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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

DOI: 10.4208/cicp.OA-2017-0065

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 $\mathcal{O}$((1+log$\frac{d}{h}$)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 = {Xiaoqiang Yue, Shi Shu, Junxian Wang and Zhiyang Zhou}, 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 $\mathcal{O}$((1+log$\frac{d}{h}$)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} }
TY - JOUR T1 - Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations AU - Xiaoqiang Yue, Shi Shu, Junxian Wang & Zhiyang Zhou JO - Communications in Computational Physics VL - 2 SP - 540 EP - 560 PY - 2018 DA - 2018/02 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0065 UR - https://global-sci.org/intro/article_detail/cicp/10537.html KW - 2-D 3-T radiation diffusion equations, nonoverlapping domain decomposition, simple coarse space, condition number, parallel scalability. AB -

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 $\mathcal{O}$((1+log$\frac{d}{h}$)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.

Xiaoqiang Yue, Shi Shu, Junxian Wang and Zhiyang Zhou. (2018). Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations. Communications in Computational Physics. 23 (2). 540-560. doi:10.4208/cicp.OA-2017-0065
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