the maximum diameters in coarse and fine grids. Moreover, we present algebraic and parallel implementations of B a h and B sm h , develop parallel PCG solvers, and provide the numerical results validating the aforementioned theoretical estimations and stating the good algorithmic and parallel scalabilities.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0065}, url = {http://global-sci.org/intro/article_detail/cicp/10537.html} }
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